University / Industry Partner Name

Average Hours

Course Description

Specialization Course Order

Specialization Description

Subtitle Language

Course Language

Johns Hopkins University

This class presents the fundamental probability and statistical concepts used in elementary data analysis. It will be taught at an introductory level for students with junior or senior college-level mathematical training including a working knowledge of calculus. A small amount of linear algebra and programming are useful for the class, but not required.

General Statistics; Probability; Confidence Interval; Confidence; Likelihood Function; Booting; Biostatistics; Studentized Residual; Variance; Euler'S Totient Function

Advanced Statistics for Data Science

Fundamental concepts in probability, statistics and linear models are primary building blocks for data science work. Learners aspiring to become biostatisticians and data scientists will benefit from the foundational knowledge being offered in this specialization. It will enable the learner to understand the behind-the-scenes mechanism of key modeling tools in data science, like least squares and linear regression.\n\nThis specialization starts with Mathematical Statistics bootcamps, specifically concepts and methods used in biostatistics applications. These range from probability, distribution, and likelihood concepts to hypothesis testing and case-control sampling.\n\nThis specialization also linear models for data science, starting from understanding least squares from a linear algebraic and mathematical perspective, to statistical linear models, including multivariate regression using the R programming language. These courses will give learners a firm foundation in the linear algebraic treatment of regression modeling, which will greatly augment applied data scientists' general understanding of regression models.\n\nThis specialization requires a fair amount of mathematical sophistication. Basic calculus and linear algebra are required to engage in the content.

Russian; Spanish; Arabic; French; Portuguese; Italian; Vietnamese; German

Algebra: Elementary to Advanced - Equations & Inequalities

Johns Hopkins University

This course is intended for students looking to create a solid algebraic foundation of fundamental mathematical concepts from which to take more advanced courses that use concepts from precalculus, calculus, probability, and statistics. This course will help solidify your computational methods, review algebraic formulas and properties, and apply these concepts model real world situations. This course is for any student who will use algebraic skills in future mathematics courses. Topics include: the real numbers, equalities, inequalities, polynomials, rational expressions and equations, graphs, relations and functions, radicals and exponents, and quadratic equations.

System Of Linear Equations; Linear Equation; Augmented Assignment; Commutative Property; Linearity; Algebra; Linear Inequality; Associative Property; Numbers (Spreadsheet); Order Of Operations

Algebra: Elementary to Advanced

This specialization is intended for students looking to solidify their algebra and geometry necessary to be successful in future courses that will require precalculus and calculus. Quantitiative skill and reasoning are presented throughout the course to train students to think logically, reason with data, and make informed decisions.

Algebra: Elementary to Advanced - Functions & Applications

Johns Hopkins University

After completing this course, students will learn how to successfully apply functions to model different data and real world occurrences. This course reviews the concept of a function and then provide multiple examples of common and uncommon types of functions used in a variety of disciplines. Formulas, domains, ranges, graphs, intercepts, and fundamental behavior are all analyzed using both algebraic and analytic techniques. From this core set of functions, new functions are created by arithmetic operations and function composition. These functions are then applied to solve real world problems. The ability to picture many different types of functions will help students learn how and when to apply these functions, as well as give students the geometric intuition to understand the algebraic techniques. The skills and objectives from this course improve problem solving abilities.

Linearity; Graphs; Euler'S Totient Function; Linear Algebra; Quadratic Equation; Linear Map; Solver; Calibration; Correlation And Dependence; Polynomial

Algebra: Elementary to Advanced

This specialization is intended for students looking to solidify their algebra and geometry necessary to be successful in future courses that will require precalculus and calculus. Quantitiative skill and reasoning are presented throughout the course to train students to think logically, reason with data, and make informed decisions.

Algebra: Elementary to Advanced - Polynomials and Roots

Johns Hopkins University

This course is the final course in a three part algebra sequence, In this course, students extend their knowledge of more advanced functions, and apply and model them using both algebraic and geometric techniques. This course enables students to make logical deductions and arrive at reasonable conclusions. Such skills are crucial in today's world. Knowing how to analyze quantitative information for the purpose of making decisions, judgments, and predictions is essential for understanding many important social and political issues. Quantitative Skills and Reasoning provides students the skills needed for evaluating such quantitatively-based arguments.\n\nThis class is important as the mathematical ideas it treats and the mathematical language and symbolic manipulation it uses to express those ideas are essential for students who will progress to calculus, statistics, or data science.

Polynomial; Augmented Assignment; Lambda Cube; 3d Lookup Table; Quadratic Form; Euclidean Distance; Convergence Of Random Variables; Quadratic Formula; Cube Root; Numbers (Spreadsheet)

Algebra: Elementary to Advanced

This specialization is intended for students looking to solidify their algebra and geometry necessary to be successful in future courses that will require precalculus and calculus. Quantitiative skill and reasoning are presented throughout the course to train students to think logically, reason with data, and make informed decisions.

Calculus through Data & Modeling: Precalculus Review

Johns Hopkins University

This course is an applications-oriented, investigative approach to the study of the mathematical topics needed for further coursework in single and multivariable calculus. The unifying theme is the study of functions, including polynomial, rational, exponential, logarithmic, and trigonometric functions. An emphasis is placed on using these functions to model and analyze data. Graphing calculators and/or the computer will be used as an integral part of the course.

Explicit Substitution; Dependent Type; Modal Μ-Calculus; Π-Calculus; Differential Calculus; Multivariable Calculus; Derivative; Function Of Several Real Variables; Modeling; Differentiable Function

Differential Calculus through Data and Modeling

This specialization provides an introduction to topics in single and multivariable calculus, and focuses on using calculus to address questions in the natural and social sciences. Students will learn to use the tools of calculus to process, analyze, and interpret data, and to communicate meaningful results, using scientific computing and mathematical modeling. Topics include functions as models of data, differential and integral calculus of functions of one and several variables, differential equations, and optimization and estimation techniques.

Calculus through Data & Modeling: Limits & Derivatives

Johns Hopkins University

This first course on concepts of single variable calculus will introduce the notions of limits of a function to define the derivative of a function. In mathematics, the derivative measures the sensitivity to change of the function. For example, the derivative of the position of a moving object with respect to time is the object's velocity: this measures how quickly the position of the object changes when time advances. This fundamental notion will be applied through the modelling and analysis of data.

Derivative; Modal Μ-Calculus; Modeling; Explicit Substitution; Differentiable Function; Function Of Several Real Variables; Calculus; Euler'S Totient Function; Graphs; Estimating Equations

Differential Calculus through Data and Modeling

This specialization provides an introduction to topics in single and multivariable calculus, and focuses on using calculus to address questions in the natural and social sciences. Students will learn to use the tools of calculus to process, analyze, and interpret data, and to communicate meaningful results, using scientific computing and mathematical modeling. Topics include functions as models of data, differential and integral calculus of functions of one and several variables, differential equations, and optimization and estimation techniques.

Calculus through Data & Modeling: Differentiation Rules

Johns Hopkins University

Calculus through Data & Modeling: Differentiation Rules continues the study of differentiable calculus by developing new rules for finding derivatives without having to use the limit definition directly. These differentiation rules will enable the calculation of rates of change with relative ease the derivatives of polynomials, rational functions, algebraic functions, exponential and logarithmic functions, and trigonometric and inverse trigonometric functions. Once these rules are developed, they are then applied to solve problems involving rates of change and the approximation of functions.

Calculus; Modal Μ-Calculus; Data Model; Differentiation Rules; Explicit Substitution; Multivariable Calculus; Function Of Several Real Variables; Derivative; Directional Derivative; Euler'S Totient Function

Differential Calculus through Data and Modeling

This specialization provides an introduction to topics in single and multivariable calculus, and focuses on using calculus to address questions in the natural and social sciences. Students will learn to use the tools of calculus to process, analyze, and interpret data, and to communicate meaningful results, using scientific computing and mathematical modeling. Topics include functions as models of data, differential and integral calculus of functions of one and several variables, differential equations, and optimization and estimation techniques.

Calculus through Data & Modeling: Applying Differentiation

Johns Hopkins University

As rates of change, derivatives give us information about the shape of a graph. In this course, we will apply the derivative to find linear approximations for single-variable and multi-variable functions. This gives us a straightforward way to estimate functions that may be complicated or difficult to evaluate. We will also use the derivative to locate the maximum and minimum values of a function. These optimization techniques are important for all fields, including the natural sciences and data analysis. The topics in this course lend themselves to many real-world applications, such as machine learning, minimizing costs or maximizing profits.

Calculus; Modal Μ-Calculus; Data Model; Modeling; Lambda Calculus; Explicit Substitution; Π-Calculus; Second Derivative; Derivative; Linearization

Differential Calculus through Data and Modeling

This specialization provides an introduction to topics in single and multivariable calculus, and focuses on using calculus to address questions in the natural and social sciences. Students will learn to use the tools of calculus to process, analyze, and interpret data, and to communicate meaningful results, using scientific computing and mathematical modeling. Topics include functions as models of data, differential and integral calculus of functions of one and several variables, differential equations, and optimization and estimation techniques.

Calculus through Data & Modelling: Series and Integration

Johns Hopkins University

This course continues your study of calculus by introducing the notions of series, sequences, and integration. These foundational tools allow us to develop the theory and applications of the second major tool of calculus: the integral. Rather than measure rates of change, the integral provides a means for measuring the accumulation of a quantity over some interval of input values. This notion of accumulation can be applied to different quantities, including money, populations, weight, area, volume, and air pollutants. The concepts in this course apply to many other disciplines outside of traditional mathematics. Through projects, we will apply the tools of this course to analyze and model real world data, and from that analysis give critiques of policy. \n\nFollowing the pattern as with derivatives, several important methods for calculating accumulation are developed. Our course begins with the study of the deep and significant result of the Fundamental Theorem of Calculus, which develops the relationship between the operations of differentiation and integration. If you are interested in learning more advanced mathematics, this course is the right course for you.

Integral; Lambda Calculus; Integration By Substitution; Mathematical Series; Calculus; Antiderivative; Approximation; Multivariable Calculus; Event (Probability Theory); Fundamental Theorem Of Calculus

Integral Calculus through Data and Modeling

This specialization builds on topics introduced in single and multivariable differentiable calculus to develop the theory and applications of integral calculus. , The focus on the specialization is to using calculus to address questions in the natural and social sciences. Students will learn to use the techniques presented in this class to process, analyze, and interpret data, and to communicate meaningful results, using scientific computing and mathematical modeling. Topics include functions as models of data, differential and integral calculus of functions of one and several variables, differential equations, and optimization and estimation techniques.

Calculus through Data & Modelling: Techniques of Integration

Johns Hopkins University

In this course, we build on previously defined notions of the integral of a single-variable function over an interval. Now, we will extend our understanding of integrals to work with functions of more than one variable. First, we will learn how to integrate a real-valued multivariable function over different regions in the plane. Then, we will introduce vector functions, which assigns a point to a vector. This will prepare us for our final course in the specialization on vector calculus. Finally, we will introduce techniques to approximate definite integrals when working with discrete data and through a peer reviewed project on, apply these techniques real world problems.

Calculus; Lambda Calculus; Explicit Substitution; Order Of Integration; Integral; Parametric Equation; Multiple Integral; Vector-Valued Function; Mathematical Model; Multivariable Calculus

Integral Calculus through Data and Modeling

This specialization builds on topics introduced in single and multivariable differentiable calculus to develop the theory and applications of integral calculus. , The focus on the specialization is to using calculus to address questions in the natural and social sciences. Students will learn to use the techniques presented in this class to process, analyze, and interpret data, and to communicate meaningful results, using scientific computing and mathematical modeling. Topics include functions as models of data, differential and integral calculus of functions of one and several variables, differential equations, and optimization and estimation techniques.

Calculus through Data & Modelling: Integration Applications

Johns Hopkins University

This course continues your study of calculus by focusing on the applications of integration. The applications in this section have many common features. First, each is an example of a quantity that is computed by evaluating a definite integral. Second, the formula for that application is derived from Riemann sums. \n\nRather than measure rates of change as we did with differential calculus, the definite integral allows us to measure the accumulation of a quantity over some interval of input values. This notion of accumulation can be applied to different quantities, including money, populations, weight, area, volume, and air pollutants. The concepts in this course apply to many other disciplines outside of traditional mathematics.\n\nWe will expand the notion of the average value of a data set to allow for infinite values, develop the formula for arclength and curvature, and derive formulas for velocity, acceleration, and areas between curves. Through examples and projects, we will apply the tools of this course to analyze and model real world data.

Calculus; Lambda Calculus; Vector-Valued Function; Curvature; Differential Calculus; Integral; Graphs; Arc Length; Euler'S Totient Function; Average

Integral Calculus through Data and Modeling

This specialization builds on topics introduced in single and multivariable differentiable calculus to develop the theory and applications of integral calculus. , The focus on the specialization is to using calculus to address questions in the natural and social sciences. Students will learn to use the techniques presented in this class to process, analyze, and interpret data, and to communicate meaningful results, using scientific computing and mathematical modeling. Topics include functions as models of data, differential and integral calculus of functions of one and several variables, differential equations, and optimization and estimation techniques.

Calculus through Data & Modelling: Vector Calculus

Johns Hopkins University

This course continues your study of calculus by focusing on the applications of integration to vector valued functions, or vector fields. These are functions that assign vectors to points in space, allowing us to develop advanced theories to then apply to real-world problems. We define line integrals, which can be used to fund the work done by a vector field. We culminate this course with Green's Theorem, which describes the relationship between certain kinds of line integrals on closed paths and double integrals. In the discrete case, this theorem is called the Shoelace Theorem and allows us to measure the areas of polygons. We use this version of the theorem to develop more tools of data analysis through a peer reviewed project.\n\nUpon successful completion of this course, you have all the tools needed to master any advanced mathematics, computer science, or data science that builds off of the foundations of single or multivariable calculus.

Modeling; Lambda Calculus; Explicit Substitution; Vector Calculus; Vector-Valued Function; Integral; Calculus; Discrete Mathematics; Multiple Integral; Path (Variable)

Integral Calculus through Data and Modeling

This specialization builds on topics introduced in single and multivariable differentiable calculus to develop the theory and applications of integral calculus. , The focus on the specialization is to using calculus to address questions in the natural and social sciences. Students will learn to use the techniques presented in this class to process, analyze, and interpret data, and to communicate meaningful results, using scientific computing and mathematical modeling. Topics include functions as models of data, differential and integral calculus of functions of one and several variables, differential equations, and optimization and estimation techniques.

University of London

“Welcome to Introduction to Numerical Mathematics. This is designed to give you part of the mathematical foundations needed to work in computer science in any of its strands, from business to visual digital arts, music, games. At any stage of the problem solving and modelling stage you will require numerical and computational tools. We get you started in binary and other number bases, some tools to make sense of sequences of numbers, how to represent space numerical using coordinates, how to study variations of quantities via functions and their graphs. For this we prepared computing and everyday life problems for you to solve using these tools, from sending secret messages to designing computer graphics. \nIf you wish to take it further you can join the BSc Computer Science degree and complete the full module ‘Numerical Mathematics’. \nEnjoy!”

Arithmetic; Mathematical Series; Hexadecimal; Octal; Discrete Mathematics; Numbers (Spreadsheet); Graphs; Congruence Relation; Number Theory; Mathematics

Introduction to Computer Science and Programming

This specialisation covers topics ranging from basic computing principles to the mathematical foundations required for computer science. You will learn fundamental concepts of how computers work, which can be applied to any software or computer system. You will also gain the practical skillset needed to write interactive, graphical programs at an introductory level. The numerical mathematics component will provide you with numerical and computational tools that are essential for the problem solving and modelling stages of computer science.

Arabic; French; Portuguese; Italian; Vietnamese; German; Russian; Spanish

The main goal of this course is to introduce topics in Discrete Mathematics relevant to Data Analysis.\n\nWe will start with a brief introduction to combinatorics, the branch of mathematics that studies how to count. Basics of this topic are critical for anyone working in Data Analysis or Computer Science. We will illustrate new knowledge, for example, by counting the number of features in data or by estimating the time required for a Python program to run.\n\nNext, we will apply our knowledge in combinatorics to study basic Probability Theory. Probability is everywhere in Data Analysis and we will study it in much more details later. Our goals for probability section in this course will be to give initial flavor of this field.\n\nFinally, we will study the combinatorial structure that is the most relevant for Data Analysis, namely graphs. Graphs can be found everywhere around us and we will provide you with numerous examples. We will mainly concentrate in this course on the graphs of social networks. We will provide you with relevant notions from the graph theory, illustrate them on the graphs of social networks and will study their basic properties. In the end of the course we will have a project related to social network graphs.\n\nAs prerequisites we assume only basic math (e.g., we expect you to know what is a square or how to add fractions), basic programming in Python (functions, loops, recursion), common sense and curiosity. Our intended audience are all people that work or plan to work in Data Analysis, starting from motivated high school students.

