M.S. Mathematics

https://www.tamuct.edu/degrees/graduate/math.html

OVERVIEW

The M.S. in Mathematics is designed to enhance and enrich training in the field of mathematics for individuals who teach at the secondary level or in community colleges, and to provide a rigorous depth and breadth of mathematical study for people who plan to work as applied mathematicians in industry or government agencies, as well as those who wish to continue their studies at the doctoral level.

Program Level Student Learning Outcomes

The student will be able to:

  1. Recognize and create good mathematical arguments, and effectively communicate them in written and oral form.

  2. Apply mathematical methods to analyze and solve problems.

  3. Demonstrate a rich understanding of complex mathematical structures, processes, and underlying theories.

  4. Conduct secondary research to demonstrate an understanding of the principles and methods of mathematical research.

Entry Requirements

Students will be admitted into the MS Mathematics major by the faculty once the following application criteria are met:

Successful admission to graduate school.

And the following:

1. All students must have either a Bachelor Science (BS) or Bachelor Art (BA) degree in Mathematics or a BS/BA degree with sufficient mathematics related coursework including but not limited to Calculus I-III (or equivalent). 

2. Students without a BS/BA degree in Mathematics will be required to complete leveling courses prior to admittance into the program. The amount and nature of the leveling courses are defined on a case-by-case basis and determined by the Mathematics Graduate Coordinator.

Master of Science Mathematics - With Thesis Program Requirements

All courses applicable to the program must be attained, at least 36 hours are required for the degree.

MATH 5305Probability & Statistics3
MATH 5308Abstract Algebra3
MATH 5320Real Analysis3
or MATH 5360 Numerical Analysis
or MATH 5315 Operations Research II
MATH 5350Applied Linear Algebra3
Approved graduate-level mathematics electives6
MATH 5198Thesis6
Approved Mathematics or other supporting field courses12
Total Credit Hours36

Master of Science Mathematics - Without Thesis Program Requirements

All courses applicable to the program must be attained, at least 36 hours are required for the degree.

MATH 5305Probability & Statistics3
MATH 5308Abstract Algebra3
MATH 5320Real Analysis3
or MATH 5360 Numerical Analysis
or MATH 5315 Operations Research II
MATH 5350Applied Linear Algebra3
Approved graduate-level mathematics electives12
Approved Mathematics or other supporting field courses12
MATH 5090Comprehensive Examination0
Total Credit Hours36

Courses

MATH 1314. College Algebra. 3 Credit Hours.

(020) In-depth study and applications of polynomial, rational, radical, exponential and logarithmic functions, and systems of equations using matrices. Additional topics such as sequences, series, probability, and conics may be included.

MATH 1316. Plane Trigonometry. 3 Credit Hours.

(020) In-depth study and applications of trigonometry including definitions, identities, inverse functions, solutions of equations, graphing, and solving triangles. Additional topics such as vectors, polar coordinates and parametric equations may be included.

MATH 1324. Mathematics for Business & Social Sciences. 3 Credit Hours.

(020) The application of common algebraic functions, including polynomial, exponential, logarithmic, and rational, to problems in business, economics, and the social sciences are addressed. The applications include mathematics of finance, including simple and compound interest and annuities; systems of linear equations; matrices; linear programming; and probability, including expected value.

MATH 1325. Calculus for Business & Social Sciences. 3 Credit Hours.

(020) This course is the basic study of limits and continuity, differentiation, optimization and graphing, and integration of elementary functions, with emphasis on applications in business, economics, and social sciences.

MATH 1332. Contemporary Mathematics. 3 Credit Hours.

(020) Intended for Non STEM (Science, Technology, Engineering, and Mathematics) majors. Topics include introductory treatments of sets and logic, financial mathematics, probability and statistics with appropriate applications. Number sense, proportional reasoning, estimation, technology, and communication should be embedded throughout the course. Additional topics may be covered.

