Undergraduate MATH Courses

- 1505 - Intermediate Algebra with Applications

This course is for pre-STEM and pre-Business majors. Topics include graphing linear equations in 2 variables; solving quadratic equations, rational equations, and linear inequalities; polynomial arithmetic; factoring, simplifying rational expressions, and simplifying expressions with rational exponents and radicals; relations and functions, including linear, quadratic, radical, absolute value, conics, exponential and logarithmic; applications. Prereq.: 1 year of high school algebra and 1 year of high school geometry or 1 year of integrated geometry/algebra. 5 s.h. (syllabus)

- 1507- Intermediate Algebra

Topics include functions of the following: linear, polynomial, rational, exponential, and logarithmic. Emphasis on function relations and graphing by algebraic techniques and technology. Solving linear, nonlinear equations and inequalities. Prereq.: MATH 1501 or Level 20 on the Math Placement Exam. Does not count towards a degree. 3 s.h. (syllabus)

- 1510 - College Algebra

Math 1510 prepares students for MATH 1552, MATH 1510 + MATH 1511 prepares STEM students for MATH 1570 and MATH 1571. Real and complex numbers; equations and inequalities; linear, quadratic, polynomial, exponential, and logarithmic functions; graphing techniques, systems of equations, binomial theorem, and applications. Fulfills general education requirements for mathematics. Prereq.: MATH 1505 or MATH 1507 or Math Placement Level 35. 4 s.h. (syllabus) (Gateway Exam Practice Problems) (Gateway Exam Practice Problem Answers) (Final Exam Review) (Final Exam Review Answers)

- 1510C Corequisite Support for College Algebra

Math 1510C is intended to provide corequisite support for students requiring remediation in

mathematics while they are concurrently enrolled in MATH 1510 (College Algebra). Emphasis

will be placed on prerequisite skills needed for college algebra as well as just in time review

through the use of appropriate technology. Does not count toward a degree. Prereq.:

Concurrent enrollment in MATH 1510. 1-3 s.h. (syllabus)

- 1511 - Trigonometry

Math 1511 (along with MATH 1510) prepares STEM students for MATH 1570 and MATH 1571. Topics include: Unit circle, angle measurement, similar triangles, trigonometric ratios in the plane, and right triangle trigonometry. Polar coordinates. Cosine and sine laws. Six trigonometric functions and their graphs. Fundamental identities, equation solving and inverse trigonometric functions. Complex numbers. Real life applications. Fulfills general education requirements for mathematics. Prereq.: MATH 1505 or MATH 1507 or Math Placement Level 35. 4 s.h. (syllabus) (Final Exam Review) (Final Exam Review Answers)

- 1511C - Corequisite Support for Trigonometry

Math 1511C is intended to provide corequisite support for students requiring remediation in

mathematics while they are concurrently enrolled in MATH 1511 (Trigonometry). Emphasis will be

placed on prerequisite skills needed for trigonometry as well as just in time review through the use of

appropriate technology. Does not count toward a degree. Prereq.: Concurrent enrollment in MATH

1511. 1-3 s.h. (syllabus)

- 1513 - Algebraic and Transcendental Functions

Math 1513 prepares STEM students for MATH 1570 and MATH 1571. Topics include: Function concepts including trigonometric, exponential, and logarithmic functions. Application problems and graphing. Supplemental topics. Fulfills general education requirements for mathematics. Prereq.: Math Placement Level 45. 5 s.h. (syllabus)

- 1552 - Applied Mathematics for Management

Apply functions, linear systems, linear programming to business including use of technology; mathematics of finance and an introduction to limits, derivatives and integrals with business applications. No credit for students who have completed MATH 1570 or 1571. Fulfills general education requirements for mathematics. Prereq.: MATH 1510 or Math Placement Level 45. 4 s.h. (syllabus) (Final Formula Sheet)

- 1564, 2665 - Foundations of Middle School Mathematics 1, 2

Conceptual foundations of topics from number theory, operations, functions, algebra, geometry, measurement, probability, and data analysis. Emphasis on multiple approaches and representations, problem solving, and communication of mathematical reasoning. Includes inquiry-based laboratory experiences with manipulatives and computing technology. Prereq.: At least Level 40 on the Mathematics Placement Test or concurrent registration in MATH 1504 for MATH 1564, MATH 1564 for MATH 2665. 4+4 s.h. (syllabus 1564, 2665)