Graphs; Graph Theory; Probability; Discrete Mathematics; Combinatorics; Mathematics; Probability Theory; Algorithms; Social Network Analysis; Categorization

Mathematics for Data Science

This Specialization is part of HSE University Master of Data Science degree program. Learn more about the admission into the program here and how your Coursera work can be leveraged if accepted into the program.\n\nBehind numerous standard models and constructions in Data Science there is mathematics that makes things work. It is important to understand it to be successful in Data Science. In this specialisation we will cover wide range of mathematical tools and see how they arise in Data Science. We will cover such crucial fields as Discrete Mathematics, Calculus, Linear Algebra and Probability. To make your experience more practical we accompany mathematics with examples and problems arising in Data Science and show how to solve them in Python.

Arabic; French; Portuguese; Italian; Vietnamese; German; Russian; Spanish

Calculus and Optimization for Machine Learning

Hi! Our course aims to provide necessary background in Calculus sufficient for up-following Data Science courses. \n\nCourse starts with a basic introduction to concepts concerning functional mappings. Later students are assumed to study limits (in case of sequences, single- and multivariate functions), differentiability (once again starting from single variable up to multiple cases), integration, thus sequentially building up a base for the basic optimisation. To provide an understanding of the practical skills set being taught, the course introduces the final programming project considering the usage of optimisation routine in machine learning. \n\nAdditional materials provided during the course include interactive plots in GeoGebra environment used during lectures, bonus reading materials with more general methods and more complicated basis for discussed themes.

Mathematical Optimization; Calculus; Integral; Continuous Function; Approximation; Euler'S Totient Function; Function Of Several Real Variables; Arithmetic; Antiderivative; Differentiable Function

Mathematics for Data Science

This Specialization is part of HSE University Master of Data Science degree program. Learn more about the admission into the program here and how your Coursera work can be leveraged if accepted into the program.\n\nBehind numerous standard models and constructions in Data Science there is mathematics that makes things work. It is important to understand it to be successful in Data Science. In this specialisation we will cover wide range of mathematical tools and see how they arise in Data Science. We will cover such crucial fields as Discrete Mathematics, Calculus, Linear Algebra and Probability. To make your experience more practical we accompany mathematics with examples and problems arising in Data Science and show how to solve them in Python.

Arabic; French; Portuguese; Italian; Vietnamese; German; Russian; Spanish

First Steps in Linear Algebra for Machine Learning

The main goal of the course is to explain the main concepts of linear algebra that are used in data analysis and machine learning. Another goal is to improve the student’s practical skills of using linear algebra methods in machine learning and data analysis. You will learn the fundamentals of working with data in vector and matrix form, acquire skills for solving systems of linear algebraic equations and finding the basic matrix decompositions and general understanding of their applicability.\n\nThis course is suitable for you if you are not an absolute beginner in Matrix Analysis or Linear Algebra (for example, have studied it a long time ago, but now want to take the first steps in the direction of those aspects of Linear Algebra that are used in Machine Learning). Certainly, if you are highly motivated in study of Linear Algebra for Data Sciences this course could be suitable for you as well.

Linear Algebra; Linearity; Algebra; Least Squares; Orthogonality; Matrices; Linear Independence; Invertible Matrix; Vector Spaces; Sigma-Algebra

Mathematics for Data Science

This Specialization is part of HSE University Master of Data Science degree program. Learn more about the admission into the program here and how your Coursera work can be leveraged if accepted into the program.\n\nBehind numerous standard models and constructions in Data Science there is mathematics that makes things work. It is important to understand it to be successful in Data Science. In this specialisation we will cover wide range of mathematical tools and see how they arise in Data Science. We will cover such crucial fields as Discrete Mathematics, Calculus, Linear Algebra and Probability. To make your experience more practical we accompany mathematics with examples and problems arising in Data Science and show how to solve them in Python.

Arabic; French; Portuguese; Italian; Vietnamese; German; Russian; Spanish

Probability Theory, Statistics and Exploratory Data Analysis

Exploration of Data Science requires certain background in probability and statistics. This course introduces you to the necessary sections of probability theory and statistics, guiding you from the very basics all way up to the level required for jump starting your ascent in Data Science. \n\nThe core concept of the course is random variable — i.e. variable whose values are determined by random experiment. Random variables are used as a model for data generation processes we want to study. Properties of the data are deeply linked to the corresponding properties of random variables, such as expected value, variance and correlations. Dependencies between random variables are crucial factor that allows us to predict unknown quantities based on known values, which forms the basis of supervised machine learning. We begin with the notion of independent events and conditional probability, then introduce two main classes of random variables: discrete and continuous and study their properties. Finally, we learn different types of data and their connection with random variables.\n\nWhile introducing you to the theory, we'll pay special attention to practical aspects for working with probabilities, sampling, data analysis, and data visualization in Python.\n\nThis course requires basic knowledge in Discrete mathematics (combinatorics) and calculus (derivatives, integrals).

Probability; General Statistics; Probability Theory; Randomness; Central Tendency; Studentized Residual; Random Variable; Covariance; Probabilistic Independence; Probability & Statistics

Mathematics for Data Science

This Specialization is part of HSE University Master of Data Science degree program. Learn more about the admission into the program here and how your Coursera work can be leveraged if accepted into the program.\n\nBehind numerous standard models and constructions in Data Science there is mathematics that makes things work. It is important to understand it to be successful in Data Science. In this specialisation we will cover wide range of mathematical tools and see how they arise in Data Science. We will cover such crucial fields as Discrete Mathematics, Calculus, Linear Algebra and Probability. To make your experience more practical we accompany mathematics with examples and problems arising in Data Science and show how to solve them in Python.

Arabic; French; Portuguese; Italian; Vietnamese; German; Russian; Spanish

Mathematics for Machine Learning: Multivariate Calculus

Imperial College London

This course offers a brief introduction to the multivariate calculus required to build many common machine learning techniques. We start at the very beginning with a refresher on the “rise over run” formulation of a slope, before converting this to the formal definition of the gradient of a function. We then start to build up a set of tools for making calculus easier and faster. Next, we learn how to calculate vectors that point up hill on multidimensional surfaces and even put this into action using an interactive game. We take a look at how we can use calculus to build approximations to functions, as well as helping us to quantify how accurate we should expect those approximations to be. We also spend some time talking about where calculus comes up in the training of neural networks, before finally showing you how it is applied in linear regression models. This course is intended to offer an intuitive understanding of calculus, as well as the language necessary to look concepts up yourselves when you get stuck. Hopefully, without going into too much detail, you’ll still come away with the confidence to dive into some more focused machine learning courses in future.

Calculus; Multivariable Calculus; Regression; Linearity; Gradient; Mathematical Optimization; Gradient Descent; Linear Regression; Explicit Substitution; Lambda Calculus

Mathematics for Machine Learning

For a lot of higher level courses in Machine Learning and Data Science, you find you need to freshen up on the basics in mathematics - stuff you may have studied before in school or university, but which was taught in another context, or not very intuitively, such that you struggle to relate it to how it’s used in Computer Science. This specialization aims to bridge that gap, getting you up to speed in the underlying mathematics, building an intuitive understanding, and relating it to Machine Learning and Data Science.\n\nIn the first course on Linear Algebra we look at what linear algebra is and how it relates to data. Then we look through what vectors and matrices are and how to work with them.\n\nThe second course, Multivariate Calculus, builds on this to look at how to optimize fitting functions to get good fits to data. It starts from introductory calculus and then uses the matrices and vectors from the first course to look at data fitting.\n\nThe third course, Dimensionality Reduction with Principal Component Analysis, uses the mathematics from the first two courses to compress high-dimensional data. This course is of intermediate difficulty and will require Python and numpy knowledge.\n\nAt the end of this specialization you will have gained the prerequisite mathematical knowledge to continue your journey and take more advanced courses in machine learning.

Arabic; French; Portuguese; Greek; Italian; Vietnamese; German; Russian; Spanish

Universidad Nacional Autónoma de México

Galileo dijo: "El Universo está escrito en lenguaje matemático y los caracteres son triángulos, círculos y otras figuras geométricas, sin las que es humanamente imposible entender una sola palabra".\n Para entender el Universo, es necesario plantear leyes que expliquen su comportamiento, como pueden ser las leyes de la gravedad, la propagación del calor, el electromagnetismo, la reproducción celular, el crecimiento poblacional, la propagación de las enfermedades, la variación de los precios de las acciones en la bolsa de valores, el comportamiento de las masas ante un conflicto, etcétera.\n Todas estas leyes se plantean utilizando ecuaciones, algunas muy sencillas, otras no tanto. Para poder aplicar estas ecuaciones para resolver problemas, es necesario manipularlas siguiendo ciertas reglas que nos da el álgebra.\n Piensa en el álgebra como la gramática, que nos dice cómo traducir nuestras ideas al lenguaje, cómo formar frases y oraciones a partir de palabras, cómo conjugar verbos, a identificar las partes de una oración, las reglas de acentuación, etcétera.\n En este curso, ofrecido por la UNAM, aprenderás a construir expresiones algebraicas a partir de frases, lo que te permitirá resolver problemas en los que conoces algunos datos numéricos y necesitas encontrar otros.\n Podrás plantear y resolver ecuaciones de primer grado, ecuaciones simultáneas y ecuaciones de segundo grado.\n Este curso te va a ser muy útil si actualmente estas llevando un curso de álgebra en la escuela y tienes problemas con él. También si ya has estudiado álgebra y necesitas repasarla, ya que necesitas recordarla para tener éxito en otros cursos más avanzados, como Geometría Analítica, Cálculo o Estadística.

Algebra; Factorization; Logic; Algebraic Expression; Elementary Algebra; Sigma-Algebra; Mathematical Logic; Quadratic Equation; Analysis; Equation Solving

Non Specialization

Non Specialization

Non Specialization

Saint Petersburg State University

На основании международного образовательного стандарта Computer Science был разработан стандарт СПбГУ с тем же названием. В дополнение к вопросам, обозначенным в международном стандарте, в этом курсе рассказывается о разработках кафедры и родственных ей IT предприятий в области создания новых архитектур ЭВМ и технологий их программирования. В курсе рассказывается о базовых понятиях архитектур ЭВМ (арифметико-логическое устройство, память, регистры, устройство управления, ввод/вывод), истории их создания, архитектурных способах ускорения ЭВМ (водопровод, RISC, спекулятивное исполнение, предсказание переходов, многопроцессорные и многомашинные архитектуры), о нетрадиционных архитектурах (систолические структуры, мобильные телефоны, встроенные системы реального времени). В теме «HLL компьютеры» подробно рассказывается о HLL компьютере "Самсон", разработанном под руководством автора этого курса. От слушателей курса не требуется начать программировать на машине "Самсон", гораздо более интересно обсудить, почему выбрана именно такая архитектура, такая система команд, какие предложены оптимизации, чем предлагаемые архитектуры лучше существующих. В заключение рассказывается о двух конкретных наиболее популярных архитектурах ЭВМ (самая старая из ныне живущих архитектур мейфрейм IBM/360 и наиболее массовая современная архитектура ARM).\n\nПо завершении этого курса учащиеся будут:\nУметь:\n- Разбираться в различных архитектурах ЭВМ, сравнивать их по длине кода, эффективность исполнения, оценивать сложность аппаратной реализации;\n- На основании знания внутренней структуры компьютера, устройства его кэш-памяти, знания реализации шин, уметь оптимизировать свои программы;\n- Спроектировать новую ЭВМ, хотя бы на бумаге.\n\nЗнать:\n- Структурные схемы современных ЭВМ;\n- Способы аппаратной реализации основных элементов ЭВМ;\n- Принципы работы устройств ввода/вывода.\n\nВладеть:\n- Навыками ускорения программного обеспечения за счет знания внутренней организации кэш-памяти и шин;\n- Навыками ускорения ввода/вывода;\n- Способами рационального создания микропрограмм ЭВМ.

Architecture; Computer Architecture

Non Specialization

Non Specialization

Non Specialization

Moscow Institute of Physics and Technology

Как правило, школьные и университетские программы по математике сильно смещают акцент в сторону формально-алгебраических выкладок и аналитических навыков. С нашей точки зрения, не менее важным является (ровно столь же важным!) является понимание сути математики - то есть её геометрического воплощения. И в первую очередь это изучение свойств фигур, инвариантных относительно действия некоторой группы преобразований.\n\nВ нашем курсе вы узнаете всё про движения прямой, плоскости, окружности, сферы, будем проецировать, отражать, растягивать/сжимать, и вращать, разберемся с геометрическим описанием комплексных чисел и кватернионов, а также пройдём начала топологии. Мы поймём, чем отличается отрезок от окружности и сфера от бублика.\n\nКурс создан при поддержке Университета Дмитрия Пожарского, который готовит высококвалифицированных исследователей в ключевых областях знания и сферах человеческой деятельности. Приоритетом деятельности университета является восстановление ценности классического фундаментального образования, науки и практики в России. \n\nПреподаватель курса — Алексей Владимирович Савватеев, ректор Университета Дмитрия Пожарского, доктор физико-математических наук, профессор Московского физико-технического института, ведущий научный сотрудник Центрального экономико-математического института РАН.\n\nwww.usdp.ru

Topology; Geometry

Non Specialization

Non Specialization

Non Specialization

Game-Theoretic Solution Concept with Spreadsheets

Coursera Project Network

In this 2-hour long project-based course, you will learn how to use 2 Game-theoretic decision rules: Maximin strategy, Minimax strategy, and the solution concept, Nash Equilibrium. You will be familiarized with key terminologies in Game Theory and learn the underlying computation mechanism of each method to solve problems. Also, you will be solving higher order payoff matrices using custom spreadsheet based solution template (one for each method) and learn to interpret the results.\n\n\nNote: This course works best for learners who are based in the North America region. We’re currently working on providing the same experience in other regions.

Spreadsheet; Game Theory; Strategy; Decision Rule; Decision Tree; Benefits; Project; Analysis; Framing; Interpretation

Non Specialization

Non Specialization

Non Specialization

Moscow Institute of Physics and Technology

Комбинаторика для начинающих - это базовый курс, закладывающий самые основы комбинаторного знания.\n\nНа этом курсе слушатели, которые почти не знают комбинаторику или прочно ее забыли, откроют ее для себя впервые или заново. Курс очень полезен всем, кому трудно с ходу включиться в продвинутый курс современной комбинаторики. Однако фактические бонусы те же: в итоге человек, прослушавший курс, получит путевку в увлекательный мир комбинаторных задач и их далеко идущих приложений. Более того, даже в нем самом мы уже расскажем об инструментах, позволяющих решать некоторые задачи такой важной прикладной области знаний, как биоинформатика.\n\nДанный курс является упрощённой версией курса "Современная комбинаторика" и рекомендуется к прохождению перед курсом "Теория вероятностей для начинающих".

Combinatorics; Human Learning; Problem Solving; Mathematics; Factorial; Thought; Reason; Intuition; Mathematical Logic; Logic

Non Specialization

Non Specialization

Non Specialization

Calculus: Single Variable Part 2 - Differentiation

University of Pennsylvania

Calculus is one of the grandest achievements of human thought, explaining everything from planetary orbits to the optimal size of a city to the periodicity of a heartbeat. This brisk course covers the core ideas of single-variable Calculus with emphases on conceptual understanding and applications. The course is ideal for students beginning in the engineering, physical, and social sciences. Distinguishing features of the course include: 1) the introduction and use of Taylor series and approximations from the beginning; 2) a novel synthesis of discrete and continuous forms of Calculus; 3) an emphasis on the conceptual over the computational; and 4) a clear, dynamic, unified approach.\n\nIn this second part--part two of five--we cover derivatives, differentiation rules, linearization, higher derivatives, optimization, differentials, and differentiation operators.

