# Mathematics

Tingxiu Wang (Department Head)

Location: Binnion Hall, 903-886-5157

Mathematics Web Site: http://www.tamuc.edu/academics/colleges/scienceEngineeringAgriculture/departments/mathematics/default.aspx

The graduate program in mathematics provides thorough training to the student in one or more areas of mathematics to stimulate independent thinking, and to provide an apprenticeship for the development of creative research. The program prepares the student for employment in a high school, junior college, or four-year college, for continued study of mathematics at the doctoral level, or in one of the many nonacademic areas in which mathematicians work. For example, our graduates are employed as actuaries, software engineers, college faculty members, school administrators, and by companies such as L3, Texas Instruments, and General Dynamics.

Graduate students in mathematics have access to powerful software packages, and many courses include computer applications.

## Programs of Graduate Work

### Master of Science in Mathematics

Graduate work leading to a Master of Science degree is offered in pure mathematics including analysis, biological mathematics, coding theory, combinatorics, complex analysis, differential equations, differential geometry, image analysis, and processing with learning, mathematics history and statistics (actuarial science). A new Master of Science degree with a mathematics education concentration is now offered. Emphases for secondary and middle school teachers are specially planned to meet their individual and particular objectives.

Students may also select courses leading to a minor in applied mathematics.

### Admission

Admission to a graduate program is granted by the Dean of the Graduate School upon the recommendation of the department. Applicants must meet the following requirements for admission in addition to meeting the general university requirements in Mathematics.

Students entering the MS program for a career in higher education, professional work, or further advanced study in mathematics must meet the background requirements which include the calculus sequence, discrete mathematics, and at least two upper-level undergraduate mathematics courses from the areas of algebra, analysis, topology, statistics, and probability.

Secondary mathematics teachers and other students entering the master’s degree program with goals other than work as a professional mathematician or advanced study in mathematics should have Calculus I, II, and at least two upper-level undergraduate mathematics courses from the areas of algebra, analysis, topology, statistics, and probability.

**Note:** The Department reserves the right to suspend from the program any student who in the judgment of the departmental graduate committee, does not meet the professional expectations of the field.

Successful completion of the Comprehensive Exam is required of all students.

**MATH 500 - Discrete Mathematics**

Hours: 3

Study of formal logic; sets; functions and relations; principle of mathematical induction; recurrence relations; and introductions to elementary number theory and graph theory; counting (basic combinatorics); asymptotic complexity of algorithms; and NPcompleteness. This course is useful to those taking graduate classes in computer science. It also helpful to secondary teachers by giving them a better understanding of the terms and ideas used in modern mathematics. This is an elective course, eligible for the non-thesis option of the MS degree in math only. The maximum credit hours can be earned towards the MS degree in math among MATH 500, 550, 560 is six. Prerequisites: A grade of C or better on MATH 2414.

**MATH 501 - Mathematical Statistics I**

Hours: 3

A graduate level course in Probability Theory intended to provide the theoretical background for a course in statistical inference. Topics covered include: probability, random variables, distributions, moments, convergence of random variables, probability inequalities, random samples. Prerequisites: MATH 2415, or Math 314, with a minimum grade of C.

**MATH 502 - Mathematical Statistics II**

Hours: 3

A graduate level course in statistical inference. Topics covered include: point estimation, interval estimation, hypothesis testing, Bayesian inference. Prerequisites: MATH 501.

**MATH 503 - Actuarial Mathematics**

Hours: 3

A course in business/financial mathematics designed as an introduction to actuarial science and as preparation for the Exam P/1 and Exam FM actuarial exams. Encounters appropriate topics from analysis, linear algebra, probability and statistics, and financial mathematics. Prerequisites: MATH 401 or MATH 402/403 or equivalent.

**MATH 511 - Real Analysis I**

Hours: 3

Properties of real numbers, continuity, differentiation, integration, sequences and series of functions, differentiation and integration of functions of several variables. Prerequisites: MATH 2415, or Math 314, or Consent of Instructor.

**MATH 512 - Real Analysis II**

Hours: 3

Properties of real numbers, continuity, differentiation, integration, sequences and series of functions, differentiation and integration of functions of several variables. Prerequisites: MATH 511.