MATH 1342. Elementary Statistical Methods. 3 Credit Hours.

(020) Collection, analysis, presentation and interpretation of data, and probability. Analysis includes descriptive statistics, correlation and regression, confidence intervals and hypothesis testing. Use of appropriate technology is recommended.

MATH 1350. Mathematics for Teachers I. 3 Credit Hours.

(020) This course is intended to build or reinforce a foundation in fundamental mathematics concepts and skills. It includes the conceptual development of the following: sets, functions, numeration systems, number theory, and properties of the various number systems with an emphasis on problem solving and critical thinking.

MATH 1351. Mathematics for Teachers II. 3 Credit Hours.

(020) This course is intended to build or reinforce a foundation in fundamental mathematics concepts and skills. It includes the concepts of geometry, measurement, probability, and statistics with an emphasis on problem solving and critical thinking.

MATH 1414. College Algebra. 4 Credit Hours.

(020) In-depth study and applications of polynomial, rational, radical, exponential and logarithmic functions, and systems of equations using matrices. Additional topics such as sequences, series, probability, and conics may be included.

MATH 1442. Elementary Statistical Methods. 4 Credit Hours.

(020) Collection, analysis, presentation and interpretation of data, and probability. Analysis includes descriptive statistics, correlation and regression, confidence intervals and hypothesis testing. Use of appropriate technology is recommended.

MATH 2305. Discrete Mathematics. 3 Credit Hours.

(020) A course designed to prepare math, computer science, and engineering majors for a background in abstraction, notation, and critical thinking for the mathematics most directly related to computer science. Topics include: logic, relations, functions, basic set theory, countability and counting arguments, proof techniques, mathematical induction, combinatorics, discrete probability, recursion, sequence and recurrence, elementary number theory, graph theory, and mathematical proof techniques.

MATH 2312. Pre-Calculus Math. 3 Credit Hours.

(020) In-depth combined study of algebra, trigonometry, and other topics for calculus readiness.

MATH 2313. Calculus I. 3 Credit Hours.

(020) Limits and continuity; the Fundamental Theorem of Calculus; definition of the derivative of a function and techniques of differentiation; applications of the derivative to maximizing or minimizing a function; the hain rule, mean value theorem, and rate of change problems; curve sketching; definite and indefinite tegration of algebraic, trigonometric, and transcendental functions, with an application to calculation of areas.

MATH 2314. Calculus II. 3 Credit Hours.

(020) Differentiation and integration of transcendental functions; parametric equations and polar coordinates; techniques of integration; sequences and series; improper integrals.

MATH 2315. Calculus III (3 credit hour version). 3 Credit Hours.

(020) Advanced topics in calculus, including vectors and vector-valued functions, partial differentiation, Lagrange multipliers, multiple integrals, and Jacobians; application of the line integral, including Green’s Theorem, the Divergence Theorem, and Stokes’ Theorem. Prerequisite(s): MATH 2414.

MATH 2318. Linear Algebra (3 credit hour version. 3 Credit Hours.

(020) Introduces and provides models for application of the concepts of vector algebra. Topics include finite dimensional vector spaces and their geometric significance; representing and solving systems of linear equations using multiple methods, including Gaussian elimination and matrix inversion; matrices; determinants; linear transformations; quadratic forms; eigenvalues and eigenvector; and applications in science and engineering. Prerequisite(s): MATH 2414.

MATH 2320. Differential Equations. 3 Credit Hours.

(020) Ordinary differential equations, including linear equations, systems of equations, equations with variable coefficients, existence and uniqueness of solutions, series solutions, singular points, transform methods, and boundary value problems; application of differential equations to real-world problems.

MATH 2412. Pre-Calculus Math. 4 Credit Hours.

(020) In-depth combined study of algebra, trigonometry, and other topics for calculus readiness.

MATH 2413. Calculus I. 4 Credit Hours.

