# Department of Mathematics

The Department of Mathematics offers courses leading to the Master of Science degree in Statistical Analytics, Computing and Modeling (SACM).

Graduate level courses may also serve to provide a supporting field for other majors.

## Department Faculty

**Agarwal, Ravi P** Professor, Department of Mathematics; M.S., Agra University (India); Ph.D., Indian Institute of Technology (India).

**Ahangar, Reza R** Professor, Department of Mathematics; B.S., Tehran University (Iran); M.S., The Catholic University of America; Ph.D., The Catholic University of America.

**Ahmed, Aden O** Associate Professor, Department of Mathematics; B.S., Université Joseph Fourier (France); M.S., Portland State University; Ph.D., Portland State University.

**Allred, Polly** Senior Lecturer, Department of Mathematics; B.S., Utah State University; M.S., Utah State University; Ed.D., Texas A&M University-Kingsville.

**Fowler, Betty Lou** Lecturer II, Department of Mathematics; B.S., North Georgia College; M.A., University of Central Arkansas.

**Hodis, Simona** Associate Professor, Department of Mathematics; B.Sc., Universitatea Al.I.Cuza (Romania); M.Sc., McMaster University (Canada); Ph.D., University of Western Ontario (Canada).

**Kim, Dongwook** Assistant Professor, Department of Mathematics; B.A., Chung Ang University (South Korea); M.A., University of Georgia; Ph.D., New Jersey Institute of Technology.

**Muzheve, Michael T** Associate Professor, Department of Mathematics; Chair; B.S., University of Zimbabwe (Zimbabwe); M.Phil., University of Zimbabwe; M.S., Texas A&M University; Ph.D., Texas A&M University.

**Singh, Sarjinder** Professor, Department of Mathematics; B.S., Punjab Agricultural University (India); M.S., Punjab Agricultural University (India); Ph.D., Punjab Agricultural University (India).

**Torres, Ramiro** Senior Lecturer, Department of Mathematics; B.S., Texas A&M University-Kingsville; M.S., Texas A&M University-Kingsville.

**Zuo, Lihua** Assistant Professor, Department of Mathematics; B.S., Nanjing University of Science and Technology (China); M.S., Fudan University (China); Ph.D., Texas A&M University.

## Emeritus

**Cecil, David** Professor of Mathematics, Department of Mathematics; B.A., Tulsa University; M.S., Oklahoma State University; Ph.D., Oklahoma State University.

## Mathematics (MATH)

**MATH 5305** Graduate Research Project **3 SCH** **(3)**

A Graduate Research Project must be completed and submitted to the Graduate Office for a grade to be assigned, otherwise IP notations are recorded. This course is specifically designed for Plan II and Plan III students. Prerequisite: departmental approval.

**MATH 5306** Thesis **3 SCH** **(3)**

Designed for thesis option students. The course requires completion of thesis research. Prerequisite: departmental approval. May be repeated for maximum of 6 semester hours.

**MATH 5321** Real Analysis **3 SCH** **(3-0)**

Lebesgue integration and Lebesgue measure. LP spaces. Differentiability properties of monotone functions.

**MATH 5322** Complex Analysis **3 SCH** **(3-0)**

The complex field, topology of the complex plane, analytic functions, conformal mappings, power series, integration, residues.

**MATH 5325** Advanced Linear Algebra **3 SCH** **(3-0)**

Vector spaces and linear transformations, orthogonality, eigenvalues, and numerical methods. Prerequisite: consent of the instructor.

**MATH 5340** Matrix Methods Linear Models **3 SCH** **(3-0)**

Common matrix methods in statistical applications, including eigenvalues and eigenvectors; the Moore-Penrose inverse; matrix differentiation; the distribution of quadratics forms. Prerequisite: STAT 4303 and MATH 3340 or equivalents.

**MATH 5341** Abstract Algebraic Theories **3 SCH** **(3-0)**

Groups and their generalizations. Homomorphism and isomorphism theorem. Direct sums and products. Linear spaces and representations. Field extensions and Galois groups. Prerequisite: MATH 4340 or its equivalent.

