# Division of Mathematics

Website: https://twu.edu/mathematics/

**Division Lead:** Brandi Falley, Ph.D.

**Location:** MCL 302

**Phone:** 940-898-2166

**Fax:** 940-898-2179

**E-Mail:** mathcs@twu.edu

## Graduate Degrees Offered

The Division of Mathematics offers graduate studies leading to the following degrees: Master of Science in Mathematics and Master of Science in Mathematics Teaching.

The Master of Science prepares the student to enter the workforce or to pursue doctoral degree programs in, mathematics, statistics, applied mathematics, or related fields.

The Master of Science in Mathematics also provides the student an opportunity to include computer science and statistics in the plan of study. Students can choose an emphasis within the MS in Mathematics degree, should they so desire.

The Master of Science in Mathematics Teaching is especially designed for elementary or secondary school teachers of mathematics. Course work emphasizes topics needed for the elementary or secondary mathematics teacher. The department also provides a plan of study designed to prepare current teachers for Master Mathematics Certification at the 4-8 or 7-12 level.

The Master of Arts in Teaching (M.A.T.) degree offered through the College of Professional Education prepares graduate students to be future mathematics teachers at the 4-8 or the 7-12 levels in mathematics. Mathematics courses required for the degree are determined in consultation with a departmental advisor.

All students must meet the University requirements as outlined in the Admission to the TWU Graduate School section of the catalog.

This academic program may have additional admission criteria that must also be completed as outlined on the program's website.

## Minors

Graduate students in other departments who desire concentrated study in mathematics as a related field should contact the Division of Mathematics to discuss an appropriate plan of study.

## Faculty

**MATH 5033. Advanced Calculus. **Development of the limit processes including continuity, sequences, series, differentiation, and integration. Emphasis on proofs of the fundamental theorems of mathematical analysis, including Rolle's and Lagrange's theorems. Multivariable analysis, constrained optimization. Prerequisite: Permission of advisor. Three lecture hours a week. Credit: Three hours.

**MATH 5203. Problem Solving in the Math Classroom. **Study of problems with multiple solutions or alternative approaches in grades 4-12; strategies for solving problems; assessment techniques; cooperative grouping methods; critical thinking skills. Three lecture hours a week. Credit: Three hours.

**MATH 5303. Algebra in the Mathematics Classroom. **Topics in algebra with an emphasis in problem solving, patterns, relationships, order pairs, prime and composite numbers, orders of operations, exponents number sentences, ratios, proportions, percents, modeling, formulas, equations, graphs, functions, and systems of equations. Three lecture hours a week. Credit: Three hours.

**MATH 5313. Geometry in the Mathematics Classroom. **Topics in geometry with an emphasis in problem solving, shapes, angles, polygons, circles, Pythagorean Theorem, symmetry, transformations, measurement of area, and volume with an emphasis on technology. Three lecture hours a week. Credit: Three hours.

**MATH 5323. Euclidean Geometry. **Euclidean geometry from a problem solving approach. Topics include shapes, measurement, perimeter, area, volume, geometric proofs, congruence, triangles, quadrilaterals, similarity, circles, and coordinate geometry. Three lecture hours a week. Credit: Three hours.

**MATH 5333. Technology in the Math Classroom. **Technologies and their use in teaching mathematical concepts in grades 4-12; includes graphing calculators, and computer software programs and pedagogical technology. Prerequisite: Permission of academic advisor. Three lecture hours a week. Credit: Three hours.

**MATH 5423. History of Mathematics. **A survey of the historical development of various mathematical topics, including geometry, algebra, and number theory. A study of the work of past mathematicians, including Archimedes, Euclid, Fermat, Newton, and mathematicians of the 19th and 20th centuries. Three lecture hours a week. Credit: Three hours.

**MATH 5483. Theory of Probability and Statistics I. **Basic principles of probability; combinations and permutations; conditional probability and independence; common discrete and continuous probability distributions, their properties, and applications. Three lecture hours a week. Credit: Three hours.