(020) Limits and continuity; the Fundamental Theorem of Calculus; definition of the derivative of a function and techniques of differentiation; applications of the derivative to maximizing or minimizing a function; the chain rule, mean value theorem, and rate of change problems; curve sketching; definite and indefinite integration of algebraic, trigonometric, and transcendental functions, with an application to calculation of areas.

MATH 2414. Calculus II. 4 Credit Hours.

(020) Differentiation and integration of transcendental functions; parametric equations and polar coordinates; techniques of integration; sequences and series; improper integrals.

MATH 2415. Calculus III. 4 Credit Hours.

(020) Advanced topics in calculus, including vectors and vector-valued functions, partial differentiation, Lagrange multipliers, multiple integrals, and Jacobians; application of the line integral, including Green’s Theorem, the Divergence Theorem, and Stokes’ Theorem.

MATH 2418. Linear Algebra (4 credit hour version). 4 Credit Hours.

(020) Introduces and provides models for application of the concepts of vector algebra. Topics include finite dimensional vector spaces and their geometric significance; representing and solving systems of linear equations using multiple methods, including Gaussian elimination and matrix inversion; matrices; determinants; linear transformations; quadratic forms; eigenvalues and eigenvector; and applications in science and engineering. Prerequisite(s): MATH 2414.

MATH 2420. Differential Equations (4 credit hour version). 4 Credit Hours.

(020) Ordinary differential equations, including linear equations, systems of equations, equations with variable coefficients, existence and uniqueness of solutions, series solutions, singular points, transform methods, and boundary value problems; application of differential equations to real-world problems. Prerequisite(s): MATH 2414 must be the 4 credit hour version.

MATH 3300. Principles of Statistics. 3 Credit Hours.

Data collection and analysis, elementary probability, discrete and continuous distributions, regression, correlation, estimation, and nonparametric methods. This course cannot be counted on a degree program for a mathematics major. Credit cannot be awarded for both MATH 3300 and MATH 3450. Prerequisite(s): MATH 1314.

MATH 3301. Number Theory. 3 Credit Hours.

The study of congruence relations, rational integers, diophantine equations, quadratic reciprocity law, linear forms, integral domains, and related topics. Prerequisite(s): 6 hours of MATH including MATH 2413.

MATH 3302. Principles of Geometry. 3 Credit Hours.

Euclidean geometry topics including logic, properties of parallel lines, triangles, quadrilaterals, circles, measurement, similarity, proportionality, and transformations. Technology will be incorporated where appropriate. Credit for both MATH 3302 and MATH 4302 will not be awarded. Prerequisite(s): MATH 2413.

MATH 3303. Concepts of Elementary Math I. 3 Credit Hours.

Problem solving, sets, functions, logic, elementary number theory, concepts of properties of whole numbers, rational numbers, integers, and real numbers. Designed for those planning to teach in elementary school. Prerequisite(s): MATH 1314 and Junior standing.

MATH 3305. Concepts of Elementary Math II. 3 Credit Hours.

Basic concepts in algebra, geometry, calculators and computers, metric system and measurement, and probability and statistics. Meets basic probability requirement for math majors, certifying teachers, and interdisciplinary studies. Prerequisite(s): MATH 3303.

MATH 3306. Differential Equations. 3 Credit Hours.

Solutions and applications of homogeneous and nonhomogeneous ordinary differential equations, including first-order equations and higher-order linear equations. Qualitative properties of solutions are investigated, as well as exact methods for solving differential equations and initial value problems including series, Laplace transform, separation of variables, variation of parameters, and undetermined coefficients. Prerequisite(s): MATH 2414.

MATH 3309. Algebraic Function. 3 Credit Hours.

Survey of elements from Algebra, Trigonometry, Geometry, Probability and Statistics, Finite Mathematics, and Calculus. The class places a strong emphasis on real-world applications and interpretation. Technology will be incorporated where appropriate.