**MATH 515 - Dynamical Systems**

Hours: 3

Topics can be chosen from discrete or/and continuous dynamical systems such as linear systems and linear algebra, local theory for nonlinear systems, local existence-uniqueness theorem, the Hartman-Grobman theorem, Liapunov functions, the stable manifold theorem, limit sets of trajectories, the Poincare-Bendixson theorem, bifurcation theory, center manifold and normal form, chaotic dynamics, iteration of functions, graphical analysis, the linear, quadratic and logistic families, fixed points, symbolic dynamics, topological conjugacy, complex iteration, Julia and Mandelbrot sets. Prerequisites: MATH 2414 and MATH 2318.

**MATH 517 - Calculus of Finite Differences**

Hours: 3

Finite differences, integration, summation of series, Bernoulli and Euler Polynomials, interpolation, numerical integration, Beta and Gamma functions, difference equations. Prerequisites: MATH 2415 or Math 314 with a minimum grade of C.

**MATH 518 - Thesis**

Hours: 3-6

This course is required of all graduate students who have an Option I degree plan. Graded on a (S) satisfactory or (U) unsatisfactory basis. Prerequisite: Consent of the instructor.

**MATH 522 - General Topology I**

Hours: 3

General Topology I - Three semester hours Ordinals and cardinals, topological spaces, identification topology, convexity, separation axioms, covering axioms. Pre-requisites : MATH 440 or consent of instructor.

**MATH 523 - General Topology II**

Hours: 3

The course is a continuation of MATH 522. Compact spaces, metric spaces, product spaces, convergence, function spaces, path connectedness, homotopy, fundamental group. Prerequisites: MATH 522.

**MATH 529 - WORKSHOP**

Hours: 3

Workshop in School Mathematics. Three semester hours. This course may be taken twice for credit. A variety of topics, taken from various areas of mathematics, of particular interest to elementary and secondary school teachers will be covered. Consult with instructor for topics.

**MATH 531 - Theory of Matrices**

Hours: 3

Vector spaces, linear equations, matrices, linear transformations, equivalence relations, metric concepts. Prerequisites: MATH 333 or 334 with a minimum grade of C.

**MATH 532 - Fourier Analysis and Wavelets**

Hours: 3

Inner Product Spaces; Fourier Series; Fourier Transform; Discrete Fourier Analysis; Haar Wavelet Analysis; Multiresolution Analysis; The Daubechies Wavelets; Applications to Signal Processing; Advanced Topics. Prerequisites: MATH 333 or the Consent of the instructor.

**MATH 533 - Linear and Nonlinear Optimization**

Hours: 3

Graphical optimization, linear programming, simplex method, interior point methods, nonlinear programming, optimality conditions, constrained and unconstrained problems, combinatorial and numerical optimization, applications. Prerequisites: MATH 333 with a minimum grade of C.

**MATH 536 - CRYPTOGRAPHY**

Hours: 3

The course begins with some classical cryptanalysis (Vigenere ciphers, etc). The remainder of the course deals primarily with number-theoretic and/or algebraic public and private key cryptosystems and authentication, including RSA, DES, AES and other block ciphers. Some cryptographic protocols are described as well. Prerequisites: MATH 437, or MATH 537, or consent of the instructor.

**MATH 537 - Theory of Numbers**

Hours: 3

Factorization and divisibility, diophantive equations, congruences, quadratic reciprocity, arithmetic functions, asymptotic density, Riemann's zeta function, prime number theory, Fermat's Last Theorem. Prerequisites: MATH 437 or Consent of instructor.

**MATH 538 - Functions of Complex Variables I**

Hours: 3

Geometry of complex numbers, mapping, analytic functions, Cauchy-Riemann conditions, complex integration. Taylor and Laurent series, residues. Prerequisites: MATH 436, or MATH 438, Consent of Instructor.

**MATH 539 - Functions of Complex Variables II**

Hours: 3

Geometry of complex numbers, mapping, analytic functions, Cauchy-Riemann conditions, complex integration. Taylor and Laurent series, residues. Prerequisites: MATH 538.

**MATH 543 - Abstract Algebra I**

Hours: 3

Groups, isomorphism theorems, permutation groups, Sylow Theorems, rings, ideals, fields, Galois Theory. Prerequisites: MATH 334 or MATH 550, or Consent of Instructor.