- 1570, 2670 - Applied Calculus 1, 2

The elements of differential and integral calculus, with emphasis on applications. Analytical geometry, differentiation and integration techniques and series representations. Introduction to differential equations, transform calculus, and Fourier analysis. This is a basic methods course particularly adapted for those who require applied topics in mathematics. Not applicable toward the Mathematics major. Credit will not be given for both MATH 1549 and 1570. Prereq.: MATH 1513 or at least Level 50 on the Mathematics Placement Test. MATH 1570 for MATH 2670. 4+5 s.h. (syllabus 1570, 2670)

- 1571, 1572, 2673 - Calculus 1, 2, 3

A sequence of integrated courses in analytic geometry and calculus. A detailed study of limits, derivatives, and integrals of functions of one and several variables with applications. Prereq.: MATH 1571 requires at least Level 70 on the Mathematics Placement Test, or MATH 1513. MATH 1571 for MATH 1572, MATH 1572 for MATH 2673. 4+4+4 s.h.

- 1571_1571H Syllabus
- 1572_1572H Syllabus
- 2673_2673H Syllabus (MATH 2673H_Dr. Madsen’s section)
- Math 1571 Exam Review and Solutions

- 1580H - Biomathematics 1

Counting techniques, probability, matrices and linear systems. Emphasis on the role of mathematical models in explaining and predicting phenomena in life sciences. Prereq.: Admission to NEOUCOM-YSU program. 2 s.h. (Syllabus)

- 1581H - Biomathematics 2

A study of functions, differential and integral calculus. Emphasis on the role of mathematical models in explaining and predicting phenomena in life sciences. Credit will not be given for both MATH 1581H and 1571. Prereq.: Admission to NEOUCOM-YSU program 4 s.h. (syllabus)

- 1585H, 2686H - Calculus 1, 2 Honors

A sequence of honors courses in analytical geometry and calculus which cover essentially the same material as MATH 1571, 1572, 2673, in two semesters instead of three. A detailed study of limits, derivatives, and integrals of functions of one and several variables and their applications. Prereq.: Level 90 on the Mathematics Placement Test for MATH 1585H. MATH 1585H for MATH 2686H. This sequence will be offered at most once during each academic year. 5+5 s.h. (1585H syllabus, 2686H syllabus)

- 1586H, 2687H - Honors Calculus Laboratory 1, 2

Introduction to mathematical modeling of topics covered in calculus. Emphasizes the use of technology such as computer algebra systems, technical document processing, and graphics software for solving problems and reporting solutions. Prereq.: MATH 1571 or concurrent with 1585H for MATH 1586H. MATH 1572 or concurrent with MATH 1586H for MATH 2687H. 1+1 s.h. (1586H syllabus) (2687H syllabus)

- 2623 - Quantitative Reasoning

Mathematics models emphasizing basic ideas in mathematics and statistics, stressing concept formation rather than manipulative skills. Prereq.: MATH 1501 or Level 20 on the Mathematics Placement Test. Credit will not be given for both MATH 2623 and 2625. 3 s.h. (syllabus)

- 2623C - Corequisite Support for Quantitative Reasoning

Math 2623C is intended to provide corequisite support for students requiring remediation in

mathematics while they are concurrently enrolled in MATH 2623 (Quantitative Reasoning). Emphasis will be placed on prerequisite skills needed for MATH 2623 as well as just in time review through the use of appropriate technology. Does not count toward a degree. Prereq.: Concurrent enrollment in MATH 2623. 1-3 s.h. (syllabus)

- 2651, 2652 - Mathematics for Early Childhood Teachers 1, 2

A conceptual development of mathematics topics underlying today’s Pre-K-grade 3 curriculum. Emphasis on multiple approaches, problem solving, and communication of mathematics. Incorporates classroom activities, manipulatives, technology, and activities developmentally appropriate for young children. Prereq.: MATH 1501 or at least Level 3 on the Mathematics Placement Test for 2651, MATH 2651 for MATH 2652. 3+3 s.h. (syllabus 2651, 2652)

- 2651C - Corequisite Support for Mathematics for Early Childhood Teachers

This course is intended to provide corequisite support for students requiring remediation in mathematics while they are concurrently enrolled in MATH 2651. Emphasis will be placed on prerequisite skills needed for Algebra, Number and Operations, and Quantity topics as well as just in time review through the use of appropriate technology. Does not count toward a degree.

