# Mathematics Graduate Certificate

## What You'll Study

We offer two courses each term (including summers) and most are fully online or hybrid, with all learning/exams available online, but in-person meetings a possibility, if desired.

We are also excited to offer a three-course Graduate Certificate in Data Analytics, comprised of the courses in the areas of Data Management, Data Visualization, and Predictive Analytics Modeling.

### Graduate Certificate in Mathematics

The Department of Mathematics and Statistics has designed a six-course Graduate Certificate in Mathematics, comprised of the following courses:

• Discrete Math for Teachers
• Algebra for Teachers
• Analysis for Teachers
• History of Mathematics
• Advanced Linear Algebra
• Advanced Data Analysis
• STAT 6940: Advanced Data Analysis

Credit Hours: 3

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 6995M: Algebra for Teachers

Credit Hours: 3

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) or Introduction into Group Theory (symmetry and groups of motion, permutations, integers mod m).

• MATH 5825: Advanced Linear Algebra

Credit Hours: 3

A study of abstract vector spaces, linear transformations, duality, canonical forms, the spectral theorem, and inner product spaces.

• MATH 6995: History of Mathematics

Credit Hours: 3

This course is aimed at in-service and pre-service high school mathematics teachers and presents the historical context of the mathematics taught in geometry, algebra, and calculus classes. Emphasis will be placed on primary sources and interpretation of mathematical texts.

• MATH 6995F: Analysis for Teachers

Credit Hours: 3

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 6995G: Discrete Mathematics for Teachers

Credit Hours: 3

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.

### Graduate Certificate in Data Analytics

• DATX 5801: Data Management

Credit Hours: 3

This course covers the basic concepts of database systems and emphasizes the real-world database applications relevant to the management of data in an organization environment. The topics include (not limited to) database environment, database development, relational database management systems, SQL/NoSQL data management language, data normalization, data warehousing, and internet database environment. Credit will not be given for both DATX 5801 and CSIS 3722.

• DATX 5803: Data Visualization

Credit Hours: 3

Data visualization refers to the graphical representation of information revealed through data analysis. With the assistance of various visualization elements, we can present data in a clear and effective manner. More importantly, turning data into impactful images, we are able to gain valuable insights and intelligence that help improve our decision-making processes. This course introduces students to various types of visualization techniques like charts, tables, graphs, maps, infographics and dashboards. It emphasizes applying appropriate visualization techniques in uncovering information from data. Moreover, it will help students develop skills of data

storytelling, i.e. effectively communicating actionable insights through the combination of data visualization and narratives

• DATX 5805: Predictive Modeling Algorithms

Credit Hours: 3

Predictive modeling (also referred to predictive analytics and machine learning) applies statistical techniques in analyzing data to predict outcomes. Through a hands-on approach, this course helps students develop basic skills in predictive analytics. Topics may include (not limited to) k-nearest neighbors, naïve-Bayes, linear and logistic regression models, time-series models, classification and regression trees, Principle Component/Factor Analysis, non-linear models, neural networks, random forests, and cluster analysis among others.