Calculus; Approximation; Linearity; Linear Approximation; Differential Calculus; Differential Operators; Differentiation Rules; Derivative; Newton'S Method; Null Coalescing Operator

Non Specialization

Non Specialization

Non Specialization

Spanish; Russian; Chinese; Portuguese; French

École normale supérieure

Le cours expose la théorie de Galois, du classique critère de non-résolubilité des équations polynomiales aux méthodes plus avancées de calcul de groupes de Galois par réduction modulo un nombre premier.\n\nLe thème général de cette théorie est l'étude des racines d'un polynôme et concerne en particulier la possibilité de les exprimer à partir des coefficients de ce polynôme. Evariste Galois considère les symétries de ces racines et associe ainsi à ce polynôme un groupe de permutations de ses racines, que l'on appelle maintenant son groupe de Galois. Il dégage à cette occasion pour la première fois, dans ce cadre, la notion de groupe, maintenant omniprésente en mathématiques. Son étude lui permet d'expliquer pourquoi les racines d'une équation prise au hasard ne s'expriment en général pas par des formules algébriques faisant intervenir ses coefficients à partir du degré 5, un résultat démontré auparavant par Abel. Plus généralement, l'étude du groupe de Galois du polynôme permet de dire exactement quand une telle formule existe. C'est ce que l'on appelle la correspondance de Galois : elle relie d'une part la théorie des corps, d'autre part la théorie des groupes.Ce cours expliquera cette théorie en n'utilisant que des résultats de base d'algèbre linéaire. Nous étudierons d'un côté la théorie des corps, c'est-à-dire la façon dont les corps s'emboîtent les uns dans les autres, en introduisant la notion de nombre algébrique (essentiellement les racines de polynômes). D'un autre côté, nous introduirons les éléments nécessaires à l'étude des groupes de permutations. Cela nous permettra d'expliquer la théorie de Galois, non seulement dans son cadre d'origine, c'est-à-dire quand les coefficients du polynôme sont des nombres entiers, mais aussi dans un cadre plus général, par exemple lorsqu'on réduit ces coefficients modulo un nombre premier p.\n\nLe cours culminera avec une comparaison des groupes de Galois dans ces deux situations (« entière » et après réduction modulo p), fournissant ainsi un outil de calcul puissant de ces groupes.\n\nCe cours est l'occasion d'aborder des notions d'algèbre variées, essentielles dans de nombreux domaines des mathématiques, de manière très simple pour très rapidement aboutir à des résultats tout à fait remarquables. Nous n'avons pas cherché la généralité maximale mais au contraire à aller rapidement à l'essentiel en utilisant le minimum de formalisme abstrait. Le FLOTeur intéressé sera alors armé pour aller plus loin, notamment grâce à la bibliographie ou à des cours plus avancés.

Mathematics; Abstract Algebra; Algebra; Gustave Le Bon; Joie De Vivre; Denominación De Origen

Non Specialization

Non Specialization

Non Specialization

National Taiwan University

這是一個機率的入門課程，著重的是教授機率基本概念。另外我們的作業將搭配臺大電機系所開發的多人競技線上遊戲方式，讓同學在遊戲中快樂的學習，快速培養同學們對於機率的洞察力與應用能力。

Probability; Mathematics; Probability Distribution

Non Specialization

Non Specialization

Non Specialization

Chinese (Traditional)

Aléatoire : une introduction aux probabilités - Partie 2

École Polytechnique

Ce cours d'introduction aux probabilités a la même contenu que le cours de tronc commun de première année de l'École polytechnique donné par Sylvie Méléard.\n\nLe cours introduit graduellement la notion de variable aléatoire et culmine avec la loi des grands nombres et le théorème de la limite centrale. \n\nLes notions mathématiques nécessaires sont introduites au fil du cours et de nombreux exercices corrigés sont proposés.\n\nCe cours propose aussi une introduction aux méthodes de simulations des variables aléatoires comme la méthode de Monte Carlo. Des expériences numériques interactives sont également mises à votre disposition pour vous permettre de visualiser diverses notions.

Borel Cantelli Lemma; Simulation; Variance; Gustave Le Bon; Joie De Vivre; Denominación De Origen

Non Specialization

Non Specialization

Non Specialization

Hebrew University of Jerusalem

קורס זה עוסק במתמטיקה של בית ספר תיכון מנקודת מבט מתקדמת. מטרתו העיקרית היא לחשוף סטודנטים לעתיד לאופן שבו מתמטיקאים רואים מקצוע זה, ובכך להכין אותם ללימודי מתמטיקה ברמת אוניברסיטה.

Mathematics; Forgetting; Thought; Factorial

Non Specialization

Non Specialization

Non Specialization

Coursera Project Network

In this 2-hour long project-based course, you will learn the game theoretic concepts of Two player Static and Dynamic Games, Pure and Mixed strategy Nash Equilibria for static games (illustrations with unique and multiple solutions), Example of Axelrod tournament. You will be building two player Nash games and analyze them using Python packages Nashpy and Axelrod, especially built for game theoretic analyses. Also, you will gain the understanding of computational mechanisms related to the aforementioned concepts.\n\nNote: This course works best for learners who are based in the North America region. We’re currently working on providing the same experience in other regions.

Game Theory; Python Programming; Models Of Computation; Project Mine; Project; Strategy; Interpretation; Illustration; Analysis; Game Design

Non Specialization

Non Specialization

Non Specialization

The Hong Kong University of Science and Technology

Numerical Methods for Engineers covers the most important numerical methods that an engineer should know. We derive basic algorithms in root finding, matrix algebra, integration and interpolation, ordinary and partial differential equations. We learn how to use MATLAB to solve numerical problems. Access to MATLAB online and the MATLAB grader is given to all students who enroll. \n\nWe assume students are already familiar with the basics of matrix algebra, differential equations, and vector calculus. Students should have already studied a programming language, and be willing to learn MATLAB. \n\nThe course contains 74 short lecture videos and MATLAB demonstrations. After each lecture or demonstration, there are problems to solve or programs to write. The course is organized into six weeks, and at the end of each week there is an assessed quiz and a longer programming project. \n\nDownload the lecture notes:\nhttp://www.math.ust.hk/~machas/numerical-methods-for-engineers.pdf\n\nWatch the promotional video: \nhttps://youtu.be/qFJGMBDfFMY

Partial Differential Equations; Computational Fluid Dynamics; Numerical Analysis; Matlab; Differential Equations; Periodic Function; Ordinary Differential Equation; Newton'S Method; Eigenvalues And Eigenvectors; Matrices

Non Specialization

Non Specialization

Non Specialization

Doğrusal Cebir I: Uzaylar ve İşlemciler / Linear Algebra I: Spaces and Operators

Bu ders doğrusal cebir ikili dizinin birincisidir. Doğrusal uzaylar kavramı, doğrusal işlemciler, matris gösterimleri ve denklem sistemlerinin hesaplanabilmesi için temel araçlar vb. konuları içermektedir. Ders gerçek yaşamdan gelen uygulamaları da tanıtmaya önem veren “içerikli yaklaşımla” tasarlanmıştır.\n\nBölümler:\nBölüm 1: Doğrusal Cebirin Matematikdeki Yeri ve Kapsamı\nBölüm 2: Düzlemdeki Vektörlerin Öğrettikleri\nBölüm 3: İki Bilinmeyenli Denklemlerin Öğrettikleri\nBölüm 4: Doğrusal Uzaylar\nBölüm 5: Fonksiyon Uzayları ve Fourier Serileri\nBölüm 6: Doğrusal İşlemciler ve Dönüşümler\nBölüm 7: Doğrusal İşlemcilerden Matrislere Geçiş\nBölüm 8: Matris İşlemleri\n-----------\nThis is the first of the sequence of two courses. It develops the fundamental concepts in linear spaces, linear operators, matrix representations and basic tools for calculations with systems of equations. The course is designed with a “content based” emphasis, answering the “why” and “where“ of the topics, as much as the traditional “what” and “how” leading to “definitions” and “proofs”.\n\nChapters:\nChapter 1: Place and Contents of Linear Algebra Cebirin\nChapter 2: Learning From Vectors in the Plane\nChapter 3: Learning From Equations For Two Unknowns\nChapter 4: Linear Spaces\nChapter 5: Function Spaces and Fourier Series\nChapter 6: Linear Operators and Transformations\nChapter 7: From Linear Operators to Matrices\nChapter 8: Matrix Operations\n-----------\nKaynak: Attila Aşkar, “Doğrusal cebir”. Bu kitap dört ciltlik dizinin üçüncü cildidir. Dizinin diğer kitapları Cilt 1 “Tek değişkenli fonksiyonlarda türev ve entegral”, Cilt 2: "Çok değişkenli fonksiyonlarda türev ve entegral" ve Cilt 4: “Diferansiyel denklemler” dir.\n\nSource: Attila Aşkar, Linear Algebra, Volume 3 of the set of Vol1: Calculus of Single Variable Functions, Volume 2: Calculus of Multivariable Functions and Volume 4: Differential Equations.

Singular Value Decomposition; Matrices; Linearity; Augmented Assignment; Linear Equation; Gratitude; Linear Algebra; Bayesian Linear Regression; Lempel Ziv Oberhumer; Radial Basis Function

Non Specialization

Non Specialization

Non Specialization

Doğrusal Cebir II: Kare Matrisler, Hesaplama Yöntemleri ve Uygulamalar / Linear Algebra II: Square Matrices, Calculation Methods and Applications

Doğrusal cebir ikili dizinin ikincisi olan bu ders birinci derste verilen temel bilgilerin üzerine eklemeler yapılarak tamamen matris işlemleri ve uygulamalarını kapsamaktadır. Cebirsel denklem sistemleri, sonuçların tekilliği ve var olup olmadığı, determinantlar ve onların doğal olarak nasıl oluştuğu, öz değer problemleri ve onların matris fonksiyonlarına uygulanışı vb. konulara derste değinilmektedir. Ders gerçek yaşamdan gelen uygulamaları da tanıtmaya önem veren “içerikli yaklaşımla” tasarlanmıştır.\n\nBölümler:\nBölüm 1: Doğrusal Cebir I'in Özeti\nBölüm 2: Kare Matrislerde Determinant\nBölüm 3: Kare Matrislerin Tersi\nBölüm 4: Kare Matrislerde Özdeğer Sorunu\nBölüm 5: Matrislerin Köşegenleştirilmesi\nBölüm 6: Matris Fonksiyonları\nBölüm 7: Matrislerle Diferansiyel Denklem Takımları\n-----------\nThis second of the sequence of two courses builds on the fundamentals of the first course, is entirely on matrix algebra and applications. Specifically, the studies include systems of algebraic equations including the existence and uniqueness of solutions, determinants and how they arise naturally, eigenvalue problems with their applications to diagonalization and matrix functions. The course is designed in the same spirit as the first one with a “content based” emphasis, answering the “why” and “where“ of the topics, as much as the traditional “what” and “how” leading to “definitions” and “proofs”.\n\nChapters:\nChapter 1: Summary of Linear Algebra I\nChapter 2: Determinant\nChapter 3: Inverse of Square Matrices\nChapter 4: Eigenvalue Problem in Square Matrices\nChapter 5: Diagonalization of Matrices\nChapter 6: Matrix Functions\nChapter 7: Matrices and Systems of Differential Equations\n-----------\nKaynak: Attila Aşkar, “Doğrusal cebir”. Bu kitap dört ciltlik dizinin üçüncü cildidir. Dizinin diğer kitapları Cilt 1 “Tek değişkenli fonksiyonlarda türev ve entegral”, Cilt 2: "Çok değişkenli fonksiyonlarda türev ve entegral" ve Cilt 4: “Diferansiyel denklemler” dir.\n\nSource: Attila Aşkar, Linear Algebra, Volume 3 of the set of Vol1: Calculus of Single Variable Functions, Volume 2: Calculus of Multivariable Functions and Volume 4: Differential Equations.

Eigenvalues And Eigenvectors; Linearity; Matrices; Spectral Theorem; Algebra; Tensor Calculus; Geometric Calculus; Fundamental Theorem Of Calculus; Radial Basis Function Network; Radial Basis Function Kernel

Non Specialization

Non Specialization

Non Specialization

Data science courses contain math—no avoiding that! This course is designed to teach learners the basic math you will need in order to be successful in almost any data science math course and was created for learners who have basic math skills but may not have taken algebra or pre-calculus. Data Science Math Skills introduces the core math that data science is built upon, with no extra complexity, introducing unfamiliar ideas and math symbols one-at-a-time. \n\nLearners who complete this course will master the vocabulary, notation, concepts, and algebra rules that all data scientists must know before moving on to more advanced material.\n\nTopics include:\n~Set theory, including Venn diagrams\n~Properties of the real number line\n~Interval notation and algebra with inequalities\n~Uses for summation and Sigma notation\n~Math on the Cartesian (x,y) plane, slope and distance formulas\n~Graphing and describing functions and their inverses on the x-y plane,\n~The concept of instantaneous rate of change and tangent lines to a curve\n~Exponents, logarithms, and the natural log function.\n~Probability theory, including Bayes’ theorem.\n\nWhile this course is intended as a general introduction to the math skills needed for data science, it can be considered a prerequisite for learners interested in the course, "Mastering Data Analysis in Excel," which is part of the Excel to MySQL Data Science Specialization. Learners who master Data Science Math Skills will be fully prepared for success with the more advanced math concepts introduced in "Mastering Data Analysis in Excel." \n\nGood luck and we hope you enjoy the course!

Probability; Bayes' Theorem; Mathematics; Bayesian; Set Theory; Probability Theory; Euler'S Totient Function; General Statistics; Factorial; Problem Solving

Non Specialization

Non Specialization

Non Specialization

Arabic; French; Portuguese; Italian; Vietnamese; German; Russian; Spanish

École Polytechnique

Une fonction discontinue peut-elle être solution d'une équation différentielle? Comment définir rigoureusement la masse de Dirac (une "fonction" d'intégrale un, nulle partout sauf en un point) et ses dérivées? Peut-on définir une notion de "dérivée d'ordre fractionnaire"? Cette initiation aux distributions répond à ces questions - et à bien d'autres.

Partial Differential Equations; Differential Equations; Partial Derivative; Analysis; Studentized Residual; Joie De Vivre; Gustave Le Bon

Non Specialization

Non Specialization

Non Specialization

University of Pennsylvania

Calculus is one of the grandest achievements of human thought, explaining everything from planetary orbits to the optimal size of a city to the periodicity of a heartbeat. This brisk course covers the core ideas of single-variable Calculus with emphases on conceptual understanding and applications. The course is ideal for students beginning in the engineering, physical, and social sciences. Distinguishing features of the course include: 1) the introduction and use of Taylor series and approximations from the beginning; 2) a novel synthesis of discrete and continuous forms of Calculus; 3) an emphasis on the conceptual over the computational; and 4) a clear, dynamic, unified approach.\n\nIn this fifth part--part five of five--we cover a calculus for sequences, numerical methods, series and convergence tests, power and Taylor series, and conclude the course with a final exam. Learners in this course can earn a certificate in the series by signing up for Coursera's verified certificate program and passing the series' final exam.

Calculus; Explicit Substitution; Modal Μ-Calculus; Π-Calculus; Mathematical Series; Differential Equations; Power Series; Approximation; Multivariable Calculus; Redos

Non Specialization

Non Specialization

Non Specialization

French; Portuguese; Russian; Spanish

Tecnológico de Monterrey

Este curso forma parte de una secuencia con la que se propone un acercamiento a la Matemática Preuniversitaria que prepara para la Matemática Universitaria.\nEn él se asocia un significado real con el contenido matemático que se aprende y se integran tecnologías digitales en el proceso de aprendizaje.\nLa transferencia a varios contextos reales permitirá fortalecer un aprendizaje con significado e integrar tecnologías digitales especializadas. El objetivo es desarrollar un pensamiento matemático en el aprendizaje de contenidos relacionados con el Modelo Cúbico.El período de acreditación para la materia Introducción a las Matemáticas ha concluido. La última fecha para recibir certificados de Coursera es 24 de julio 2017. Informaremos oportunamente cuando la opción de acreditación esté disponible de nuevo. \n\nCurso con crédito académico para alumnos admitidos y aspirantes a ingresar a su primer semestre de un programa de profesional en el Tecnológico de Monterrey. Si estás inscrito en este MOOC con el fin de obtener el crédito académico para el curso de Introducción a las matemáticas (Matemáticas Remedial), confirma tu interés en la acreditación a la cuenta: mooc@servicios.itesm.mx. Consulta las preguntas frecuentes para conocer el proceso de acreditación.