**MATH 5360** Analytic Decision Theory **3 SCH** **(3-0)**

Introduction to mathematical decision theory and game theoretic analysis. Classification of games, definitions in game theory, sequential-/simultaneous-move games, pure and mixed strategies, equilibrium concepts and matrix games. Prerequisite: MATH 3340 or equivalent.

**MATH 5374** Numerical Analysis **3 SCH** **(3-0)**

Underlying principles of numerical analysis. Topics include: finite differences and interpolation, numerical differentiation and integration, solving algebraic and transcendental equations, computations with matrices, the method of lease squares, and numerical solutions of differential equations. Attention is given to the solutions of problems using computer. Prerequisite: MATH 4341 or equivalent.

**MATH 5390** Advanced Topics in Math **1-3 SCH** **(1-3)**

Different areas of advanced mathematics with emphasis on rigor, critical reasoning and the concept of proof. May be repeated as topic changes.

## Statistics (STAT)

**STAT 5305** Graduate Research Project **3 SCH** **(0-3)**

Designed for project option students. A Graduate Research Project must be completed and submitted to the Graduate Office for a grade to be assigned, otherwise S/U (Satisfactory/Unsatisfactory) notations are recorded. Prerequisite: departmental approval.

**STAT 5306** Thesis **3 SCH** **(0-0-3)**

Designed for thesis option students. The course requires completion of thesis research. Prerequisite: departmental approval. Maximum credit applicable towards the degree is 6 semester hours.

**STAT 5332** Big Data and Computing **3 SCH** **(3-0)**

Introduction to use of SAS (and R)/PC statistical software, including data entry, data summaries, descriptive statistics, and interpretation of SAS (and R) output for some standard statistical procedures. Prerequisites: graduate standing and approval of instructor.

**STAT 5344** Predictive Analytics **3 SCH** **(3-0)**

**STAT 5346** Design of Experiments **3 SCH** **(3-0)**

Hypothesis testing, principles of design of an experiment, t-test, completely randomized design, randomized block design, multiple comparison techniques, factorial designs, random effect models, fixed effect models, BIBD, nested designs, analysis of covariance and split plot design. Prerequisite: STAT 4301 or STAT 4303 or equivalent.

**STAT 5350** Probability for Analytics **3 SCH** **(3-0)**

Mathematical treatment of probability distributions, probability concepts and laws; sample spaces, combinations and permutations, Bayes' theorem, discrete/continuous random variables, expected value, distribution of functions of random variable, two-dimensional variables, central limit theorem; t, F, and chi-square distributions. Prerequisite: STAT 4301 or STAT 4303 or equivalent.

**STAT 5351** Inferential Analytics **3 SCH** **(3-0)**

Theory of estimation and hypothesis testing, maximum likelihood, method of moments, likelihood ratio tests, consistency, bias, efficiency and sufficiency. Prerequisite: STAT 5350 or equivalent.

**STAT 5361** Multivariate Statistics **3 SCH** **(3-0)**

**STAT 5362** Nonparametric Statistics **3 SCH** **(3-0)**

**STAT 5370** Survey Sampling Analytics **3 SCH** **(3-0)**

Survey sampling from initial planning phases through collection and storage of the data; simple random sampling, stratified random sampling, auxiliary information, estimators, chi-square contingency table analysis for two and three way tables, handling of small expected frequencies, matched pairs, measures of association; use of statistical software on big survey data. Prerequisite: STAT 4301 or STAT 4303 or equivalent.

**STAT 5372** Model Assisted Survey Methods **3 SCH** **(3-0)**

Probability proportional to size sampling, auxiliary information, Horvitz and Thompson estimator, calibration of design weights, model assisted calibration techniques, GREG and linear regression estimator, imputation of missing data, bootstrap and jackknifing. Prerequisite: STAT 5370 [requested] or equivalent.

**STAT 5374** Survey Models Social Science **3 SCH** **(3-0)**

Sensitive data and privacy issues in survey sampling. Randomized response models and variations. Estimation of prevalence of two or more sensitive characteristics. Use of Cramer-Rao lower bound of variance. Measures of protection of respondents. Models using complex designs. Prerequisite: PSYC/SOCI 3381.