**MATH 544 - Abstract Algebra II**

Hours: 3

Groups, isomorphism theorems, permutation groups, Sylow Theorems, rings, ideals, fields, Galois Theory. Prerequisites: MATH 543.

**MATH 546 - Numerical Methods and Learning**

Hours: 3

The course will include numerical methods for derivatives and integrals approximation, teach Euler's and Runge-Kutta methods for solving ordinary differential equations, and study methods for approximate solution of partial differential equations (PDE), including parabolic PDE. Students will learn also how to program the basic methods in MatLab, improving their skills in working with this software. Prerequisites: Consent of the instructor or MATH 2415 or MATH 314 with min grade of C.

**MATH 550 - Foundations of Abstract Algebra**

Hours: 3

This course will cover the fundamental properties of algebraic structures such as properties of the real numbers, mapping, groups, rings, and fields. The emphasis will be on how these concepts can be related to the teaching of high school algebra. Note: This course will be helpful to secondary teachers by giving them a better understanding of the terms and ideas used in modern mathematics. This is an elective course, eligible for the non-thesis option only. The maximum credit hours can be earned towards the MS degree in math among MATH 500, 550, 560 is six. Prerequisites: MATH 332 or or MATH 500 with a minimum grade of C. Crosslisted with: MATH 334.

**MATH 560 - Euclidean and NonEuclidean Geometry**

Hours: 3

The National Council of Teachers of Mathematics (NCTM) in its Principles and Standards states the geometric skills that students should be able to use when they finish high school.This course trains students, particularly, middle and high-school teachers for understanding and mastering these geometric skills. This is an elective course, eligible for the non-thesis option of the MS degree in math only. The maximum credit hours can be earned towards the MS degree in math among MATH 500, 550, 560 is six. Prerequisites: MATH 332 or MATH 500.

**MATH 561 - Regression Analysis**

Hours: 3

A computer oriented statistical methods course which involves concepts and techniques appropriate to design experimental research and the application of the following methods and techniques: methods of estimating parameters and testing hypotheses about them; analysis of variance, multiple regression methods, orthogonal comparisons, experimental designs with applications. Prerequisites: MATH 401 or 502, or 402 and 403.

**MATH 563 - Image Processing with Elements of Learning**

Hours: 3

Introduction to image processing, with applications to images from medicine, agriculture, satelite imagery, physics, etc. Students will learn techniques such as edge detection, 2D image enhancement using laplacian and gradient operators, fourier transforms and the FFT, filtering, and wavelets, as time allows. Students will acquire practical skills in image manipulation by implementing the above mentioned algorithms. Prerequisites: MATH 2414 with a grade of C or better.

**MATH 569 - Image Analysis and Recognition with Learning**

Hours: 3

Description: This class will start with an introduction to color image processing using vector functions. The basics of Wavelets theory will be developed in order to expand a function for the purpose of multiresolution imaging. The following step is the objects representation and description. Then, basic Mathematical Morphology operations will be formulated. Two different set of methods will be taught from the field of Objects/Pattern Recognition: Decision theoretic methods- build up a decision function on the base of a metric; structural methods- based on correlation; and templates with radial and circular lines. The course will end with teaching methods for image segmentation to objects and background. The students program image analysis methods or their components in Java/C++/Matlab. Prerequisites: Instructor approval. Crosslisted with: CSCI 569.

**MATH 572 - Modern Applications of Mathematics**

Hours: 3

This course, specifically designed for teachers, covers a range of applications of mathematics. Topics may include classical encryption, data compression ideas, coding theory, private and public key cryptography, data compression including wavelets, difference equations, GPS systems, computer tomography, polynomial interpolation/Belier curves, construction and use of mathematical models, probability theory, Markov chains, network analysis, linear programming, differentiation and integration, linear algebra, complex variables, Fourier-series, Fourier and Laplace transforms and their applications, differential equations, integral equations, calculus of variations, and topics from student presentations. Prerequisites: MATH 2414 or MATH 192 with a minimum grade of C.