Algebra; Sigma-Algebra; Calculus; Explicit Substitution; Mathematical Optimization; Denominación De Origen; Gustave Le Bon

Non Specialization

Non Specialization

Non Specialization

Математика в тестировании дискретных систем

National Research Tomsk State University

Математика является базой для программиста, инженера, тестировщика. Математические модели важны для понимания того, как будет работать та или иная система, цифровая схема, программа. В нашем курсе вы познакомитесь с классической моделью дискретного устройства – конечным автоматом. Вы разберетесь, поведение каких систем можно описать этой моделью. Научитесь строить проверяющие тесты. Кроме того, мы предлагаем вам услышать мнение специалистов-практиков о роли тестирования при разработке и отладке программного обеспечения.\n\nПомимо видеолекций и традиционных тестовых заданий в курсе предусмотрен тренажер, имитирующий процесс тестирования дискретной системы. \n\nЦель курса: научить слушателя извлекать математическую модель из описания дискретной системы, строить на основе этой модели полный проверяющий тест и применять его при тестировании предъявленной реализации.\n\nТребования к знаниям слушателей: знание математики в объёме средней школы (11 классов), а также базовые знания дискретной математики и информатики. Приветствуется знание основ цифровой техники. \n\nРезультаты обучения:\n1. Слушатель поймет, что такое тестирование и роль формальных моделей в тестировании\n2. Слушатель научится применять формальные модели для описания поведения дискретных систем\n3. Слушатель научится осуществлять тестирование дискретных систем и анализировать результаты

Non Specialization

Non Specialization

Non Specialization

University of Pennsylvania

Calculus is one of the grandest achievements of human thought, explaining everything from planetary orbits to the optimal size of a city to the periodicity of a heartbeat. This brisk course covers the core ideas of single-variable Calculus with emphases on conceptual understanding and applications. The course is ideal for students beginning in the engineering, physical, and social sciences. Distinguishing features of the course include: 1) the introduction and use of Taylor series and approximations from the beginning; 2) a novel synthesis of discrete and continuous forms of Calculus; 3) an emphasis on the conceptual over the computational; and 4) a clear, dynamic, unified approach.\n\nIn this first part--part one of five--you will extend your understanding of Taylor series, review limits, learn the *why* behind l'Hopital's rule, and, most importantly, learn a new language for describing growth and decay of functions: the BIG O.

Calculus; Series Expansions; L'Hôpital'S Rule; Euler'S Totient Function; Mathematics; Limits (Mathematics); Adaptive Grammar; Explicit Substitution; Venture Round; Series A Round

Non Specialization

Non Specialization

Non Specialization

Spanish; Russian; German; Vietnamese; Italian; Chinese; Portuguese; French; Arabic

University of Minnesota

Mathematical Matrix Methods lie at the root of most methods of machine learning and data analysis of tabular data. Learn the basics of Matrix Methods, including matrix-matrix multiplication, solving linear equations, orthogonality, and best least squares approximation. Discover the Singular Value Decomposition that plays a fundamental role in dimensionality reduction, Principal Component Analysis, and noise reduction. Optional examples using Python are used to illustrate the concepts and allow the learner to experiment with the algorithms.

Matrices; Linear Algebra; Singular Value Decomposition; Linear Equation; System Of Linear Equations; Least Squares; Linear Map; Linear Least Squares; Linearity; Approximation

Non Specialization

Non Specialization

Non Specialization

French; Portuguese; Russian; Spanish

Universidad de los Andes

En este tercer curso de acceso gratuito* del programa especializado Educación Matemática para profesores de primaria, conocerás los conceptos y técnicas para planificar e implementar tus clases.\n\nEl curso tiene una duración aproximada de seis semanas, con una dedicación promedio de 4 horas semanales. Todas las evaluaciones tienen retroalimentación y podrás descargar la mayoría de los recursos del curso.\n\nEste curso se basa en la información y los conocimientos que desarrollamos en los dos cursos anteriores de nuestro programa: Contenido de las matemáticas de primaria y Aprendizaje de las matemáticas de primaria. Te recomendamos tomar esos dos cursos antes de tomar este. Estos cursos también están disponibles en Coursera.\n\nEste curso incluye videos de presentación y explicación de los temas, actividades de aprendizaje y evaluación, revisión por pares, mapas conceptuales, y bibliografía adicional. La evaluación está diseñada para que recibas realimentación que queda registrada en la plataforma, de manera que puedas continuar con tu progreso al conectarte nuevamente. Puedes descargar la mayoría de los contenidos para que los uses sin conexión a Internet. \n\nLa Universidad de los Andes desarrolló el programa especializado Educación Matemática para profesores de primaria gracias al apoyo de United Way Colombia, el Fondo Puentes de Caña, la Fundación SM y la Fundación Compartir, con la colaboración de la Fundación de la Universidad de los Andes en Nueva York, Estados Unidos. \n\n* Al inscribirte al curso, puedes elegir la opción que más te interese: sin certificación, en cuyo caso tendrás acceso a todo el contenido del curso de forma gratuita; o con certificación, en cuyo caso deberás aprobar un cuestionario de evaluación por módulo y cumplir con los demás requisitos de la plataforma: hacer la verificación de identidad al presentar las evaluaciones obligatorias, lograr el porcentaje mínimo para pasar el curso y pagar directamente a Coursera el precio de la certificación anunciado en la plataforma.

Cmos; Trade Name; Gustave Le Bon; Denominación De Origen

Non Specialization

Non Specialization

Non Specialization

The Hong Kong University of Science and Technology

This course is about differential equations and covers material that all engineers should know. Both basic theory and applications are taught. In the first five weeks we will learn about ordinary differential equations, and in the final week, partial differential equations.\n\nThe course is composed of 56 short lecture videos, with a few simple problems to solve following each lecture. And after each substantial topic, there is a short practice quiz. Solutions to the problems and practice quizzes can be found in instructor-provided lecture notes. There are a total of six weeks in the course, and at the end of each week there is an assessed quiz.\n\nDownload the lecture notes: \nhttp://www.math.ust.hk/~machas/differential-equations-for-engineers.pdf\n\nWatch the promotional video: \nhttps://youtu.be/eSty7oo09ZI

Differential Equations; Ordinary Differential Equation; Partial Differential Equations; Partial Derivative; Laplace Transform Applied To Differential Equations; Numerical Analysis; Eigenvalues And Eigenvectors; Matrices; Integral; Periodic Function

Non Specialization

Non Specialization

Non Specialization

Arabic; French; Portuguese; Italian; Vietnamese; German; Russian; Spanish

Tecnológico de Monterrey

Este curso forma parte de una secuencia con la que se propone un acercamiento a la Matemática Preuniversitaria que prepara para la Matemática Universitaria.\nEn él se asocia un significado real con el contenido matemático que se aprende y se integran tecnologías digitales en el proceso de aprendizaje. \nEl contexto real de llenado de tanques permitirá hacer una primera transferencia de significado y recapitularemos contenidos preuniversitarios relacionados con el Modelo Cuadrático. El período de acreditación para la materia Introducción a las Matemáticas ha concluido. La última fecha para recibir certificados de Coursera es 24 de julio 2017. Informaremos oportunamente cuando la opción de acreditación esté disponible de nuevo. \n\nCurso con crédito académico para alumnos admitidos y aspirantes a ingresar a su primer semestre de un programa de profesional en el Tecnológico de Monterrey. Si estás inscrito en este MOOC con el fin de obtener el crédito académico para el curso de Introducción a las matemáticas (Matemáticas Remedial), confirma tu interés en la acreditación a la cuenta: mooc@servicios.itesm.mx. Consulta las preguntas frecuentes para conocer el proceso de acreditación.

Software Equation; Problem Solving; Physics; Geogebra; Sigma-Algebra; Software; Visa Inc.; Algebra; Denominación De Origen

Non Specialization

Non Specialization

Non Specialization

Universidad de los Andes

En este segundo curso de acceso gratuito* del programa especializado Educación Matemática para profesores de primaria, conocerás las cuestiones particulares sobre el aprendizaje de las matemáticas y las dificultades y los errores más frecuentes que tienen que enfrentar los estudiantes al aprenderlas.\n\nEl curso tiene una duración aproximada de seis semanas, con una dedicación promedio de 4 horas semanales. Todas las evaluaciones tienen retroalimentación y podrás descargar la mayoría de los recursos del curso.\n\nEste curso se basa en la información que presentamos en el primer curso del programa (Contenido) y su información se usará en el tercer curso (Enseñanza). Estos cursos también están disponibles en Coursera.\n\nEste curso incluye videos de presentación y explicación de los temas, actividades de aprendizaje y evaluación, mapas conceptuales, y bibliografía adicional. La evaluación está diseñada para que recibas realimentación que queda registrada en la plataforma, de manera que puedas continuar con tu progreso al conectarte nuevamente. Puedes descargar la mayoría de los contenidos para que los uses sin conexión a Internet. \n\nLa Universidad de los Andes desarrolló el programa especializado Educación Matemática para profesores de primaria gracias al apoyo de United Way Colombia, el Fondo Puentes de Caña, la Fundación SM y la Fundación Compartir, con la colaboración de la Fundación de la Universidad de los Andes en Nueva York, Estados Unidos.\n\n* Al inscribirte al curso, puedes elegir la opción que más te interese: sin certificación, en cuyo caso tendrás acceso a todo el contenido del curso de forma gratuita; o con certificación, en cuyo caso deberás aprobar un cuestionario de evaluación por módulo y cumplir con los demás requisitos de la plataforma: hacer la verificación de identidad al presentar las evaluaciones obligatorias, lograr el porcentaje mínimo para pasar el curso y pagar directamente a Coursera el precio de la certificación anunciado en la plataforma.

Thought; Switched Multi-Megabit Data Service; Cmos; Labor; Problem Solving; Approximation; Approximation Error; Vista; Type I And Type Ii Errors; Mathematics

Non Specialization

Non Specialization

Non Specialization

Universidad Nacional Autónoma de México

En este curso podrás apoyar tu formación en temas de estadística y probabilidad I.\n\nMás allá de que encuentres aquí un apoyo para lograr una calificación, el curso busca ayudarte a que adquieras los aprendizajes que comprenden temas de estadística descriptiva, datos bivariados y probabilidad, los cuales te serán de utilidad en tu paso por la licenciatura y en tu vida profesional.

General Statistics; Probability; Probability & Statistics; Standard Deviation; Statistical Charts And Diagrams; Chart; Computer Graphics; Basic Descriptive Statistics; Financial Analysis; Mathematics

Non Specialization

Non Specialization

Non Specialization

Это стандартный курс линейной алгебры, содержащий все необходимые для статистики и многомерного анализа приложения и алгоритмы, но не всегда содержащий подробные доказательства.\n\nДанный курс пригодится вам для того, чтобы изучить азы линейной алгебры и ознакомиться с базовыми определениями, понятиями и алгоритмами, научиться решать задачи, в которых необходим данный инструментарий. Многие пространственные задачи требуют знания линейной алгебры, а так же ряд задач экономики находит более простое решение, если владеть механизмами решения таких задач; эта наука находит себе применение во всех направлениях математики и ее приложениях, которые только можно представить. После прохождения данного курса вы научитесь корректно использовать понятия вектора, базиса, линейного пространства и линейной зависимости, оператора и матрицы, а так же овладеете несложными инструментами для решения и анализа задач линейной алгебры, научитесь оперировать матрицами и находить максимально подходящие условия для поиска ответа; ознакомитесь с классическими теоремами и узнаете красивые задачи данной науки, а также научитесь проверять свои решения на корректность, а результаты на адекватность, а еще мы обсудим теорему Перрона-Фробениуса и ее приложение к индексированию страниц в интернете.\nВнимательно смотрите лекции и вовремя выполняйте все необходимые задания. Удачи!\n\nПоявились технические трудности? Обращайтесь на адрес: coursera@hse.ru

Linear Algebra; Linearity; Algebra; Machine Learning; Sigma-Algebra; Matrices; Operations Management; Linear Operators; Human Learning; Least Squares

Non Specialization

Non Specialization

Non Specialization

Moscow Institute of Physics and Technology

Издавна среди жителей Кёнигсберга была распространена такая загадка: как пройти по всем мостам через реку Преголя, не проходя ни по одному из них дважды. Многие кёнигсбержцы пытались решить эту задачу как теоретически, так и практически во время прогулок. Доказать или опровергнуть возможность существования такого маршрута никто не мог до 1736 года, когда выдающийся математик Леонард Эйлер не написал письмо своему другу с решением. Ответ был «нельзя». Так и родилась теория графов. Но что будет, если процесс, который описывает граф – случаен?\n\nТеория случайных графов находится на стыке теории графов и теории вероятностей. Наука появилась в середине ХХ века, и она сразу же привлекла огромное внимание как со стороны чистых математиков, так и со стороны прикладников. В курсе мы изучим как основы теории случайных графов, так и настоящие ее жемчужины.\n\nМы научимся воспринимать многие сложные системы как "случайные графы". Среди них – интернет, социальные сети (Фейсбука, Вконтакте), биологические, межбанковские сети.\n\nПрослушав этот курс, вы проникнетесь чрезвычайно красивой математической теорией и научитесь решать комбинаторные и алгоритмические задачи на случайных графах. Все эти знания позволят нам затем перейти к курсу веб-графов, в котором мы расскажем о самых современных приложениях вероятностно-графовых моделей и конструкций.\n\nДля освоения материала будет достаточно математики школьного уровня, базовых знаний комбинаторики и теории вероятностей.

Bisimulation; Chernoff Bound

Non Specialization

Non Specialization

Non Specialization

Calculus: Single Variable Part 4 - Applications

University of Pennsylvania

Calculus is one of the grandest achievements of human thought, explaining everything from planetary orbits to the optimal size of a city to the periodicity of a heartbeat. This brisk course covers the core ideas of single-variable Calculus with emphases on conceptual understanding and applications. The course is ideal for students beginning in the engineering, physical, and social sciences. Distinguishing features of the course include: 1) the introduction and use of Taylor series and approximations from the beginning; 2) a novel synthesis of discrete and continuous forms of Calculus; 3) an emphasis on the conceptual over the computational; and 4) a clear, dynamic, unified approach.\n\nIn this fourth part--part four of five--we cover computing areas and volumes, other geometric applications, physical applications, and averages and mass. We also introduce probability.

Calculus; Integral; Probability; Volume Element; Arc Length; Probability Density Function; Geometry; Modal Μ-Calculus; Euler'S Totient Function; Recursively Enumerable Set

Non Specialization

Non Specialization

Non Specialization

Spanish; Russian; Portuguese; French

The Hong Kong University of Science and Technology

This course is all about matrices, and concisely covers the linear algebra that an engineer should know. The mathematics in this course is presented at the level of an advanced high school student, but typically students should take this course after completing a university-level single variable calculus course. There are no derivatives or integrals in this course, but students are expected to have attained a sufficient level of mathematical maturity. Nevertheless, anyone who wants to learn the basics of matrix algebra is welcome to join.\n\nThe course contains 38 short lecture videos, with a few problems to solve after each lecture. And after each substantial topic, there is a short practice quiz. Solutions to the problems and practice quizzes can be found in instructor-provided lecture notes. There are a total of four weeks in the course, and at the end of each week there is an assessed quiz.\n\nDownload the lecture notes:\nhttp://www.math.ust.hk/~machas/matrix-algebra-for-engineers.pdf\n\nWatch the promotional video: \nhttps://youtu.be/IZcyZHomFQc

Matrices; Algebra; Linearity; Linear Algebra; Eigenvalues And Eigenvectors; Matrix Theory; Vector Spaces; Determinants; Sigma-Algebra; Gaussian Elimination

Non Specialization

Non Specialization

Non Specialization

Arabic; French; Portuguese; Italian; Vietnamese; German; Russian; Spanish

Теория вероятностей - наука о случайности

National Research Tomsk State University

Курс познакомит с основными правилами исчисления вероятностей, обращая внимание на базовые идеи и концепции, научит решать вероятностные задачи, пользуясь формальным аппаратом. Курс позволит освоить элементарные вероятностные методы и применять их в быту и профессиональной деятельности, будет способствовать развитию рационального мышления и способности выражать мысли в математической форме.\n\nПонятие вероятности становится необходимым рациональным инструментом ориентации в современном мире полном неопределенности. Касается ли это проблем бизнеса, управления, науки, повседневной жизни, нам, как правило, приходится принимать решения в условиях риска и неопределенности. Вообще говоря, теорию вероятностей можно рассматривать как математическую модель интуитивного понятия неопределенности. Курс является введением в элементарную теорию вероятностей и снабжен многочисленными примерами разной степени сложности, часто взятыми из жизни, показывающими как строятся вероятностные модели. Даются англоязычные аналоги основных терминов.