MATH 3310. Discrete Mathematics. 3 Credit Hours.

Introduces students to the techniques and tools of reasoning, decision making, and combinational problem solving. Topics include sets and logic, combinations, probability, relations and functions, Boolean properties, and graph theory. Prerequisite(s): MATH 1314 or MATH 3309.

MATH 3311. Probability & Statistics I. 3 Credit Hours.

This course contains the fundamentals of probability theory and the basics of statistics. Topics include probability axioms, sampling distributions, descriptive statistics, finite random variables, infinite discrete random variables, continuous random variables, and the Central Limit Theorem. Prerequisite(s): MATH 2414 and MATH 3305 or an elementary probability course.

MATH 3315. Mathematics & Technology. 3 Credit Hours.

Use of current technologies related to creating interactive presentations/documents for math as well as use of current technologies related to mathematical analysis and state certification exams.

MATH 3332. Linear Algebra. 3 Credit Hours.

A study of the theory of real vector spaces and linear transformations. Topics include vector spaces, inner product, norm, distance, subspaces, spanning sets, linear dependence and independence, bases, dimension, linear systems, coordinates, linear transformations, kernel, image, isomorphisms, inverse linear transformations, matrix representations of linear transformations, similarity, direct sums, and canonical forms. Prerequisite(s): MATH 2414 MATH 3310 or instructor's permission.

MATH 3350. Principles of Bio-Statistics. 3 Credit Hours.

An introduction to statistical methods that are applied in biology and agriculture. Use of technology and hands-on spreadsheet assignments are required in this course. Prerequisite(s): MATH 2413.

MATH 3360. Numerical Analysis I. 3 Credit Hours.

An introduction to numerical analysis. Topics are being selected from error analysis, solving algebraic equations, interpolation, numerical differentiation and integration, methods for solving systems of equations, approximation theory, and initial value problems of ordinary differential equations. Prerequisite(s): MATH 2414 and 3 hours of COSC.

MATH 3370. An Introduction to Linear Programming. 3 Credit Hours.

The topics will include Convexity, Extreme Points, Linear Programming for efficiency of mixtures, transportation, and other economic models. Basic analysis of the simplex method and duality will be used to solve such problems and to determine the long-term usefulness of models.

MATH 3375. An introduction to Partial Differential Equations. 3 Credit Hours.

The topics will include advanced vector calculus, the heat and wave equations, separation of variables, Fourier Transforms, convolution, and geometric analysis. Prerequisite(s): MATH 2414 and PHYS 2425.

MATH 3433. Calculus III. 4 Credit Hours.

The calculus of two dimensional vectors, parametric equations, cylindrical and spherical coordinates, multivariable differential calculus, directional derivatives and their applications, multiple integration, vector analysis, line and surface integrals, Green's Theorem, Stokes' Theorem. Use of computer technology and laboratory assignments will be required in this course. Prerequisite(s): MATH 2414.

MATH 4302. College Geometry. 3 Credit Hours.

Euclidean geometry topics including logic, properties of parallel lines, triangles, quadrilaterals, circles, measurement, similarity, proportionality, and transformations. Additional topics include projective and non-Euclidean geometry. Technology is incorporated where appropriate. Substitutes for MATH 3302 for 4-8 certifying students. Prerequisite(s): MATH 2413.

MATH 4304. Survey of Mathematical Ideas. 3 Credit Hours.

This course is designed to bring together and supplement the technical material of other mathematics courses to communicate mathematics effectively. Topics in algebra, trigonometry, geometry, statistics, and discrete mathematics will be explored. Technology will be used where appropriate. Prerequisite(s): MATH 2413 and MATH 3302 or MATH 4302 or concurrent registration.

MATH 4304L. Survey of Mathematical Ideas Lab. 1 Credit Hour.