**MATH 580 - Topics in the History of Mathematics**

Hours: 3

A chronological presentation of historical mathematics. The course presents historically important problems and procedures. Prerequisites: MATH 332 or MATH 500.

**MATH 589 - Independent Study**

Hours: 1-4

Individualized instruction/research at an advanced level in a specialized content area under the direction of a faculty member. Note: May be repeated when the topic varies. Prerequisites: Consent of department head.

**MATH 595 - Research Literature & Techniques**

Hours: 3

This course provides a review of the research literature pertinent to the field of mathematics. The student is required to demonstrate competence in research techniques through literature investigation and formal reporting of a problem. Graded on a (S) satisfactory or (U) unsatisfactory basis. Prerequisites: Consent of instructor.

**MATH 597 - Special Topics**

Hours: 3

Organized class. May be repeated when topics vary. Prerequisites: Consent of instructor.

**MTE 504 - Foundations of Complex Analysis**

Hours: 3

This course covers the fundamentals of classical complex analysis: the complex numbers; holomorphic functions; conformal mapings the representation of holomorphic functions by Cauchy's integral formula and its generalization; the representation of holomorphic functions by power series and Laurent Series, and their applications such as singularities of holomorphic functions, Meromorphic functions, computation of indefinite integrals by residues, the Laplace transform, the inverse Laplace transform, Fourier transform, and inverse Fourier transform; and finally the topic of harmonic functions will be explored. Note: This course will be helpful to secondary teachers by giving them a better understanding of the terms and ideas used in modern mathematics. This is an elective course, eligible fo Prerequisites: Admission to MS Math or MATH 2415 Calculus III with grade of "C" or higher. Crosslisted with: MATH 438.

**MTE 505 - Foundations of Analysis**

Hours: 3

The theory of the real number system, the convergence of sequences and series, the limit, continuity, differentiation, and integration of functions with emphasis on the mathematical ideas, analytic skills and learning the proofs. Some topics like continuity in a metric space or a topological space may be included. This is helpful to secondary teachers by giving them a better understanding of the terms and ideas used in modern mathematics. This is an elective course, eligible for the non-thesis option of the MS degree in math only. The maximum credit hours can be earned towards the MS degree in math among MATH 500, 550, 560 is six. Prerequisites: Admission to MS Math, MATH 332, Methods of Mathematical Proof, with grade of "C" or higher. Crosslisted with: MATH 436.

**MTE 540 - Foundations of Topology**

Hours: 3

Logic and Proofs, Sets, Functions, indexing sets and Cartesian products, equivalence and order relations, countable and uncountable sets, ordinal and cardinal numbers, sequences, convergence and uniform convergence, topology of the real line, metric spaces, separation axioms. Prerequisites: Admission to MS Math or MATH 332 Methods of Mathematics Proofs with grade of "C" or higher. Crosslisted with: MATH 440.

**MTE 551 - Fundamental Math for Tch**

Hours: 3

Fundamental Mathematics for Teachers - Three semester hours This course is specifically designed for teachers K-8. The National Council of Teachers of Mathematics (NCTM) explains in its Principles and Standards (2000) that all mathematical learning is grounded in number and operations: Students should be able to “understand numbers, ways of representing numbers, relationships among numbers and number systems; and understand meanings of operations and how they relate to each other.” This course is designed to prepare the teachers to create learning environments conducive to meeting the national and state standards regarding number and operation.

**MTE 552 - Math Modeling Tch**

Hours: 3

Mathematical Modeling for Teachers - Three semester hours This course is specifically designed for teachers K-8. The National Council of Teachers of Mathematics (NCTM) explains in its Principles and Standards (2000) that all mathematical learning should be grounded in problem solving and mathematical reasoning. This course is designed to prepare the teachers to create learning environments conducive to meeting the national and state standards regarding problem solving, mathematical modeling, and the judicious use of technology.

**MTE 553 - Geometric Structures for Tch**

Hours: 3

Geometric Structures for Teachers - Three semester hours This course is specifically designed for teachers K-8. The National Council of Teachers of Mathematics (NCTM) explains in its Principles and Standards (2000) that “geometry and spatial sense are fundamental components of mathematics learning.” This course is designed to prepare the teachers to create learning environments conducive to meeting the national and state standards regarding geometry. Topics include characteristics of 2 and 3 dimensional shapes, mathematical proofs, spatial relationships, transformations and symmetry.