Non Specialization

Non Specialization

Non Specialization

Гладкие многообразия являются одним из фундаментальных понятий современной математики. Это связано с тем, что на языке многообразий описываются многие законы естествознания. Цель данного курса - ввести слушателя в круг возникающих в теории многообразий понятий и научиться с ними работать. Сложность предмета связана с большим количеством новых для слушателя объектов. Для облегчения освоения материала, мы прибегли к использованию наглядных иллюстраций. Кроме этого помочь слушателю освоить пройденный материал должно прохождение тестов после каждой недели курса. \n\nПредварительными требованиями к слушателю являются освоение курсов математического анализа (в том числе нескольких переменных), линейной алгебры и знание основных фактов курса обыкновенных дифференциальных уравнений.

Non Specialization

Non Specialization

Non Specialization

Universidad de los Andes

En este curso de acceso gratuito*, conocerás algunos temas de las matemáticas escolares con la profundidad necesaria para que puedas ayudar a tus estudiantes a aprenderlas.\n\nEl curso tiene una duración aproximada de seis semanas, con una dedicación promedio de 4 horas semanales. Todas las evaluaciones tienen retroalimentación y podrás descargar la mayoría de los recursos del curso.\n\nEn este curso, podrás conocer las matemáticas desde cuatro perspectivas: su historia, los conceptos y procedimientos que las caracterizan, las distintas formas en que se hacen presentes (p. ej., tablas, gráficas o expresiones simbólicas), y los fenómenos y situaciones que les dan sentido.\n\nEste curso incluye videos de presentación y explicación de los temas, actividades de aprendizaje y evaluación, mapas conceptuales, y bibliografía adicional. La evaluación está diseñada para que recibas realimentación que queda registrada en la plataforma, de manera que puedas continuar con tu progreso al conectarte nuevamente. Puedes descargar la mayoría de los contenidos para que los uses sin conexión a Internet. \n\nEste es el primer curso del programa especializado Educación Matemática para profesores de primaria que la Universidad de los Andes desarrolló gracias al apoyo de United Way Colombia, el Fondo Puentes de Caña, la Fundación SM y la Fundación Compartir, con la colaboración de la Fundación de la Universidad de los Andes en Nueva York, Estados Unidos. El segundo curso Aprendizaje de las matemáticas de primaria y el tercero Enseñanza de las matemáticas de primaria están disponibles en Coursera.\n\n* Al inscribirte al curso, puedes elegir la opción que más te interese: sin certificación, en cuyo caso tendrás acceso a todo el contenido del curso de forma gratuita; o con certificación, en cuyo caso deberás aprobar un cuestionario de evaluación por módulo y cumplir con los demás requisitos de la plataforma: hacer la verificación de identidad al presentar las evaluaciones obligatorias, lograr el porcentaje mínimo para pasar el curso y pagar directamente a Coursera el precio de la certificación anunciado en la plataforma.

Estimation; Pedagogy; Materials; Conceptualization (Information Science); Logic; Tutor; Evaluation; Vista; Unos (Operating System); Ingres (Database)

Non Specialization

Non Specialization

Non Specialization

Shanghai Jiao Tong University

Discrete mathematics forms the mathematical foundation of computer and information science. It is also a fascinating subject in itself.\n\nLearners will become familiar with a broad range of mathematical objects like sets, functions, relations, graphs, that are omnipresent in computer science. Perhaps more importantly, they will reach a certain level of mathematical maturity - being able to understand formal statements and their proofs; coming up with rigorous proofs themselves; and coming up with interesting results.\n\nThis course attempts to be rigorous without being overly formal. This means, for every concept we introduce we will show at least one interesting and non-trivial result and give a full proof. However, we will do so without too much formal notation, employing examples and figures whenever possible.\n\nThe main topics of this course are (1) sets, functions, relations, (2) enumerative combinatorics, (3) graph theory, (4) network flow and matchings. It does not cover modular arithmetic, algebra, and logic, since these topics have a slightly different flavor and because there are already several courses on Coursera specifically on these topics.

Discrete Mathematics; Graphs; Closed-Form Expression; Polynomial; Spanning Tree; Augmented Assignment; Numbers (Spreadsheet); Euler'S Totient Function; Order By; Internet Slang

Non Specialization

Non Specialization

Non Specialization

Arabic; French; Portuguese; Italian; Vietnamese; German; Russian; Spanish

Wesleyan University

This course provides an introduction to complex analysis which is the theory of complex functions of a complex variable. We will start by introducing the complex plane, along with the algebra and geometry of complex numbers, and then we will make our way via differentiation, integration, complex dynamics, power series representation and Laurent series into territories at the edge of what is known today. Each module consists of five video lectures with embedded quizzes, followed by an electronically graded homework assignment. Additionally, modules 1, 3, and 5 also contain a peer assessment. \n \nThe homework assignments will require time to think through and practice the concepts discussed in the lectures. In fact, a significant amount of your learning will happen while completing the homework assignments. These assignments are not meant to be completed quickly; rather you'll need paper and pen with you to work through the questions. In total, we expect that the course will take 6-12 hours of work per module, depending on your background.

Complex Analysis; Analysis; Power Series; Mapping; Integral; Euler'S Totient Function; Numbers (Spreadsheet); Mathematics; Calculus; Differentiable Function

Non Specialization

Non Specialization

Non Specialization

Arabic; French; Portuguese; Italian; Vietnamese; German; Russian; Spanish

Princeton University

Analytic Combinatorics teaches a calculus that enables precise quantitative predictions of large combinatorial structures. This course introduces the symbolic method to derive functional relations among ordinary, exponential, and multivariate generating functions, and methods in complex analysis for deriving accurate asymptotics from the GF equations.\n\nAll the features of this course are available for free. It does not offer a certificate upon completion.

Analytics; Complex Analysis; Combinatorics; Analytic Combinatorics; Euler'S Totient Function; Approximation; Standard Deviation; Number Theory; Symbolic Method; Coefficient

Non Specialization

Non Specialization

Non Specialization

Spanish; Russian; Portuguese; French

The Chinese University of Hong Kong

The lectures of this course are based on the first 11 chapters of Prof. Raymond Yeung’s textbook entitled Information Theory and Network Coding (Springer 2008). This book and its predecessor, A First Course in Information Theory (Kluwer 2002, essentially the first edition of the 2008 book), have been adopted by over 60 universities around the world as either a textbook or reference text.\n\nAt the completion of this course, the student should be able to:\n1) Demonstrate knowledge and understanding of the fundamentals of information theory.\n2) Appreciate the notion of fundamental limits in communication systems and more generally all systems.\n3) Develop deeper understanding of communication systems.\n4) Apply the concepts of information theory to various disciplines in information science.

Information Theory; Markov Chain; Chain Rule; Random Variable; Noise; Mutual Information; Forward Error Correction; Memorylessness; Probability Distribution; Coding Theory

Non Specialization

Non Specialization

Non Specialization

French; Portuguese; Russian; Spanish

The Hong Kong University of Science and Technology

Vector Calculus for Engineers covers both basic theory and applications. In the first week we learn about scalar and vector fields, in the second week about differentiating fields, in the third week about multidimensional integration and curvilinear coordinate systems. The fourth week covers line and surface integrals, and the fifth week covers the fundamental theorems of vector calculus, including the gradient theorem, the divergence theorem and Stokes’ theorem. These theorems are needed in core engineering subjects such as Electromagnetism and Fluid Mechanics.\n\nInstead of Vector Calculus, some universities might call this course Multivariable or Multivariate Calculus or Calculus 3. Two semesters of single variable calculus (differentiation and integration) are a prerequisite. \n\nThe course is organized into 53 short lecture videos, with a few problems to solve following each video. And after each substantial topic, there is a short practice quiz. Solutions to the problems and practice quizzes can be found in instructor-provided lecture notes. There are a total of five weeks to the course, and at the end of each week there is an assessed quiz.\n\nDownload the lecture notes:\nhttp://www.math.ust.hk/~machas/vector-calculus-for-engineers.pdf\n\nWatch the promotional video: \nhttps://youtu.be/qUseabHb6Vk

Vector Calculus; Calculus; Explicit Substitution; Lambda Calculus; Adaptive Grammar; Integral; Π-Calculus; Modal Μ-Calculus; Partial Derivative; Derivative

Non Specialization

Non Specialization

Non Specialization

Limits for AP®(Calculus AB,BC) & Data Science -with Visuals

Coursera Project Network

The limit of a function is a fundamental concept in calculus and analysis concerning the behavior of that function near a particular input. This guided project is for students who want to ace the concepts of Calculus using “Wolfram Mathematica” .Highly beneficial for students of AP Physics, IB Diploma SL/HL, Cambridge(AS, A Level), US, Grade 11 & 12th.Very useful for Data Science ,Big Data learners .\nThis project gives you easy access to the invaluable learning techniques used by experts in maths.\nUsing these approaches, no matter what your skill levels in topics you would like to master, you can change your thinking and change your life. If you’re already an expert, this peep under the mental hood will give you ideas for turbocharging successful learning, including counter-intuitive test-taking tips and insights that will help you make the best use of your time on homework and problem sets. If you’re struggling, you’ll see a structured treasure trove of practical techniques that walk you through what you need to do to get on track. If you’ve ever wanted to become better at anything, this project will help serve as your guide. \nIn this project we will drill down and grasp the following concepts using Wolfram Mathematica illustrations-->Basic Limits-Type set limits -Limits of Elementary functions-Limits at infinity-Oscillatory functions Limits-Limits of Trigonometrical functions at infinity-Limits of exponential and logarithm function at Infinity-Visualize a set of limits-Limits of bounded functions

Euler'S Totient Function; Modal Μ-Calculus; Graphs; Project Mine; Continuous Function; Parasolid; Project; Lambda Calculus; Derivative; Calculus

Non Specialization

Non Specialization

Non Specialization

École Polytechnique Fédérale de Lausanne

Les nouvelles technologies de l’information ont facilité l’accès à de nombreuses bases de données offrant au grand public, mais surtout aux professionnels, une multitude de services. Le domaine de l’information géographique a également suivi ce mouvement en modernisant l’ensemble des supports, des plans, des cartes topographiques et de tous les types de données à référence spatiale. Face au déploiement massif des cartes numériques et des nombreux services basés sur la localisation, il s’agit de rester critique et surtout de développer les capacités nécessaires afin de choisir les outils et jeux de géodonnées adaptés aux besoins professionnels. \n\nC’est dans cette optique que ce cours propose de développer les éléments fondamentaux de la géomatique en décrivant les domaines clés que sont: les références géodésiques, les techniques d’acquisition des géodonnées, la topométrie, la localisation par satellites et la modélisation et représentation du terrain.\n\nCet enseignement est proposé aux futurs ingénieurs et architectes qui ont recours aux géodonnées pour la réalisation de projets d’aménagement, de construction, de gestion de l’environnement, de transport et de développement territorial. Dans ces domaines, l’accès aux données à référence spatiale ainsi qu’une connaissance des sources d’information et de leur qualité sont donc primordiales pour la conduite de projets.

Global Positioning System; Mergers & Acquisitions; Global; Ascii Art; Boosterism; Human Learning; Databases; Lecture; Spatial Databases; Surveying

Non Specialization

Non Specialization

Non Specialization

Moscow Institute of Physics and Technology

Среди жителей Кёнигсберга была распространена такая практическая головоломка: можно ли пройти по всем мостам через реку Преголя, не проходя ни по одному из них дважды? В 1736 году выдающийся математик Леонард Эйлер заинтересовался задачей и в письме другу привел строгое доказательство того, что сделать это невозможно. В том же году он доказал замечательную формулу, которая связывает число вершин, граней и ребер многогранника в трехмерном пространстве. Формула таинственным образом верна и для графов, которые называются "планарными". Эти два результата заложили основу теории графов и неплохо иллюстрируют направление ее развития по сей день. \n\nГраф как математический объект оказался полезным во многих теоретических и практических задачах. Наверное, дело в том, что сложность его структуры хорошо отвечает возможностям нашего мозга: это структура наглядная и понятно устроенная, но, с другой стороны, достаточно богатая, чтобы улавливать многие нетривиальные явления. Если говорить о приложениях, то, конечно, сразу же на ум приходят большие сети: Интернет, карта дорог, покрытие мобильной связи и т.п. В основах поисковых машин, таких, как Yandex и Google, лежат алгоритмы на графах. Помимо computer science, графы активно используются в биоинформатике, химии, социологии.\n\nЭтот курс служит введением в современную теорию графов. Мы, конечно, обсудим классические задачи, но и поговорим про более недавние результаты и тенденции, например, про экстремальную теорию графов. \n\nМатериал изложен с самых основ и на доступном языке. Целью этого курса является не только познакомить вас с вопросами и методами теории графов, но и развить у неподготовленных слушателей культуру математического мышления. Поэтому курс доступен широкому кругу слушателей. Для освоения материала будет достаточно знания математики на хорошем школьном уровне и базовых знаний комбинаторики.\n\nКурс состоит из 7 учебных недель и экзамена. Для успешного решения большинства задач из тестов достаточно освоить материал, рассказанный на лекциях. На семинарах разбираются и более сложные задачи, которые смогут заинтересовать слушателя, уже знакомого с основами теории графов.

Graphs; Graph Theory; Mathematics; Network Analysis; Factorial; Social Network Analysis; Reason; Analysis; Social Network

Non Specialization

Non Specialization

Non Specialization

Image and Video Processing: From Mars to Hollywood with a Stop at the Hospital

In this course, you will learn the science behind how digital images and video are made, altered, stored, and used. We will look at the vast world of digital imaging, from how computers and digital cameras form images to how digital special effects are used in Hollywood movies to how the Mars Rover was able to send photographs across millions of miles of space.\n \nThe course starts by looking at how the human visual system works and then teaches you about the engineering, mathematics, and computer science that makes digital images work. You will learn the basic algorithms used for adjusting images, explore JPEG and MPEG standards for encoding and compressing video images, and go on to learn about image segmentation, noise removal and filtering. Finally, we will end with image processing techniques used in medicine.\n \nThis course consists of 7 basic modules and 2 bonus (non-graded) modules. There are optional MATLAB exercises; learners will have access to MATLAB Online for the course duration. Each module is independent, so you can follow your interests.

Image Processing; Image Segmentation; Image Compression; Image Restoration; Sparse; Digital Image Processing; Digital Image; Image Analysis; Analysis; Noise Reduction

Non Specialization

Non Specialization

Non Specialization

German; Russian; Spanish; Arabic; French; Portuguese; Chinese; Italian; Vietnamese

Moscow Institute of Physics and Technology

Курс состоит из нескольких жизненных сюжетов, каждый из которых разбирается "по косточкам" и, как выясняется, содержит внутри себя нетривиальное математическое ядро. Это ядро далее также бьётся на "элементарные частицы" - так, что у слушателей возникает понимание всех глубинных механизмов рассматриваемой ситуации.\n\nСюжеты сгруппированы по смыслу: каждая группа сюжетов вращается вокруг одной и той же основополагающей математической идеи. Таких идей всего пять: инвариант, шаг через бесконечность, непрерывность физических процессов, самоподобие природы и нашего её восприятия, и, наконец, алгебраическая природа различных чисел.\n\nКурс предназначен для всех, кто хочет лучше представлять себе тот мир, в котором мы живём. Не имея никаких предварительных знаний, слушатели будут введены в курс дела: какая техника используется в математике ("абсолютное доказательство" как главное отличие математического знания от любого иного) и как строить рассуждения.\n\nВскоре выйдет вторая часть, "Математика для энтузиастов", которую нужно будет уже изучать "с листочком бумаги и ручкой в руках". В ней встретится более нетривиальный материал, в том числе "приводные ремни" современной математики - "группы" и "поля". Кроме того, будут вскрыты весьма нетривиальные подоплёки многих школьных задач.\n\nКурс состоит из 6 недель и 6 контрольных работ по окончании каждой недели. Для успешного прохождения курса необходимо успешно преодолеть все 6 испытаний.