**MATH 5493. Theory of Probability and Statistics II. **Sampling distribution theory and the Central Limit Theorem; point and interval estimation; hypothesis testing. Prerequisite: MATH 5483 or equivalent. Three lecture hours a week. Credit: Three hours.

**MATH 5513. Matrix Algebra. **Development of theory of solutions of simultaneous linear equations. Matrices, determinants, matrix inversion, eigenvalue problems, real quadratic forms, and Cayley-Hamilton Theorem. Matrix Calculus. Applications. Three lecture hours a week. Credit: Three hours.

**MATH 5523. Introduction to Number Theory. **Understanding and creating proofs related to divisibility, congruences, Diophantine equations, and applications. Three lecture hours a week. Credit: Three hours.

**MATH 5543. Symbolic Logic. **Development of Symbolic Logic as a mathematical system. Starting with axioms and definitions, theorems will be proved. Application of Symbolic Logic to set theory is considered. Three lecture hours a week. Credit: Three hours.

**MATH 5573. Statistical Methods I. **Probability distributions, graphical representations, curve fitting, hypothesis testing, regression and correlation, and applications. Prerequisite: Permission of the instructor. Three lecture hours a week. Credit: Three hours.

**MATH 5583. Statistical Methods II. **Statistical research tools including analysis of variance, chi-square tests, regression (simple and multiple), logistic regression, correlation, non parametric method, and survival analysis. Use of SPSS for the PC. Prerequisite: MATH 5573 or consent of instructor. Three lecture hours a week. Credit: Three hours.

**MATH 5593. Differential Equations. **The existence and uniqueness for differential equations and systems of differential equations. General theory to specific types of differential equations of a single variable. Basic theory for linear and nonlinear systems; linearization; stability; Hamiltonian Systems; applications with MAPLE. Three lecture hours a week. Credit: Three hours.

**MATH 5833. Computer-Aided Mathematical Modeling. **Using mathematics to model economic, biological, physical, and other real life processes. Study of deterministic and stochastic models, discrete, and continuous models. Implementation of models in software packages and programming languages used in computer-aided mathematical modeling. Three lecture hours a week. Credit: Three hours.

**MATH 5863. Applied Statistics and Convex Optimization. **Organizing, analyzing, and summarizing data through statistical methods. Combination of computational and statistical methods and convex optimization techniques to find solutions to big data found in diverse fields such as business, engineering, biological, and health sciences. Regularized and large-scale modeling techniques such as boosting and the lasso as well as model averaging techniques. Consideration of both Frequentist and Bayesian perspectives. Prerequisites: Calculus, probability, and statistical concepts; or permission of instructor. Three lecture hours a week. Credit: Three hours.

**MATH 5873. Real Analysis and Topology. **Metric Spaces and Measure and Integration Theories such as integration theory on general measure spaces including the Lebesgue integral and Lebesgue-Stieltjes integral on the line, Lusin's Theorem, Egoroff's Theorem, Fatou's Lemma, and the Monotone and Dominated Convergence Theorems. Three lecture hours a week. Credit: Three hours.

**MATH 5903. Special Topics. **Variable content. May be repeated for additional credit. Three lecture hours a week. Credit: Three hours.

**MATH 5911. Independent Study. **Selected topics in advanced mathematics. May be repeated for additional credit. Credit: One hour.

**MATH 5913. Independent Study. **Selected topics in advanced mathematics. May be repeated for additional credit. Credit: Three hours.

**MATH 5953. Internship. **Cooperative work-study arrangement between business, industry, or selected institutions with the University. Nine practicum hours a week. Credit: Three hours.

**MATH 5973. Professional Paper. **Credit: Three hours.

**MATH 5981. The Professional Portfolio. **Development of a professional portfolio by students in the Master of Arts in Teaching program demonstrating the student's growth in the Learner-Centered Competencies. Pass-fail grade only. May be repeated. Credit: One hour.

**MATH 5983. Thesis. **Credit: Three hours.

**MATH 5993. Thesis. **Prerequisite: MATH 5983. Credit: Three hours.