Graduate Certificate in Mathematics Info

Stat 6940 - Advanced Data Analysis (CRN: 32987)

An overview of techniques in data analysis. Includes strong emphasis on visual interpretation of data. Topics include one or more samples, proportions, odds, regression, and multiple comparisons.

Math 6995 – ST: Algebra for Teachers (CRN: 32984)

This is an introduction into modern algebra with an emphasis on connections to high-school curriculum, problem-solving, examples, and applications. The topics covered may include:

- Newton's Binomial Formula
- Complex Numbers and Trigonometry (De Moivre's Theorem, complex exponentiation, Euler's Theorem, roots of unity), Quaternions and Octonians
- Integers and Divisibility, Congruences (Fermat's Little Theorem, Wilson's Theorem, Chinese Remainder Theorem, Dates and Days)
- Primality Testing, Introduction into Public-Key Cryptography
- Introduction into Ring Theory (integers mod m and polynomials; irreducible polynomials)
- Geometric Constructions
- Fields (definition and examples)
- Introduction into Group Theory (symmetry and groups of motion, permutations, integers mod m)

No formal prerequisites are required.

Stat 6943 - Mathematical Statistics I (Fall 2015)

Random variables, their distributions and densities. Families and exponential families of distribution. Independence, joint distributions, conditional probability and expectation. Convergence and limit theorems.

Math 6995 – ST: Mathematical Modeling for Teachers (Spring 2016)

This course is aimed at in-service and pre-service high-school mathematics teachers. A goal is to give an idea of how applied mathematicians are trained and what they do. A major part of the activity of “applied mathematics” is concerned with building and analyzing mathematical models of processes in a variety of areas, including the physical, engineering, biological, and social sciences. We will illustrate by examples the iterative approach to developing simple models by successively adding features and complexity, distinguishing deterministic models from probabilistic ones. We will also show how computer environments (spreadsheets, in particular) can be used to explore and analyze mathematical models.

Math 6995 – ST: Analysis for Teachers (Summer 2016)

This course will cover applications of real analysis in the high school mathematics curriculum. This course will cover the basic properties of numbers, the completeness of the real numbers, a rigorous development of Calculus, integration, exponentials and logarithms, trigonometric functions, transcendental numbers, Taylor series, Fourier series, and other topics. Applications to high school mathematics will be considered throughout the course.

Math 6995 – ST: Discrete Mathematics for Teachers (Summer 2016)

Discrete mathematics is rich with problem solving strategies and applications. It covers a wide area of mathematics including a study of patterns and important basic principles of mathematical induction, pigeonhole and inclusion and exclusion. The topics covered in this course will be arithmetic and algebra of integers including modular arithmetic and matrices. In the process, we will learn arithmetic sequences, geometric sequences, Fibonacci sequence, recurrence relations and solving simple recurrence relations, Binomial theorem, LCM and GCD, Euclidean algorithm, Fermat’s little theorem, Chinese Remainder Theorem, system of linear equations, and coding with matrices. If time permits, we will cover some concepts from Graph Theory, Design theory and modeling.