This lab is required for all math majors and must be taken with MATH 4304. This lab addresses and prepares students for content on the state certification exam and will reflect current state requirements for the mathematics state examinations for grade levels 7-12. All other majors requiring MATH 4304 will continue to take base course, but will not take this lab. Prerequisites: MATH 2413 and MATH 3302 or MATH 4302 or concurrent registration and Senior Standing.

MATH 4305. Concepts of Elem Math III. 3 Credit Hours.

This course is designed to develop and extend the mathematical content knowledge of prospective middle school teachers. Topics include the development of algebraic reasoning through the use of patterns, relations, and functions with an emphasis on multiple representations (numerical, graphical, verbal, and/or symbolic). Technology is being integrated into the curriculum where appropriate. Prerequisite(s): MATH 3305 for EC-6 and 4-8 Mathematics majors; MATH 2413 for all other students.

MATH 4309. Advanced Analysis I. 3 Credit Hours.

(WI) A study of the theory of the calculus of functions of a single variable. Topics include the topology of the real line, functions, sequences and their limits, continuity, differentiation, and integration. Prerequisite(s): MATH 2414.

MATH 4311. Probability & Statistics II. 3 Credit Hours.

Continuation of MATH 3311 with focus on statistical inference. Topics include the Central Limit Theorem, sampling distributions, confidence intervals, hypothesis testing, inferences based on two samples, and an introduction to ANOVA. Prerequisite(s): MATH 3311.

MATH 4320. Mathematical Modeling. 3 Credit Hours.

An advanced introduction to models related to applied sciences. Topics include applications of linear programming, scheduling, graph theory, and game theory. Prerequisite(s): MATH 2414 and 6 hours of advanced mathematics or pre-calculus.

MATH 4332. Abstract Algebra. 3 Credit Hours.

(WI) An introduction to abstract algebraic structures, including groups, rings, ideals, polynomial rings, and applications. Prerequisite(s): MATH 3332.

MATH 4380. Undergraduate Research Project. 1-3 Credit Hours.

Methods of research in the mathematical sciences or in mathematics education through a research project directed by a departmental faculty member. The student is required to prepare a final report and presentation. No credit is earned until the student has enrolled in at least 3 credit hours, and the final report and presentation are certified as completed by the faculty member directing the project, at which time the student will receive 3 credit hours. Prerequisite(s): Mathematics major, senior standing, and 24 semester hours of MATH courses and permission of department chair.

MATH 4389. Special Topics in Math. 3 Credit Hours.

Topics are being selected from areas of mathematics suitable for upper level study. This course may be repeated once with permission of department chair, as topics change. Prerequisite(s): MATH 2414 and 6 hours of advanced MATH.

MATH 4488. Mathematic Problems. 1-4 Credit Hours.

Special problems in mathematics. Not covered by any course in the curriculum. Work may be either theory or laboratory. May be repeated with permission of department chair for additional credit when fewer than four credits have been earned. Prerequisite(s): Permission of department chair.

MATH 5090. Comprehensive Examination. 0 Credit Hours.

Non-thesis students should register for the comprehensive examination during their final semester of graduate coursework, or upon permission of advisor. All comprehensive examinations will be written, but an oral component may also be required. A maximum of three attempts will be allowed. Thesis student do not take this examination.

MATH 5198. Thesis. 1-6 Credit Hours.

Scheduled when the student's committee chair determines the student is ready to begin the thesis. No credit is earned until the student has enrolled in at least 6 credit hours of thesis and the thesis is certified as completed by the student's committee, at which time the student will be awarded 6 credit hours of thesis.

MATH 5301. Nonparametric Statistics. 3 Credit Hours.

Introduction to nonparametric statistics. Topics will include hypothesis testing, contingency tables, rank tests, and goodness-of-fit tests. Prerequisite(s): MATH 3300 or MATH 3311 or MATH 3450 or MATH 5305.

MATH 5305. Probability & Statistics. 3 Credit Hours.