Prereq.: Concurrent enrollment in MATH 2651. (syllabus)

- 3701 - Biomathematics Seminar

Introduction to interdisciplinary research in biology and mathematics. Topics include current research by faculty and students, cross disciplinary communication, report writing, technical presentations, literature reading, laboratory techniques and safety. May be repeated once. Listed also as BIOL 3701. Prereq.: MATH 1571 or BIOL 2601 or BIOL 2602. 1 s.h. (syllabus)

- 3702 - Problem Solving Seminar for Secondary Mathematics

Approaches to and practice with problem solving with examples from a broad spectrum of mathematics. Emphases include problems at the level of the Praxis II examination for mathematics and problems suitable for high school contests such as the American Mathematics Competition 10 and 12. Prereq.: MATH 1572 or consent of instructor. 3 s.h. (syllabus)

- 3705 - Differential Equations

Methods and theory of solving differential equations with applications. Existence, uniqueness. First order equations. Higher order linear equations. Introduction to partial differential equations and boundary value problems, including Laplace’s equation. Prereq.: MATH 2673. 3 s.h. (syllabus)

- 3705H - Honors Differential Equations

Methods and theory of solving differential equations with applications.Existence, uniqueness. First order equations. Higher order linear equations.Introduction to partial differential equations and boundary value problems,including Laplace's equation.Prereq.: MATH 2673. (syllabus)

- 3715 - Discrete Mathematics

A course in discrete mathematical structures to prepare students for advanced courses. Topics include set theory, functions and relations, logic and quantifiers, truth tables and Boolean expressions, induction and other techniques of proof, and graphs. Credit will not be given for both CSCI 3710 and MATH 3715. Prereq.: MATH 1572. 3 s.h. (syllabus)

- 3720 - Linear Algebra and Matrix Theory

Matrices; matrix operations; linear transformations; applications. Prereq.: MATH 1572. 3 s.h. (syllabus)

- 3721 - Abstract Algebra 1

Introduction to abstract algebra investigating fundamental concepts in group and ring theory. Topics include groups, subgroups, cyclic groups, permutation groups, cosets, direct products, homomorphisms, factor groups, rings, integral domains and polynomial rings. Prereq.: MATH 3715 and 3720. 3 s.h. (syllabus)

- 3750 - History of Mathematics

A survey of the historical development of mathematics. Prereq.: MATH 2673 or 3715. 3 s.h. (syllabus)

- 3751 - Real Analysis 1

Introduction to the properties of the real number system and metrics and metric properties, with critical analysis of limits, continuity, differentiability, integration, and other fundamental concepts underlying the calculus. Prereq.: MATH 2673 and 3715. 3 s.h. (syllabus)

- 3760 - Numerical Analysis 1

The theory and techniques of numerical computation. The solution of a single equation, interpolation methods, numerical differentiation and integration, direct methods for solving linear systems. Prereq.: MATH 3720 and CSIS 2610. 3 s.h. (syllabus)

- 3767, 3768 - Algebra/Geometry for Middle School Teachers

An integrated, conceptual, and function-centered approach to the foundations of algebra, geometry, and trigonometry for preservice middle childhood mathematics specialists. Emphasis on multiple approaches and representations, problem solving, and communication of mathematical reasoning. Includes inquiry-based laboratory experiences. Not applicable to the mathematics major. Prereq.: MATH 2665 for MATH 3767 and MATH 3767 for MATH 3768. 4+4 s.h.. (syllabus 3767, 3768)

- 3785 - Numerical Methods

Matrices, matrix operations, and the application of numerical methods. Not applicable to the Mathematics major. Prereq.: MATH 2670 and ENTC 1505, or equivalent. 3 s.h. (syllabus)

- 3795 - Topics in Mathematics

The study of a mathematical topic or the development of a special area of mathematics. May be repeated once. Prereq.: MATH 1549 or 1570 or 1571 or 2623 or 2651. 2-3 s.h. (3795C Syllabus) (3795H Syllabus)