**STAT 5375** Operations Research **3 SCH** **(3-0)**

Geometric linear programming, the Simplex method, duality theory, sensitivity analysis, project planning and integer programming. Optional topics include, but are not limited to: the transportation problem, the upper bounding technique, the dual Simplex method, parametric linear programming, queuing theory, decision analysis, and simulation. Prerequisite: Any introductory course in linear algebra.

**STAT 5380** Survival Analysis **3 SCH** **(3-0)**

Statistical analysis of time-to-event or survival data. Basic Terminology and both parametric and non-parametric techniques. Continuous and discrete time regression models and partial likelihood estimation. Includes competing risk models, unobserved heterogeneity, and multivariate survival models including event history. Prerequisite: STAT 5350 and STAT 5351 or equivalents.

**STAT 5390** Advanced Topic in Statistics **3 SCH** **(3-0)**

Different areas of advanced statistics will be covered at separate offerings of this course. Topics include sampling techniques, multivariate analysis, quality control techniques. May be repeated once. Prerequisite: 6 semester hours of advanced statistics or the equivalent.

Fee: $15.00

## Statistical Analytics, Computing and Modeling (SACM), M.S.

This program is designed to provide the student with competency in the major areas of statistical and mathematical application, a working knowledge of mathematical and/or statistical software and a sufficient theoretical background to serve as a foundation for continued professional development. A student entering the program is expected to have completed at least 6 semester hours of advanced mathematics beyond multivariate calculus and differential equations. Students lacking these prerequisites may be admitted conditionally.

### Thesis Option

The thesis option requires 30 SCH to complete the M.S. degree of which 24 hours must be from core courses including Thesis. Elective courses comprise 6 hours of the curriculum. Students have the flexibility to select the elective hours from a list of courses to meet degree requirements. *Elective hours may be taken from other disciplines with advisor's approval.*

### Project Option

The project option requires 36 SCH to complete the M.S. degree of which 21 hours must be from core courses including Project. Elective courses comprise 15 hours of the curriculum. Students have the flexibility to select the electives hours from a list of courses to meet degree requirements. *Elective hours may be taken from other disciplines with advisor's approval.*

The curriculum as been **designed to emphasize Statistical Analytics and Applied Mathematics courses.** The curriculum required 15 SCH of Statistical Analytics courses and 6 SCH **of Applied Mathematics** courses. However, the

**curriculum also permits students the flexibility**needed to pursue coursework that emphasizes their career interests.

- For example,
**if SACM students want to emphasize Applied Mathematics as a career option,**and if they completed the 12 hours of Applied Mathematics courses provided as electives, they could use Applied Mathematics as supporting field.

Code | Title | Semester Credit Hours |
---|---|---|

Required Courses | ||

STAT 5350 | Probability for Analytics | 3 |

STAT 5351 | Inferential Analytics | 3 |

STAT 5332 | Big Data and Computing | 3 |

STAT 5344 | Predictive Analytics | 3 |

STAT 5306 | Thesis | 3 - 6 |

or STAT 5306 | Thesis | |

MATH 5340 | Matrix Methods Linear Models | 3 |

MATH 5360 | Analytic Decision Theory | 3 |

Total Semester Credit Hours | 21-24 |

Code | Title | Semester Credit Hours |
---|---|---|

Elective Courses | ||

STAT 5361 | Multivariate Statistics | 3 |

STAT 5362 | Nonparametric Statistics | 3 |

STAT 5346 | Design of Experiments | 3 |

STAT 5370 | Survey Sampling Analytics | 3 |

STAT 5372 | Model Assisted Survey Methods | 3 |

STAT 5374 | Survey Models Social Science | 3 |

MATH 5375 | 3 | |

STAT 5380 | Survival Analysis | 3 |

MATH 5374 | Numerical Analysis | 3 |

MATH 5323 | 3 | |

Total Semester Credit Hours | 30 |