Mathematical Logic; Machine Learning; Factorial; Databases; Thought; Logic; Elementary Mathematics; Mathematics; Human Learning

Non Specialization

Non Specialization

Non Specialization

Play with Graphs using Wolfram Mathematica

Coursera Project Network

Sometimes the visual understanding of a mathematical problem is quite helpful in solving it fast and correctly. Play with graph is an attempt to ease the minds of all mathematics lovers and engineering aspirants who wish to solve the tricky and knotty mathematics problem involving functional approach. This project will help you make intuitive connections between the graphs of the function in the problem with the exact solution of the problem.\n\nThe project starts with plotting basic functions ,labelling & fillings and later takes up the topic such as curve filling 'below' and 'between' the two curves ,plotting of sample points where the curve changes quickly, ranges where function becomes non real, plotting curve where there are discontinuities and finally labelling and legending of illustrative curves.\nIt is highly recommended to all those who sincerely desire to master problem solving in mathematics.

Wolfram Mathematica; Mathematics; Euler'S Totient Function; Graphs; Functional Approach; Label; Project; Fasting; Problem Solving; Desire

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Non Specialization

В течение жизни мы постоянно взаимодействуем с другими людьми. Маленькие дети, пытаясь добиться того, чтобы родители купили понравившуюся конфетку, часто шантажируют родителей своими слезами. Принимая решение заплакать, ребенок рискует — он не знает, как поведут себя папа с мамой. В чуть более взрослом возрасте абитуриенты, выбирающие вуз, принимают сложное решение о том, в какие университеты подать документы. Ошибка может стоить дорого: при неправильной стратегии можно оказаться в слабом университете или вообще остаться без заветного студенческого билета. Окончив вуз, юноши и девушки начинают искать работу. Перед интервью с работодателем они штудируют статьи в интернете о том, что можно и чего нельзя говорить на интервью, — они пытаются найти наилучшую стратегию своего поведения, исходя из ожиданий компании, в которую они устраиваются. Все эти ситуации объединяет то, что решения, которые принимают одни люди, оказывают влияние на других людей. Такие взаимодействия называются стратегическими. Именно их изучает теория игр.\n\nЧтобы проанализировать ту или иную реальную жизненную ситуацию стратегического взаимодействия и найти оптимальный вариант поведения в ней, необходимо сделать две вещи. Во-первых, необходимо формально записать ситуацию на языке теории игр, то есть создать модель (игру). Во-вторых, после того как модель (игра) составлена, ее необходимо решить. Этому мы будем учиться в течение курса. Мы разберем основные виды игр (одновременные и последовательные, с совершенной и несовершенной информацией, коалиционные и некоалиционные), приведем способы их решения и обсудим их на многочисленных примерах.\n\nКурс будет интересен желающим разобраться в том, как конкурируют друг с другом несколько компаний и можно ли гарантированно выиграть в шашки, есть ли смысл угрожать на переговорах и с кем стоит объединяться в коалиции в парламенте.\n\nFAQ\n\nВ: Требуется ли предварительная подготовка для прохождения курса?\nО: Курс является базовым, поэтому он не требует специальной подготовки. Для его успешного освоения достаточно уверенных знаний курса математики в объеме школьной программы. В одном-двух примерах могут пригодиться знания начал математического анализа (дифференцирование функций одной переменной, необходимое условие экстремума) и знания начал теории вероятностей (понятие математического ожидания случайной величины).\n\nВ: Что требуется для успешного окончания курса?\nО: Итоговая оценка за курс складывается из результатов 10 оцениваемых тестов. Для успешного окончания курса необходимо дать не менее 80 % правильных ответов на каждый из этих тестов.\n\nПоявились технические трудности? Обращайтесь на адрес: coursera@hse.ru

Game Theory; Economics; Logic; Matching; Operations Management; Decision Making; Strategic Planning; Methodology; Modeling; Thought

Non Specialization

Non Specialization

Non Specialization

Cálculo Diferencial e Integral unidos por el Teorema Fundamental del Cálculo

Tecnológico de Monterrey

Los cursos de Cálculo Diferencial y Cálculo Integral tradicionalmente se ofrecen separados y respetando ese orden. El primero estudia la derivada, y el segundo, la integral, siendo este momento en el que aparece el Teorema Fundamental del Cálculo (TFC) para establecer la relación entre ambos conceptos. En el presente curso vamos a hacer una diferencia: introduciremos la derivada y la integral como conceptos relacionados desde un principio. \n\nVamos a iniciar con la interpretación del Teorema Fundamental del Cálculo, con esto nos referimos a descubrir su significado real en la solución de problemas. Llegaremos a asociar con él la actividad práctica de calcular el valor de una magnitud que está cambiando. Habiendo realizado esta interpretación, los conceptos de derivada e integral se verán relacionados desde un principio, lo que te permitirá predecir el valor de una magnitud que está cambiando. Las nociones fundamentales de derivada e integral las identificaremos con las ideas de “razón de cambio” y de “acumulación del cambio”, y el TFC nos proveerá de la estrategia de solución.\n \nRecordarás que la Matemática Elemental incluye el Álgebra, la Geometría y la Geometría Analítica. Podemos decir que éstas son Matemáticas que estudian lo estático. En cambio, la Matemática Superior, que incluye el Cálculo, estudia lo dinámico. Con el Cálculo se inicia el estudio del cambio, una realidad presente en nuestro entorno cotidiano sin duda alguna. Costos, temperaturas, poblaciones, velocidades, energías, capitales de inversión, longitudes, etc., son algunos ejemplos de esto. En este curso podrás entender al Cálculo como una estrategia de solución para el estudio del cambio y diferenciarlo de las Matemáticas Elementales, aunque utilice de ellas bastante información.\n \nAl finalizar este curso podrás:\n\nDescribir de qué manera los modelos matemáticos polinomial, exponencial natural, y trigonométricos (seno y coseno), son una construcción que responde a esta práctica de predicción. Los verás a todos ellos surgir de esta práctica cuando una magnitud real particular cumple ciertas condiciones en su “razón de cambio” con respecto a la magnitud de la que depende. \n\nUtilizar la introducción de procesos infinitos (¡no imposibles!) en la construcción de la respuesta de predicción, con ello entenderás por qué se habla de Matemática Superior y de un pensamiento matemático avanzado.\n\nValorar una forma de pensar diferente, donde nuestro razonamiento matemático trascienda la sola manipulación de fórmulas algebraicas.

Integral; Calculus; Differential Calculus; Derivative; Modeling; Graphical Model; Euler'S Totient Function; Trigonometric Integral; Unos (Operating System); Microsoft Excel

Non Specialization

Non Specialization

Non Specialization

Universidad Autónoma Metropolitana

Líneas rectas, círculos, parábolas, elipses e hipérbolas son figuras geométricas que encontramos en nuestro derredor. Por ejemplo, mucha gente sabe que los planetas en nuestro sistema solar se mueven en órbitas elípticas teniendo al astro rey en un foco de esta figura. Sin embargo, pocos saben que la plaza de San Pedro en el Vaticano está construída sobre elipses donde sus focos se encuentran sobre las fuentes donde mucha gente se toma fotos. Estos son dos ejemplos que muestran la importancia de las figuras geométricas en nuestra vida.\nDespués de este curso podrás reconocer fácilmente una línea recta, una parábola, una elipse, una circunferencia o una hipérbola a partir de una ecuación de segundo grado de dos variables. Además, sabrás manipular estas ecuaciones para escribirlas en su forma canónica y obtener así los elementos geométricos de cada curva. El punto de partida del curso es el concepto de función y sobre todo lo que representan los ceros (raíces) de una función de segundo grado de dos variables.\nUn curso de este tipo es fascinante, ya que mientras muchas personas ven símbolos matemáticos, tu podrás ver una figura geométrica al reconocer una ecuación. Es parecido a una película de ciencia ficción de los años noventa, donde se veía gente haciendo sus actividades diarias, pero no eran más que símbolos verdes sobre una pantalla obscura. Solamente los que podían descifrar estos símbolos eran capaces de ver la realidad. Seguramente este curso te permitirá ver al mundo de otra manera.

Geometry; Analytics; Denominación De Origen; Gustave Le Bon

Non Specialization

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Non Specialization

This course is an important part of the undergraduate stage in education for future economists. It's also useful for graduate students who would like to gain knowledge and skills in an important part of math. It gives students skills for implementation of the mathematical knowledge and expertise to the problems of economics. Its prerequisites are both the knowledge of the single variable calculus and the foundations of linear algebra including operations on matrices and the general theory of systems of simultaneous equations. Some knowledge of vector spaces would be beneficial for a student. \n\nThe course covers several variable calculus, both constrained and unconstrained optimization. The course is aimed at teaching students to master comparative statics problems, optimization problems using the acquired mathematical tools. \nHome assignments will be provided on a weekly basis.\n\nThe objective of the course is to acquire the students’ knowledge in the field of mathematics and to make them ready to analyze simulated as well as real economic situations.\n\nStudents learn how to use and apply mathematics by working with concrete examples and exercises. Moreover this course is aimed at showing what constitutes a solid proof. The ability to present proofs can be trained and improved and in that respect the course is helpful. It will be shown that math is not reduced just to “cookbook recipes”. On the contrary the deep knowledge of math concepts helps to understand real life situations.\n\nDo you have technical problems? Write to us: coursera@hse.ru

Partial Derivative; Mathematics; Economics; Euler'S Totient Function; Linear Algebra; Chain Rule; Directional Derivative; Mathematical Optimization; Econometrics; Derivative

Non Specialization

Non Specialization

Non Specialization

Arabic; French; Portuguese; Italian; Vietnamese; German; Russian; Spanish

Введение в теорию кибернетических систем

Saint Petersburg State University

В основе предлагаемого курса лежат лекции, которые читаются студентам математико-механического факультета на 3-ем году обучения сразу после поступления на кафедру теоретической кибернетики.\n\nЦели курса:\nИзложить по возможности строго и полно основы теории управления в следующем объеме: линейная теория, синтез обратных связей для стабилизации линейных систем, линеаризация нелинейных систем в малом, линеаризация обратными связями, дискретизация непрерывных систем, анализ нелинейных систем.\nЗаинтересовать студентов и подготовить их к восприятию более углубленных специальных курсов.\nВыявить у обучаемых и убедить их заняться устранением пробелов в базовом математическом образовании.

Non Specialization

Non Specialization

Non Specialization

Saint Petersburg State University

Every day, almost every minute we make a choice. Right now you have made the choice to read this text instead of scrolling further. Choices can be insignificant: to go by tram or by bus, to take an umbrella or not. Sometimes they can be very significant and even crucial: the choice of University, life partner. However, the importance of choice may not be realized initially. Sometimes a decision "not to take an umbrella" radically changes everything. \n\nThe choice may affect a small group of people or entire countries. In game тtheory, we call it the choice of strategy. Constantly interacting with society and adopting certain strategies, many of us wonder: why can't everyone exist peacefully and cooperate with each other? Why do those who have agreed to cooperate, suddenly break the agreement? What if one is cooperative and the other is not? How profitable should the interaction be for the opponent to change his opinion? When are long-term stable prospects better than short-term benefits, and when not? \n\nThe answers to these and other questions you will find out in our course. \n\nThis course will be useful for those who want to make choices based on mathematical calculations rather than relying on fate. Who is interested in world politics and at least once heard about the "Prisoner's Dilemma". \n\nThe course is basic and does not require any special knowledge. In several sections, definitions and theorems from mathematical analysis and elements of probability theory will be used.

Game Theory; Trading; Mathematical Optimization; Number Theory; Strategy; Mathematical Finance; Bargaining; Exercise; Minimax; Computer Programming

Non Specialization

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Non Specialization

Games without Chance: Combinatorial Game Theory

Georgia Institute of Technology

This course will cover the mathematical theory and analysis of simple games without chance moves.

Thought; Number Theory; Autonomous System (Internet); Game Theory; Combinatorics; Combinatorial Game Theory; Surveying; Numbers (Spreadsheet); Game Programming; Resource

Non Specialization

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Non Specialization

French; Portuguese; Russian; Spanish

École Polytechnique Fédérale de Lausanne

Ce cours contient les 7 premiers chapitres d'un cours donné aux étudiants bachelor de l'EPFL. Il est basé sur le livre "Introduction à l'analyse numérique", J. Rappaz M. Picasso, Ed. PPUR. Des outils de base sont décrits dans les 5 premiers chapitres. Les deux derniers chapitres abordent la question de la résolution numérique d'équations différentielles. Plus précisement, nous allons étudier les chapitres suivants du livre :\n\n Chapitre 1 : interpolation, comment approcher une fonction par un polynôme?\n Chapitre 2 : comment approcher des dérivées par des formules de différences finies?\n Chapitre 3 : comment approcher des intégrales par des formules de quadrature?\n Chapitres 4,5,6 : comment résoudre des (grands) systèmes linéaires?\n Chapitre 8 : comment résoudre des équations et systèmes d’équations nonlinéaires?\n Chapitre 9 : comment approcher la solution d’une équations différentielle (problème à valeur initiale)?\n Chapitre 10 : comment approcher la solution d’un problème aux limites unidimensionnel par une méthode de différences finies?\n\nUn cours de deux heures est donc remplacé par des "video lectures" ainsi que les "quiz" correspondant. L'heure d'exercices est remplacée par un "exercice" où vous devrez faire des expériences numériques avec un programme matlab ou octave, et démontrer des résultats théoriques "peer review". Un questionnaire a choix multiple aura lieu à la fin du cours (30% de la note).\n\nIl faut obtenir 60% de la note pour avoir le “Course Certificate”.\n\nPour les étudiants EPFL, les heures de cours selon l'horaire is-academia sont maintenues. Vous devez visionner les "video lectures" de la semaine et faire les "quiz" avant l'heure de cours. Lors de la première heure de cours, je résoudrai l'exercice théorique (cet exercice theorique sera proposé comme "peer review" pour les étudiants externes). Une question du même type pourrait être posée lors de l'examen de juin. Lors de la deuxième heure de cours, je répondrai aux questions et je vous aiderai à faire l'"exercice" si nécessaire.\n\nLe temps de travail estimé est le suivant. Il faut compter deux heures pour visualiser les "video lectures" et répondre aux "quiz". Il faut compter une heure pour faire l'"exercice", qui demande de compléter un programme matlab (ou octave) et une heure pour faire l'exercice théorique "peer review" soit cinq heures en tout. Après ces cinq heures, vous devriez avoir acquis la matière.