- 4822 - Abstract Algebra 2

A continuation of MATH 3721 with special emphasis of fields. Additional topics in pure or applied algebra. Prereq.: MATH 3721 or equivalent. 3 s.h. (syllabus)

- 4823 - Abstract Algebra 3

This course introduces advanced topics in field theory. Topics may include principal ideal domains, irreducibility, quotient rings, algebraic extensions, finite fields, splitting fields, and the Galois group. Prereq.: MATH 4822 or equivalent. 3 s.h. (syllabus)

- 4830 - Foundations of Geometry

The development of Euclidean and non-Euclidean geometries from postulate systems. Prereq.: MATH 3715. 3 s.h. (syllabus)

- 4832 - Euclidian Transformations

General properties of functions and transformations; isometries and transformations of the Euclidean plane; the complex plane, its geometry and subfields; transformational, analytical, and vector approaches to Euclidean geometry; connections to other branches of mathematics and applications. Prereq.: MATH 3720 and 4830. 3 s.h. (syllabus)

- 4855 - Ordinary Differential Equations

A second course in differential equations with emphasis on nonlinear problems and qualitative methods or on boundary value problems. Topics are chose from: proofs of fundamental theorems, phase plane analysis, limit cycles and the Poincare-Bendixon theorem, biological models, stability via Liapunov functions, asymptotic methods, and boundary value problems. Prereq.: MATH 3705 and 3720. 3 s.h. (syllabus)

- 4857- Partial Differential Equations

Introduction to partial differential equations (PDE) including solution techniques and applications. Classifications of the basic types of PDE’s (hyperbolic, parabolic and elliptic) and dependence on boundary and initial conditions. Topics include Fourier series, integral transforms (Fourier, Laplace), and applications in vibrations, electricity, heat transfer, fluids or other selected topics. Prereq.: MATH 3705 and MATH 3720. 3 s.h. (syllabus)

- 4869 - Functions, Calculus, and Applications for Middle School Teachers

Polynomial and exponential functions, limits, derivatives, integrals, and applications.

Interpretation of slope and area in graphs of functions from applied settings. Applications of limits to the derivations of geometric formulas. Relations between tables, graphs, and the symbolic representation of functions. Prereq.: MATH 3768 or consent of instructor. 3 s.h. (syllabus)

- 4870 - Mathematics Seminar for Middle School Teachers

Problem solving from a broad spectrum of mathematics topics (Number Sense and Operations; Algebra, Functions, and Calculus; Measurement and Geometry; Statistics, Probability, and Discrete Mathematics) designed to prepare future middle school mathematics teachers to address Common Core Standards. May be repeated 2 times. Prereq.: MATH 3767, MATH 3768, MATH 4869, and either STAT 2601 or MATH 2625. 2 s.h. (syllabus)

- 4875 - Complex Variables

Complex numbers and their geometric representation, analytic functions of a complex variable, contour integration, Taylor and Laurent series, residues and poles, conformal mapping. Prereq.: MATH 3751 or equivalent. 3 s.h. (syllabus)

- 4880 - Introduction to Topology

An introduction to the basic concepts of general topology: compactness,connectedness, and continuity in topological spaces. Prereq.: MATH 3721 and 3751. 3 s.h. (syllabus)

- 4882 - Biomathematics Research

Interdisciplinary and individualized study of a topic in biology and mathematics. Student project mentored jointly by faculty in biology and mathematics. May be repeated once. Grading is Traditional/PR. Listed also as BIOL 4882. Prereq.: MATH/BIOL 3701, senior status and permission of the department chairperson. 1-2 s.h. (syllabus)

- 4893 - Mathematics Internship

A program of work and study in the public or private sector centered upon the development of a significant mathematics project, under the direction of University faculty member(s) and designated member(s) of the participating agency. This course can be substituted for MATH 4896 to fulfill the major requirements with approval from the department chairperson. See department for more details. Prereq.: 24 s.h. of mathematics applicable to the mathematics major including either MATH 3721 or 3751 and consent of the department chairperson. May be repeated twice. 2 s.h.