**MTE 554 - Algebraic Structures for Tch**

Hours: 3

Algebraic Structures for Teachers - Three semester hours This course is specifically designed for teachers K-8. The National Council of Teachers of Mathematics (NCTM) explains in its Principles and Standards (2000) that algebraic reasoning is a important part of mathematical study. This course is designed to prepare the teachers to create learning environments conducive to meeting the national and state standards regarding algebraic reasoning. Topics include understanding patterns, relations, functions; representing and analyzing mathematical situations and structures using algebraic symbols; using mathematical models to represent and understand quantitative relationships; and analyzing change in various contexts.

**MTE 555 - Research Techniques for STEM and Education**

Hours: 3

This course, Research Techniques for STEM and Education, will focus on Math and Education research topics that are necessary for the person who is pursuing a graduate degree and/or who wishes to work in higher education. Students will explore concepts that are integral to the research process at this level in higher education. Particular areas of study include: Institutional Review Boards (IRBs); topics of Research Conduct (Responsibility and Ethics that are related to research); grant writing for STEM areas; preparation for a MATH 595, thesis, or even a dissertation; writing research articles; and other research areas. This course is a Special Topics course and will offer students a unique opportunity to experience some areas of research, such as IRB proceedings. Prerequisites: Graduate student status.

**MTE 556 - Stat Reasoning for Tch**

Hours: 3

Statistical Reasoning for Teachers - Three semester hours This course is specifically designed for teachers K-8. The National Council of Teachers of Mathematics (NCTM) explains in its Principles and Standards (2000) that statistical reasoning is essential to being an informed citizen, employee, and consumer; thus it is essential for all students. This course is designed to prepare the teachers to create learning environments conducive to meeting the national and state standards regarding statistical reasoning. Topics include formulating questions that can be addressed with data; collecting, organizing, and displaying relevant data to answer questions; selecting and using appropriate statistical methods to analyze data; developing and evaluating inferences and predictions based on data; understanding and applying basic concepts of probability.

**MTE 557 - Prob Based Lrng Math Sci**

Hours: 3

Problem Based Learning in Mathematics and Science - Three semester hours This course is specifically designed for teachers K-12. The National Council of Teachers of Mathematics (NCTM) explains in its Principles and Standards (2000) that all mathematical learning should be grounded in problem solving and mathematical reasoning. This course focuses on project-based and problem-based learning (PBL); conducting PBL and its applications in the classroom.

**MTE 589 - Independent Study**

Hours: 1-6

Independent Study - Hours: One to Six Individualized instruction/research at an advanced level in a specialized content area under the direction of a faculty member. Prerequisites Consent of department head. Note May be repeated when the topic varies.

**MTE 597 - Special Topics**

Hours: 1-4

Hours: One to four - Organized class Note May be graded on a satisfactory (S) or unsatisfactory (U) basis. May be repeated when topics vary

## Mathematics

**Thomas Boucher**

Associate Professor

B.S., University of Massachusetts, M.S., University of Massachusetts, and Ph.D. Texas A&M University

**Robert Cavender Campbell**

Assistant Professor

B.S., Abilene Christian University; M.S., Ph.D., University of Texas at Arlington

**Rebecca Dibbs**

Associate Professor

B.A., M.A., Eastern Michigan University; M.S. Western Michigan University, M.S., Ph.D., University of Northern Colorado

**Minchul Kang**

Assistant Professor

B.S., Korea University; M.S., Ph.D., The University of Minnesota;

**Ye-Lin Ou**

Professor

B.S., Guangxi Inst.; M.S., Ph.D., The University of Oklahoma.

**Padmapani Seneviratne**

Associate Professor

B.S., University of Peradeniya, Sri Lanka; M.S., Ph.D., Clemson University

**Nikolay Sirakov**

Professor

M.S., Sofia University; Ph.D., Bulgarian Academy of Sciences.

**Tingxiu Wang**

Professor and Department Head

B.S., Shandong University; M.S., Ph.D., Southern Illinois University

**Pamela Webster**

Associate Professional Track

B.S., M.S., Ed.D., Texas A&M University-Commerce.