Numerical Analysis; Interpolation; Algorithms; Matlab; Analysis; Simulation; Computational Thinking; Gnu Octave; Gustave Le Bon; Joie De Vivre

Non Specialization

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The purpose of this course is to equip students with theoretical knowledge and practical skills, which are necessary for the analysis of stochastic dynamical systems in economics, engineering and other fields.\nMore precisely, the objectives are \n1. study of the basic concepts of the theory of stochastic processes;\n2. introduction of the most important types of stochastic processes;\n3. study of various properties and characteristics of processes;\n4. study of the methods for describing and analyzing complex stochastic models.\nPractical skills, acquired during the study process:\n1. understanding the most important types of stochastic processes (Poisson, Markov, Gaussian, Wiener processes and others) and ability of finding the most appropriate process for modelling in particular situations arising in economics, engineering and other fields;\n2. understanding the notions of ergodicity, stationarity, stochastic integration; application of these terms in context of financial mathematics; \nIt is assumed that the students are familiar with the basics of probability theory. Knowledge of the basics of mathematical statistics is not required, but it simplifies the understanding of this course.\nThe course provides a necessary theoretical basis for studying other courses in stochastics, such as financial mathematics, quantitative finance, stochastic modeling and the theory of jump - type processes.\n\nDo you have technical problems? Write to us: coursera@hse.ru

Stochastic; Process; Stochastic Processes; Stochastic Calculus; Calculus; Probability; Lévy Processes; Modeling; Gaussian Process; Probability Theory

Non Specialization

Non Specialization

Non Specialization

Arabic; French; Portuguese; Italian; Vietnamese; German; Russian; Spanish

Çok değişkenli Fonksiyon I: Kavramlar / Multivariable Calculus I: Concepts

Ders çok değişkenli fonksiyonlardaki ikili dizinin birincisidir. Burada çok değişkenli fonksiyonlardaki temel türev ve entegral kavramlarını geliştirmek ve bu konulardaki problemleri çözmekteki temel yöntemleri sunmaktadır. Ders gerçek yaşamdan gelen uygulamaları da tanıtmaya önem veren “içerikli yaklaşımla” tasarlanmıştır.\n\nBölümler\nBölüm 1: Genel Konular ve Düzlemdeki Vektörler\nBölüm 2: Uzayda Vektörler, Doğrular ve Düzlemler; Vektör Fonksiyonları\nBölüm 3: Düzlem Eğrilerinden Hatırlatmalar ve Uzay Eğrileri, İki Değişkenli ve İkinci Derece Fonksiyonlar ve Karşıt Gelen Yüzeyler\nBölüm 4: Özel Yapıdaki İki Değişkenli Olarak Karmaşık Fonksiyonlar, İki Değişkenli Fonksiyonlarda Kısmi Türev ve İki Katlı Entegralin Temel Tanımları; Limit Kavramının Gerekliliği ve Anlatımı\nBölüm 5: Türev Hesaplama Yöntemleri\nBölüm 6: Türev Uygulamaları\nBölüm 7: İki Katlı Entegraller ve Uygulamaları\n-----------\nThe course is the first of the sequence of calculus of multivariable functions. It develops the fundamental concepts of derivatives and integrals of functions of several variables, and the basic tools for doing the relevant calculations. The course is designed with a “content-based” approach, i. e. by solving examples, as many as possible from real life situations. \n\nChapters\nChapters 1: General Topics and Vectors in the Plane\nChapters 2: Vectors in Space, Lines and Planes; Vector Functions\nChapters 3: Reminders of Plane Curves and Space Curves, Quadratic Functions and Variables, Surfaces\nChapters 4: Special Two Variables Complex Functions, the Basic Definition of Partial Derivatives and Two Storey Integrals in Two Unknown Functions ; Necessity and Details of Limits\nChapters 5: Methods of Derivative Calculations\nChapters 6: Application of Derivatives\nChapters 7: Two Storey Integrals and Applications\n-----------\nKaynak: Attila Aşkar, “Çok değişkenli fonksiyonlarda türev ve entegral”. Bu kitap dört ciltlik dizinin ikinci cildidir. Dizinin diğer kitapları Cilt 1 “Tek değişkenli fonksiyonlarda türev ve entegral”, Cilt 3: “Doğrusal cebir” ve Cilt 4: “Diferansiyel denklemler” dir.\n\nSource: Attila Aşkar, Calculus of Multivariable Functions, Volume 2 of the set of Vol1: Calculus of Single Variable Functions, Volume 3: Linear Algebra and Volume 4: Differential Equations. All available online starting on January 6, 2014

Multivariable Calculus; Calculus; Explicit Substitution; Steve Mann; Arthur Janov; Borel Cantelli Lemma; Sss*; Addresssanitizer; Factorial; Chi-Squared Distribution

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Explorando os recursos educacionais da Khan Academy

Fundação Lemann

O curso "Explorando os recursos educacionais da Khan Academy" tem como objetivo ajudar todos aqueles que desejam utilizar a plataforma como um recurso pedagógico. No decorrer do curso, você terá a oportunidade de conhecer a plataforma do ponto de vista do estudante e do ponto de vista do tutor, sabendo exatamente como utilizá-la em favor da aprendizagem. Ao longo do curso, você terá todas as orientações de que precisa para utilizar a plataforma com seus alunos.\n\nA plataforma Khan Academy foi concebida para oferecer aprendizado personalizado para todas as idades, com exercícios, vídeos e um painel de acompanhamento que habilita os estudantes a aprender no seu próprio ritmo. Para o professor, a Khan Academy é uma poderosa ferramenta pedagógica que possibilita personalizar o percurso de aprendizagem dos alunos, dinamizar a experiência educacional com recursos de gamificação e monitorar o progresso de todos e de cada um, com relatórios simples e objetivos.\n\nEste curso é autoinstrucional, ou seja, a aprendizagem acontece na interação com o conteúdo, com outros participantes e por meio da realização das atividades propostas. Assim, o cursista tem mais flexibilidade para estudar no seu próprio ritmo, de acordo com a sua disponibilidade de tempo.\n\nComo material didático, disponibilizamos textos, links, vídeo tutoriais, quizzes e uma proposta de atividade final, que envolve a sistematização da experiência de uso da plataforma como recurso pedagógico.\n\nPara ser certificado, o cursista deve obter 100% de aproveitamento nas avaliações ofertadas ao longo do curso, que são apresentadas em formato de teste, com possibilidade de mais de uma tentativa. \n\n\nInstituições envolvidas no projeto Khan Academy no Brasil:\n\nA Fundação Lemann é parceira internacional da Khan Academy no Brasil e tem experiência na implementação da plataforma em diferentes contextos educacionais, incluindo ONGs, instituições de ensino públicas e privadas.\n\nComo instituições parceiras do projeto no Brasil, temos o Instituto Península, o Instituto Natura e o Ismart. Ainda, agradecemos o apoio do Instituto Singularidades no desenvolvimento deste programa de formação.\n\nParticipe de outros cursos da Fundação Lemann no Coursera - https://www.coursera.org/lemann

Education; Com File; Unos (Operating System); Vista; Cabeza; Gustave Le Bon; Joie De Vivre; Edward De Bono; Denominación De Origen

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Portuguese (Brazil)

Saint Petersburg State University

Каждый день, почти каждую минуту мы делаем выбор. Прямо сейчас Вы сделали выбор прочитать этот текст, вместо того чтобы пролистать дальше. Выборы могут быть несущественными: поехать на трамвае или на автобусе, взять зонт или нет. А могут быть очень значительными и даже судьбоносными: выбор ВУЗа, спутника жизни. Впрочем, существенность выбора – относительное понятие. Бывает, что решение «не брать зонт» кардинально меняет судьбу. \n\nВыбор может затрагивать небольшую группу людей или целые государства. В теории игр мы называем выбор стратегией. Постоянно взаимодействуя с социумом и принимая те или иные стратегии, многие задаются вопросом: почему нельзя всем существовать мирно, и сотрудничать друг с другом? И правда, почему? Почему те, кто договорились сотрудничать, внезапно разрывают договоренности? Что делать, если один настроен на сотрудничество, а второй нет? Насколько выгодным должно быть взаимодействие, чтобы противник изменил свое мнение? Когда долгосрочные стабильные перспективы лучше сиюминутной выгоды, а когда нет? \n\nОтветы на эти и другие вопросы Вы узнаете из нашего курса. \n\nЭтот курс будет полезен тем, кто хочет делать выбор, основываясь на математических расчетах, а не полагаясь на судьбу. Кто интересуется мировой политикой и хоть раз слышал о «Дилемме заключенного». \n \nКурс является базовым и не требует специальной подготовки, достаточно освоенного школьного курса математики. В отдельных главах будут использован аппарат математического анализа и элементы теории вероятности.

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Aléatoire : une introduction aux probabilités - Partie 1

École Polytechnique

Ce cours d'introduction aux probabilités a la même contenu que le cours de tronc commun de première année de l'École polytechnique donné par Sylvie Méléard.\n\nLe cours introduit graduellement la notion de variable aléatoire et culmine avec la loi des grands nombres et le théorème de la limite centrale. \n\nLes notions mathématiques nécessaires sont introduites au fil du cours et de nombreux exercices corrigés sont proposés.\n\nCe cours propose aussi une introduction aux méthodes de simulations des variables aléatoires comme la méthode de Monte Carlo. Des expériences numériques interactives sont également mises à votre disposition pour vous permettre de visualiser diverses notions.

Aleatoricism; Probability; Analysis; Gustave Le Bon; Joie De Vivre; Variance; Probability Theory

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University of Pennsylvania

Calculus is one of the grandest achievements of human thought, explaining everything from planetary orbits to the optimal size of a city to the periodicity of a heartbeat. This brisk course covers the core ideas of single-variable Calculus with emphases on conceptual understanding and applications. The course is ideal for students beginning in the engineering, physical, and social sciences. Distinguishing features of the course include: 1) the introduction and use of Taylor series and approximations from the beginning; 2) a novel synthesis of discrete and continuous forms of Calculus; 3) an emphasis on the conceptual over the computational; and 4) a clear, dynamic, unified approach.\n\nIn this third part--part three of five--we cover integrating differential equations, techniques of integration, the fundamental theorem of integral calculus, and difficult integrals.

Integral; Calculus; Differential Equations; Antiderivative; Integration By Parts; Improper Integral; Partial Fraction Decomposition; Trigonometric Substitution; Thought; Integration By Substitution

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Spanish; Russian; Portuguese; French

A very beautiful classical theory on field extensions of a certain type (Galois extensions) initiated by Galois in the 19th century. Explains, in particular, why it is not possible to solve an equation of degree 5 or more in the same way as we solve quadratic or cubic equations. You will learn to compute Galois groups and (before that) study the properties of various field extensions.\n\nWe first shall survey the basic notions and properties of field extensions: algebraic, transcendental, finite field extensions, degree of an extension, algebraic closure, decomposition field of a polynomial. \nThen we shall do a bit of commutative algebra (finite algebras over a field, base change via tensor product) and apply this to study the notion of separability in some detail. \nAfter that we shall discuss Galois extensions and Galois correspondence and give many examples (cyclotomic extensions, finite fields, Kummer extensions, Artin-Schreier extensions, etc.). \nWe shall address the question of solvability of equations by radicals (Abel theorem). We shall also try to explain the relation to representations and to topological coverings. \nFinally, we shall briefly discuss extensions of rings (integral elemets, norms, traces, etc.) and explain how to use the reduction modulo primes to compute Galois groups.\n\nPREREQUISITES \nA first course in general algebra — groups, rings, fields, modules, ideals. Some knowledge of commutative algebra (prime and maximal ideals — first few pages of any book in commutative algebra) is welcome. For exercises we also shall need some elementary facts about groups and their actions on sets, groups of permutations and, marginally, \nthe statement of Sylow's theorems.\n\nASSESSMENTS\nA weekly test and two more serious exams in the middle and in the end of the course. For the final result, tests count approximately 30%, first (shorter) exam 30%, final exam 40%.\n\nThere will be two non-graded exercise lists (in replacement of the non-existent exercise classes...)\n\n\nDo you have technical problems? Write to us: coursera@hse.ru

Algebra; Topology; Integral; Polynomial; Sigma-Algebra; Commutative Property; Factorization; Lambda Calculus; Abstract Algebra; Stemming

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French; Portuguese; Russian; Spanish

Tecnológico de Monterrey

Este curso forma parte de una secuencia con la que se propone un acercamiento a la Matemática Preuniversitaria que prepara para la Matemática Universitaria.\nEn él se asocia un significado real con el contenido matemático que se aprende y se integran tecnologías digitales en el proceso de aprendizaje.\nEl contexto real del movimiento en línea recta será el marco con el cual asociamos un primer significado y recapitulamos contenidos preuniversitarios relacionados con el Modelo Lineal.\n\nCurso con crédito académico para alumnos admitidos y aspirantes a ingresar a su primer semestre de un programa de profesional en el Tecnológico de Monterrey. Si estás inscrito en este MOOC con el fin de obtener el crédito académico para el curso de Introducción a las matemáticas (Matemáticas Remedial), confirma tu interés en la acreditación a la cuenta: mooc@servicios.itesm.mx . Consulta las preguntas frecuentes para conocer el proceso de acreditación.

Linear Model; Algebra; Modeling; Linearity; Cmos; Calculus; Adaptive Grammar; Human Learning; Factorial; Stochastic

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University of Amsterdam

This course provides a very brief introduction to basic mathematical concepts like propositional and predicate logic, set theory, the number system, and proof techniques. At the end of the course, students will be able to\n(1) detect the logical structure behind simple puzzles\n(2) be able to manipulate logical expressions\n(3) explain the connection between logic and set theory\n(4) explain the differences between natural, integer, rational, real and complex numbers\n(5) recognise different basic proof techniques

Logic; Set Theory; Propositional Calculus; Relative Change And Difference; Well-Formed Formula; Proposition; Numbers (Spreadsheet); Π-Calculus; Explicit Substitution; Euler'S Totient Function

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French; Portuguese; Russian; Spanish

Çok değişkenli Fonksiyon II: Uygulamalar / Multivariable Calculus II: Applications

Ders çok değişkenli fonksiyonlardaki iki derslik dizinin ikincisidir. Birinci ders türev ve entegral kavramlarını geliştirmekte ve bu konulardaki problemleri temel çözme yöntemlerini sunmaktadır. Bu ders, birinci derste geliştirilen temeller üzerine daha ileri konuları işlemekte ve daha kapsamlı uygulamalar ve çözümlü örnekler sunmaktadır. Ders gerçek yaşamdan gelen uygulamaları da tanıtmaya önem veren “içerikli yaklaşımla” tasarlanmıştır. \n\nBölümler\nBölüm 1: Multivar 1'in Özeti, Dairesel Koordinatlarda Entegraller\nBölüm 2: Türev Uygulamalarından Seçme Konular\nBölüm 3: Çok Değişkenle Zincirleme Türev ve Jakobiyan\nBölüm 4: Uzayda Yüzey ve Hacım Entegralleri\nBölüm 5: Düzlemde Akı Entegralleri\nBölüm 6: Düzlemde Green, Uzayda Stokes ve Green-Gauss Teoremleri\nBölüm 7: Stokes ve Green-Gauss Teoremleri ve Doğanın Korunum Yasaları\n-----------\nThe course is the second of the two course sequence of calculus of multivariable functions. The first course develops the concepts of derivatives and integrals of functions of several variables, and the basic tools for doing the relevant calculations. This course builds on the foundations of the first course and introduces more advanced topics along with more advanced applications and solved problems. The course is designed with a “content-based” approach, i. e. by solving examples, as many as possible from real life situations.\n\nBölümler\nBölüm 1: Summary of Multivar I, Integral in Circular Coordinates\nBölüm 2: Topics of Derivative Applications\nBölüm 3: Chain Derivatives with Multi Variables and Jacobian\nBölüm 4: Surface and Volume Integrals in Space\nBölüm 5: Flux Integrals in the Plane\nBölüm 6: Green in Plane, Stokes in Space and Green-Gauss Theorems\nBölüm 7: Stokes and Green-Gauss Theorem and Nature Conservation Laws\n-----------\nKaynak: Attila Aşkar, “Çok değişkenli fonksiyonlarda türev ve entegral”. Bu kitap dört ciltlik dizinin ikinci cildidir. Dizinin diğer kitapları Cilt 1 “Tek değişkenli fonksiyonlarda türev ve entegral”, Cilt 3: “Doğrusal cebir” ve Cilt 4: “Diferansiyel denklemler” dir.\n\nSource: Attila Aşkar, Calculus of Multivariable Functions, Volume 2 of the set of Vol1: Calculus of Single Variable Functions, Volume 3: Linear Algebra and Volume 4: Differential Equations. All available online starting on January 6, 2014

Steve Mann; Moore Penrose Pseudoinverse; Bradbury Thompson; Chi-Squared Distribution; Sss*; Fundamental Theorem Of Calculus; Lists Of Integrals; Durbin Wu Hausman Test; Radial Basis Function Network; Borel Cantelli Lemma

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This is a master course given in Moscow at the Laboratory of Algebraic Geometry of the National Research University Higher School of Economics by Valery Gritsenko, a professor of University Lille 1, France.\nJacobi forms are holomorphic functions in two complex variables. They are modular in one variable and abelian (or double periodic) in another variable. The theory of Jacobi modular forms became an independent research subject after the famous book of Martin Eichler and Don Zagier “Jacobi modular forms” (Progress in Mathematics, vol. 55, 1985) which was cited more than a thousand times in research papers. This is due to many applications of Jacobi forms in arithmetic, topology, algebraic and differential geometry, mathematical and theoretical physics, in the theory of Lie algebras, etc. The list of mentioned subjects shows that my course might be useful for master and Ph.D. students working in different directions.\nMotivated undergraduate students can also study this subject. To follow the course one has to know only elementary basic facts from the theory of modular forms (for example, the paragraphs 1-4 of the chapter VII of Serre’s “A Course in Arithmetic” are enough).\nThe main hero of the course is the Jacobi theta-series. Using it we will construct a lot of concrete examples of Jacobi forms in one or many abelian variables, in particular, Jacobi forms for root systems.\nFor some of you, who will be successful with the theoretical exercises of the course, I am ready to formulate research problems for Master or Ph.D. thesis. (Ph.D. support might be available at CEMPI in Lille or at the Faculty of Mathematics of National Research University Higher School of Economics in Moscow)\n\nDo you have technical problems? Write to us: coursera@hse.ru

Form 3; Peer Review; Lecture; Weighting; Null Coalescing Operator; Peering; Topology; Calibration; Exercise; Continuous Function

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Moscow Institute of Physics and Technology

Теория вероятностей - это, вне всякого сомнения, один из самых важных и богатых приложениями разделов современной математики.\n\nС помощью методов этой замечательной науки можно как оценивать классические вероятности выигрышных стратегий в азартных играх, так и решать весьма серьезные прикладные задачи, возникающие буквально в каждой области науки. В нашем курсе мы познакомим слушателей прежде всего с самыми основами предмета. И сделаем мы это в уникальном формате - иллюстрируя вероятностные объекты и методы на примерах решения с их помощью комбинаторных задач. Суть в том, что, конечно, в базовой вероятности много комбинаторики, и это все знают; мы же расскажем не только об этом, но и о том, как, наоборот, вероятностные методы позволяют работать с комбинаторными задачами. Это позволит нам впоследствии выйти на приложения вероятности в теории графов, случайных графов и, наконец, веб-графов и прочих сложных сетей. Также в рамках курса мы оторвемся от чисто комбинаторных интерпретаций и обсудим более общие вероятностные модели. Но интуиция все равно сохранится, и в этой комбинаторной подоплеке уникальность курса.\n\nКурс построен так, что будет по плечу даже тем, кто изучал математику последний раз только в школе. Тем не менее, так как для понимания курса необходимы знания основ комбинаторики, мы рекомендуем пройти наш курс по комбинаторике прежде чем прослушивать данный курс.\n\nВнутри курса также все просто – каждую неделю вас ждут видеолекции и проверочные задания, которые нужно выполнять в срок. В конце – итоговая проверочная работа. Студенты, которые набрали достаточное количество баллов, смогут получить сертификат.

