# Department of Mathematics and Computer Science

http://www.twu.edu/math-computer-science/

**Chair:** Don E. Edwards, Professor

**Location:** MCL 302

**Phone:** 940-898-2166

**Fax:** 940-898-2179

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

## Graduate Degrees Offered

- M.S. in Mathematics
- M.S. in Mathematics Teaching
- M.A.T. (emphasis in Mathematics or Computer Science)

The Department of Mathematics and Computer Science 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, or related fields. The Master of Science in Mathematics provides the student an opportunity to include computer science and statistics in the plan of study. An emphasis in statistics is available for those interested in careers as applied statisticians or statistical programmers.

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 8-12 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 computer science teachers at the 7-12 levels in mathematics or the 7-12 level in computer science. Mathematics or computer science courses required for the degree are determined in consultation with a departmental advisor.

## Admission Requirements

In addition to the general requirements for admission to the TWU Graduate School , the Department of Mathematics and Computer Science requires the following:

A bachelor’s degree with a grade of ‘C’ or better in the following courses:

- two semesters of introductory calculus,
- two additional departmentally approved advanced mathematics courses,
- two letters of reference.

- Post-Baccalaureate Certificate in Interprofessional Informatics (offered through the College of Nursing)

## Minors Offered to Students from Other Departments

Graduate students in other departments who desire concentrated study in mathematics or computer science as a related field should contact the Department of Mathematics and Computer Science to discuss an appropriate plan of study.

### Computer Science Courses

**CSCI 5643. Internet/Intranet Services: Design and Implementation. **Design and implementation of Internet/Intranet network information services including FTP, World Wide Web, and conferencing. Preparation and integration of digital graphics, animation, video, audio, and script-based (Java/Java Script) content. Students will design and build an intranet, install and maintain servers, and prepare multimedia rich content. Prerequisites: CSCI 1403 and CSCI 3002, or equivalents. Three lecture hours a week. Credit: Three hours.

**CSCI 5653. Technology Issues, Achievements and Challenges in Education. **Current developments and open research issues for technology in education. Includes current and future trends in multimedia, simulation, communication, networks, AI, intelligent tutoring systems, learning communities, learning technologies, security concerns, communication strategies, ethical, and leadership issues. Prerequisites: Completion of other Master Technology Teacher courses or permission of instructor. Three lecture hours a week. Credit: Three hours.

**CSCI 5663. Statistical Programming. **Design of statistical programs to manipulate raw data, generate reports, and analyze data. Numerous case studies demonstrate appropriate analysis based on the experimental design. Advanced statistical research methods such as ANOVA, MANOVA, repeated measures ANOVA, Multiple Linear and Logistic regression, factor analysis, and survival analysis SAS. Prerequisite: Six hours undergraduate statistics, or three hours graduate level statistics, or equivalent. Three lecture hours a week. Credit: Three hours.

**CSCI 5793. Statistical Computer Packages. **Survey of major statistical computation program systems with special emphasis on SPSSX and BMDP. Basic concepts of control language and data set preparation, program execution, and interpretation of statistical program output. Prerequisite: Intermediate statistics or permission of the instructor. Three lecture hours a week. Credit: Three hours.

**CSCI 5813. Concepts of Data Warehousing and Data Mining. **Review of the basic concepts of file systems, databases, data warehousing, data mining, and related statistics. Summary of database management, modeling, design, and life cycle is provided as related to data warehousing. Methods for extracting information from a large database by use of data mining techniques are studied. Techniques include: machine learning, decision algorithms, statistical modeling, and clustering. Prerequisites: CSCI 3423 and MATH 1713, or equivalent. Three lecture hours a week. Credit: Three hours.

**CSCI 5893. Statistical Packages II. **A further survey of major statistical computation program systems. Concepts of control language and data set preparation, program execution, and interpretation of statistical program output will be studied. Prerequisite: CSCI 5793. Three lecture hours a week. Credit: Three hours.

**CSCI 5913. Independent Study. **Selected topics in advanced computer science. May be repeated for additional credit. Credit: Three hours.

**CSCI 5921. Statistical Analysis With Computers. **Exposure to available University resources in research design and data analysis, including fully computerized statistical analysis techniques. Appropriate for graduate students who are at least in the proposal/prospectus phase. May be repeated for additional credit. Prerequisite: Permission of the instructor. Credit: One hour.

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

**CSCI 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.

### Mathematics Courses

**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 Roelle'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 Caley-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 5563. Logic, Sets, and Real Numbers. **Applications of logic and set theory to the development of the real number system. Equivalence relations will be used to define the natural numbers and create the reals from them. 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 5883. Algebraic Geometry. **The connection between algebra and geometry via problem-solving and visualization techniques: topics including conies, cubics. quartics and higher-degree curves and real-world applications such as modern cryptography. Prerequisite: MATH 5513. 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. Cooperative Education. **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.