- 4896 - Senior Undergraduate Research Project

Individualized study of a topic in mathematics culminating in a written report and an oral presentation at a national or regional meeting or a local seminar. May be repeated once. Prereq.: 24 s.h. of mathematics applicable to the mathematics major including either MATH 3721 or 3751 and permission of the department chairperson. 2 s.h.

- 4897H - Thesis

Individualized study of a topic in mathematics culminating in a written report and an oral presentation at a national or regional meeting or a local seminar. Prereq.: 24 s.h. of mathematics applicable to the mathematics major including both MATH 3721 and 3751 and permission of the department chairperson. 2 s.h.

- 5821 - Topics in Abstract Algebra

A course in abstract algebra aimed at developing a broad understanding of the subject. Credit will not be given for both MATH 3721 and 4821. Prereq.: MATH 3715 and 3720. 3 s.h. (syllabus)

- 5825 - Advanced Linear Algebra

A study of abstract vector spaces, linear transformations, duality, canonical forms, the spectral theorem, and inner product spaces. Prereq.: MATH 3721. 3 s.h. (syllabus)

- 5828 - Number Theory

A study of congruences, Diophantine equations, quadratic residues, special number theory functions, and selected applications. Prereq.: MATH 3721. 3 s.h. (syllabus)

- 5835 - Introduction to Combinatorics and Graph Theory

The pigeonhole principle; permutations, combinations, the binomial theorem; the inclusionexclusion principle; recurrence relations; graphs and digraphs, paths and cycles, trees, bipartite graphs and matchings. Prereq.: MATH 3715 and 3720. 3 s.h.(syllabus)

- 5843 - Theory of Probability

The mathematical foundation of probability theory including the study of discrete and continuous distributions. Other topics selected from limit theorems, generating functions, applications. Credit will not be given for MATH 5843 and STAT 5843. Prereq.: STAT 3743 and MATH 2673. 3 s.h. (syllabus)

- 5844 - Theory of Statistics

The mathematical theory of statistical inferences including likelihood principle, sufficient statistics, theory of statistical estimation, hypothesis testing and related topics. Credit will not be given for MATH 5844 and STAT 5844. Prereq.: MATH 5843. 3 s.h. (syllabus)

- 5845 - Operations Research

An introduction to operations research with emphasis on mathematical methods. Topics may include: linear programming, sensitivity analysis, duality theory, transportation problems, assignment problems, transshipment problems, and network problems. Prereq.: MATH 3715 and 3720. 3 s.h (syllabus)

- 5851 - Topics in Analysis

A course in analysis aimed at developing a broad understanding of the subject. Credit will not be given for both MATH 3751 and 5851. Prereq.: MATH 2673, 3720, and 3715. 3 s.h. (syllabus)

- 5852 - Real Analysis 2

Uniform convergence of sequences of functions and some consequences; functions on n-space: derivatives in vector spaces, mean value theorem, Taylor’s formula, inverse mapping theorem, implicit mapping theorem. Prereq.: MATH 3720 and 3751 or equivalent. 3 s.h (syllabus)

- 5860 - Topics in Numerical Analysis

A course in numerical analysis aimed at developing a broad understanding of the subject. Credit will not be given for both MATH 3760 and 4860. Prereq.: MATH 3720 and CSIS 2610. 3 s.h. (syllabus)

- 5861 - Numerical Analysis 2

Numerical methods of initial-value problems, eigenvalue problems, iterative methods for linear and nonlinear systems of equations, and methods involving least squares, orthogonal polynomials, and fast Fourier transforms. Prereq.; MATH 2673 and 3760 or equivalent. 3 s.h. (syllabus)

- 5884- Mathematical Logic

An introduction to the study of theories in formalized languages and to the theory of models. Prereq.: MATH 3721 or PHIL 3719. 3 s.h. (syllabus)

- 5895 - Selected Topics in Mathematics

The study of a standard mathematical topic in depth or the development of a special area of mathematics. May be repeated twice. Prereq.: 24 s.h. of mathematics applicable to the mathematics major including either MATH 3721 or 3751. 2-3 s.h. (5895H syllabus) (5895M syllabus) (5895N Syllabus) (5895O Syllabus) (5895P Syllabus) (5895S Syllabus) (5895T Syllabus) (5895V Syllabus) (5895W Syllabus) (5895X Syllabus)