Mathematics; Factorial; Probability Theory; Probability; K-Distribution; Broyden Fletcher Goldfarb Shanno Algorithm; K-Svd; Pascal'S Rule; K-Medoids

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The Hong Kong University of Science and Technology

Learn the mathematics behind the Fibonacci numbers, the golden ratio, and how they are related. These topics are not usually taught in a typical math curriculum, yet contain many fascinating results that are still accessible to an advanced high school student. \n\nThe course culminates in an explanation of why the Fibonacci numbers appear unexpectedly in nature, such as the number of spirals in the head of a sunflower.\n\nDownload the lecture notes:\nhttps://www.math.ust.hk/~machas/fibonacci.pdf\n\nWatch the promotional video:\nhttps://youtu.be/VWXeDFyB1hc

Numbers (Spreadsheet); Mathematical Induction; Mathematics; Square (Algebra); Approximation; Game Theory; Geometry; Analysis; A/Rose; Dissection

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Arabic; French; Portuguese; Italian; Vietnamese; German; Russian; Spanish

Novosibirsk State University

Не секрет, что математика — универсальный язык для исследований. А графы в математике — универсальные высоко симметричные структуры, с помощью которых можно изучать множество объектов различной природы и их свойства. Вы сталкиваетесь с ними каждый день в повседневных ситуациях. Например, когда строите оптимальный маршрут до университета или работы. Ещё такие объекты встречаются в прикладных научных задачах из разных сфер: графы эффективно используются в теории межкоммуникационных сетей, помогают моделировать эволюционные мутационные процессы в биологии и не только. Структура графов необходима и при создании биокомпьютера или в квантовой химии — в общем, методы алгебраической теории графов универсальны. \n\nВ нашем курсе вы узнаете о свойствах графов и о том, как их исследовать. Вы научитесь самостоятельно строить такие структуры, анализировать их и находить ответ на любой вопрос. Вы сможете применять инструменты алгебраической теории графов для оптимального решения задач в химии, биологии, биоинформатике, физике, социологии, теории кодирования, криптографии и многих других областях.\n\nПервые модули курса помогут вспомнить основы теории графов, теории групп и линейной алгебры, чтобы постепенно познакомить вас с современными математическими исследованиями. В последних модулях вы узнаете об актуальных новых вопросах, которые возникли благодаря алгебраической теории графов и открыты для исследований.\n\n\nДля кого этот курс:\n- для студентов математических специальностей;\n- для специалистов в сфере IT;\n- для студентов факультетов естественных наук: химиков, биологов, физиков, геологов, инженеров;\n- для всех, кому интересна математика и кто хочет развивать математическое мышление и логику\n \nМатериалы курса разработаны группой исследователей Математического центра в Академгородке (соглашение с Министерством науки и высшего образования РФ номер 075-15-2019-1675)

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Современная комбинаторика (Modern combinatorics)

Moscow Institute of Physics and Technology

Комбинаторика - это наука, которая, с одной стороны, богата исключительно красивыми постановками задач, зачастую доступными школьнику, а с другой стороны, это очень глубокая современная область знаний, без овладения инструментами которой невозможно серьезное понимание как большинства других фундаментальных дисциплин - анализа, алгебры, теории графов, теории вероятностей и др., - так и многих прикладных проблем.\n\nСовременная комбинаторика, таким образом, это своего рода основа основ: это и красивейшая теория с массой нетривиальных задач и методов, но это и прекрасная база для приложений в computer science, в анализе сложных сетей, в теории кодирования и криптографии, в биоинформатике и др. В курсе мы познакомим слушателей с наиболее важными областями и инструментами современной комбинаторики, причем многие темы курса по сути уникальны: здесь не только классические комбинаторные величины и тождества, но также и общая теория обращения Мебиуса, и диаграммы Юнга, и рекурсия, и производящие функции. Это позволит нам в дальнейших курсах выйти на реальные приложения в анализе таких сложных сетей, как Интернет, социальные, биологические сети, сети межбанковских взаимодействий и др.\n\nДля участия в курсе слушателю необходимо иметь базовые представления о теории множеств и началах анализа. Все остальные понятия будут введены в ходе курса.\n\nКурс состоит из 7 недель лекций и 1 недели экзамена. Каждую неделю слушатель выполняет задания, составляющие 10% от всего курса (5% тест и 5% задачи с ответом). Экзамен также состоит из теста и задач с ответом, каждая часть оценивается в 15% от общей суммы. Для успешного прохождения курса необходимо в каждом задании набрать не менее 50% от общего числа баллов.\n\nДанный курс рекомендуется к прохождению перед курсом Теория вероятностей.

Combinatorics; Recurrence Relations; Algebra; Power Series; Algorithms; Analysis; Problem Solving; Computational Mathematics; Applied Mathematics; Computer Graphics (Computer Science)

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The University of Sydney

The focus and themes of the Introduction to Calculus course address the most important foundations for applications of mathematics in science, engineering and commerce. The course emphasises the key ideas and historical motivation for calculus, while at the same time striking a balance between theory and application, leading to a mastery of key threshold concepts in foundational mathematics. \n\nStudents taking Introduction to Calculus will: \n•\tgain familiarity with key ideas of precalculus, including the manipulation of equations and elementary functions (first two weeks), \n•\tdevelop fluency with the preliminary methodology of tangents and limits, and the definition of a derivative (third week),\n•\tdevelop and practice methods of differential calculus with applications (fourth week),\n•\tdevelop and practice methods of the integral calculus (fifth week).

Calculus; Integral; Explicit Substitution; Differential Calculus; Lambda Calculus; Π-Calculus; Derivative; Mathematics; Adaptive Grammar; Integral Calculus

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Arabic; French; Portuguese; Italian; Vietnamese; German; Russian; Spanish

Enumerative combinatorics deals with finite sets and their cardinalities. In other words, a typical problem of enumerative combinatorics is to find the number of ways a certain pattern can be formed. \n\nIn the first part of our course we will be dealing with elementary combinatorial objects and notions: permutations, combinations, compositions, Fibonacci and Catalan numbers etc. In the second part of the course we introduce the notion of generating functions and use it to study recurrence relations and partition numbers. \n\nThe course is mostly self-contained. However, some acquaintance with basic linear algebra and analysis (including Taylor series expansion) may be very helpful.\n\nDo you have technical problems? Write to us: coursera@hse.ru

Combinatorics; Enumerative Combinatorics; Euler'S Totient Function; Recurrence Relations; Polynomial; Permutations; Mathematics; Ordinary Differential Equation; Closed-Form Expression; Representation Theory

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Введение в математические методы физики

Цель курса - дать слушателям начальные представления и навыки обращения с приближенными аналитическими вычислениями. Такие методы широко используются в практической работе физиков, но почти не излагаются в регулярных лекционных курсах, что препятствует включению студентов в исследовательский процесс. Большинство лекций также содержат в себе семинарскую часть с разбором задач. Важная часть курса – полноценные задачи для самостоятельного решения с целью закрепления практических навыков применения излагаемых методов вычислений. Предполагается, что слушатели знакомы с основами стандартных математических курсов: математического анализа, линейной алгебры, обыкновенных дифференциальных уравнений.\n\nПоявились технические трудности? Обращайтесь на адрес: coursera@hse.ru

Eigenvalues And Eigenvectors; Evaluation; Integral; Matrices; Algebra; Online Learning Community; Interactive Learning; Offline Learning

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Introduction to Ordinary Differential Equations

Korea Advanced Institute of Science and Technology(KAIST)

In this introductory course on Ordinary Differential Equations, we first provide basic terminologies on the theory of differential equations and then proceed to methods of solving various types of ordinary differential equations. We handle first order differential equations and then second order linear differential equations. We also discuss some related concrete mathematical modeling problems, which can be handled by the methods introduced in this course.\n\nThe lecture is self contained. However, if necessary, you may consult any introductory level text\non ordinary differential equations. For example, "Elementary Differential Equations and Boundary Value Problems\nby W. E. Boyce and R. C. DiPrima from John Wiley & Sons" is a good source for further study on the subject.\n\nThe course is mainly delivered through video lectures. At the end of each module, there will be a quiz consisting of several problems related to the lecture of the week.

Differential Equations; Ordinary Differential Equation; Problem Solving; Linear Independence; Factorization; Spring; Mathematical Model; System Of Linear Equations; Linear Equation; Linearity

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Arabic; French; Portuguese; Italian; Vietnamese; German; Russian; Spanish

Линейная алгебра и аналитическая геометрия

Peter the Great St. Petersburg Polytechnic University

Курс является связующим звеном между математическими курсами общеобразовательной средней школы и вузовскими математическими курсами, частично входящими в основные образовательные программы высшего образования. Отбор содержания курса и его компоновка носит авторский характер.\nСлушатель, освоивший программу, должен: \nвладеть:\n•\tметодами аналитической геометрии для решения задач, возникающих при формализации простых геометрических моделей;\n•\tметодами линейной алгебры для решения систем линейных уравнений второго и третьего порядка;\n•\tметодом координат для решения задач аналитической геометрии.\nуметь:\n•\tрешать задачи на проценты, арифметические прогрессии, геометрические прогрессии;\n•\tрешать линейные и квадратичные уравнения;\n•\tрешать неравенства методом интервалов;\n•\tвыполнять действия с векторами и их проекциями;\n•\tпроводить тригонометрические преобразования;\n•\tрешать тригонометрические уравнения;\n•\tвычислять определители второго и третьего порядка;\n•\tрешать системы третьего порядка методом Крамера;\n•\tперемножать матрицы;\n•\tпереходить от декартовых координат к полярным;\n•\tрешать задачи о сложных процентах;\n•\tрешать задачи о сложном движении под действием разнонаправленных сил.\nзнать:\n•\tбазовые математические понятия;\n•\tсистемы счисления;\n•\tтипы множеств вещественных чисел;\n•\tосновные функции и их свойства, область определения и область существования функции;\n•\tскалярное произведение и его свойства;\n•\tрешать задачи на нахождение угла между прямыми;\n•\tопределения и свойства эллипса, гиперболы, параболы;\n•\tопределения тригонометрических функций;\n•\tтеорему Пифагора, теорему косинусов, теорему синусов;\n•\tматрицы, определители, миноры, алгебраические дополнения;\n•\tметоды решения задач с параметрами.

Matrices; Algebra

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Introducción al análisis de Costos para la Dirección de Empresas

Universidad Austral

A través de un caso de negocios y de ejercicios prácticos tendrás la oportunidad de sumergirte en el desafiante mundo de los costos dentro de la empresa. \nPara ello podrás complementar la visión estrictamente contable de los costos con una más enfocada a las decisiones recurrentes que se toman en el día a día de las empresas.\n Para ello incorporaremos las distintas visiones del universo de los costos y cuál de ellas es útil para el tipo de decisión que tengas entre manos por un lado y como es la forma en que tenemos que sistematizar la construcción de los números por otro.\nDurante el desarrollo combinarás las resoluciones de problemas prácticos con el desarrollo conceptual que sirva de soporte.\nEste curso ha sido pensado para todos aquellos que quieran empezar a construir conocimientos sobre el tema por lo cual no es necesario contar con ningún requisito previo para su realización.

Analysis; Finance; Financial Analysis; Benefits; Cost Benefit Analysis; Cost Control; Balance Sheet; Dependent And Independent Variables; Denominación De Origen; Cost

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Universidad Nacional Autónoma de México

En este curso estudiarás las funciones algebraicas y trascendentes desde su definición y notación.\nResolverás problemas de la vida cotidiana que se modelan a través de funciones:\nPolinomiales\nRacionales\nCon Radicales\nExponenciales\nLogarítmicas\nTrigonométricas\nPara las cuales utilizarás conceptos y procedimientos de aritmética, álgebra y trigonometría, así como de la geometría euclidiana y de la analítica.\nUtilizarás un Software dinámico (libre) que te apoyará en la exploración de la representación gráfica de la función para comprender las relaciones entre los parámetros de la representación algebraica.\nRealizarás generalizaciones para obtener la regla de correspondencia de la función.\nDeducirás e inferirás gracias a este estudio apoyado siempre en las tres representaciones:\nTablas numéricas\nGráfica\nExpresión algebraica

Algebra; Geogebra; Gustave Le Bon

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National Taiwan University

這是一個機率的入門課程，著重的是教授機率基本概念。課程內容和作業都使用生活化的例子，希望讓同學們快樂學習、快速培養同學們對於機率的洞察力與應用能力。

Mathematics; Exponential Distribution; Bayesian Probability; Poisson Distribution; Random Variable; Thought; Probability; Python Programming; Probability Distribution; Randomness

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Chinese (Traditional)

Moscow Institute of Physics and Technology

Algebra is one of the definitive and oldest branches of mathematics, and design of computer algorithms is one of the youngest. Despite this generation gap, the two disciplines beautifully interweave. Firstly, modern computers would be somewhat useless if they were not able to carry out arithmetic and algebraic computations efficiently, so we need to think on dedicated, sometimes rather sophisticated algorithms for these operations. Secondly, algebraic structures and theorems can help develop algorithms for things having [at first glance] nothing to do with algebra, e.g. graph algorithms. One of the main goals of the offered course is thus providing the learners with the examples of the above mentioned situations. We believe the course to contain much material of interest to both CS and Math oriented students. The course is supported by programming assignments.

Mathematics; Algebra; Abstract Algebra; Linear Algebra; Calculus; Algorithms; Graph Theory; Moscow Method; Boolean Algebra; Quantum Computing

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Tecnológico de Monterrey

Este curso forma parte de una secuencia con la que se propone un acercamiento a la Matemática Preuniversitaria que prepara para la Matemática Universitaria.\nEn él se asocia un significado real con el contenido matemático que se aprende y se integran tecnologías digitales en el proceso de aprendizaje. \nSe propone la reinterpretación de los contenidos matemáticos relativos a Modelos con Radicales y Exponentes en términos de nociones y procesos del Cálculo Diferencial. Esto servirá como puente para el desarrollo de un pensamiento matemático avanzado con el que se trabajará en la Matemática Universitaria. El período de acreditación para la materia Introducción a las Matemáticas ha concluido. La última fecha para recibir certificados de Coursera es 24 de julio 2017. Informaremos oportunamente cuando la opción de acreditación esté disponible de nuevo. \n\nCurso con crédito académico para alumnos admitidos y aspirantes a ingresar a su primer semestre de un programa de profesional en el Tecnológico de Monterrey. Si estás inscrito en este MOOC con el fin de obtener el crédito académico para el curso de Introducción a las matemáticas (Matemáticas Remedial), confirma tu interés en la acreditación a la cuenta: mooc@servicios.itesm.mx. Consulta las preguntas frecuentes para conocer el proceso de acreditación.

Patty; Wimax; Operating Systems; Π-Calculus; Analysis; Alegra; Software; Unos (Operating System); Denominación De Origen

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Universitat Autònoma de Barcelona

Curso diseñado para facilitar la entrada del estudiante en los cursos de cálculo de primer semestre de prácticamente cualquier grado universitario, con especial énfasis en Ciencias e Ingeniería.

Integral; Calculus; Derivative; Problem Solving; Algebra; Thought; Dependent Type; Factorial; Euler'S Totient Function; Sigma-Algebra

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