Topics will be selected from: distributions and stochastic processes, parametric and nonparametric statistics, and time series analysis. Prerequisite(s): MATH 3311.

MATH 5308. Abstract Algebra. 3 Credit Hours.

Topics will be selected from: groups, homomorphism, isomorphism, direct products and sums, invariant properties, rings, and fields. Prerequisite(s): MATH 4332.

MATH 5311. Operations Research. 3 Credit Hours.

This course examines the theoretical support and applications of the simplex algorithm for linear programming and for dynamic programming. Transportation and scheduling problems are among the applications to be emphasized. Prerequisite(s): MATH 3332.

MATH 5312. Design of Experiments. 3 Credit Hours.

Students will learn about planning and conducting an experiment. Data analysis using appropriate software is covered. Prerequisite(s): MATH 5305 or permission of department chair.

MATH 5315. Operations Research II. 3 Credit Hours.

Selected topics in Operations Research, chosen from among the following: Search, Selection and Optimization Techniques; System Modeling; Network Analysis; Inventory and Production Modeling; Sequencing and Scheduling; Decision Theory; Queuing Theory; Simulation and Monte Carlo Techniques; and Markov Chains.

MATH 5320. Real Analysis. 3 Credit Hours.

Topics will be chosen from: sets and operators; cardinal numbers and ordinal types; metric spaces and Lebesgue measure; metric properties of sets; differentiation and integration. Prerequisite(s): MATH 4309.

MATH 5330. Mathematical Modeling. 3 Credit Hours.

An advanced course in mathematical modeling. Topics will be selected from scaling, dimensional analysis, regular and singular perturbation theory, stability theory, and asymptotic analysis. Prerequisite(s): MATH 3306 and MATH 3332.

MATH 5335. Statistics II. 3 Credit Hours.

This is an advanced course in probability distributions, joining distributions, covariance and problems related to the actuary field. Prerequisite(s): MATH 5305.

MATH 5350. Applied Linear Algebra. 3 Credit Hours.

An advanced course in linear algebra. Topics to be selected from linear spaces and operators, canonical forms, quadratic forms and optimization, computation and condition, and compatible systems. Prerequisite(s): MATH 3332.

MATH 5360. Numerical Analysis. 3 Credit Hours.

An advanced study of numerical analysis. Topics will be selected from linear systems, approximation theory, numerical differential and integral equations, integration theory. Prerequisite(s): MATH 4309 and MATH 3360 or 6 hours of COSC.

MATH 5375. Statistical Reasoning and Probability. 3 Credit Hours.

Topics in applied statistics including ANOVA, experimental design, single and multiple linear regression, hypothesis testing of linear models, forecast errors and confidence intervals. Prerequisite(s): MATH 3311 or equivalent.

MATH 5376. Topics in Secondary Math. 3 Credit Hours.

This course applies the standards of the National Council of Teachers of Mathematics to the curriculum of secondary mathematics. It explores techniques to implement the standards through the use of manipulatives, graphing handhelds, and computer technology. Prerequisite(s): 24 hours of MATH, including MATH 2413.

MATH 5378. Technology-Aided Mathematics. 3 Credit Hours.

Students will engage in mathematical problem-solving using technological tools. Technologies may include graphing handhelds, data collection devices, computer software packages, and internet resources. This course may be repeated for credit as the topic changes. Prerequisite(s): 24 hours of MATH, including MATH 120.

MATH 5379. Topics In Mathematics Theory. 3 Credit Hours.

An examination of topics in mathematical theory appropriate for secondary mathematics educators. Topics will be selected from geometry and topology, number theory, modern algebra, and library research in mathematics. This course may be repeated for credit as the topic changes. Prerequisite(s): Permission of department chair.

MATH 5380. Selected Topics in Mathematics. 3 Credit Hours.

An examination of topics in applied mathematics. Topics for study will be selected from advanced mathematical modeling, advanced numerical techniques, practical optimizations, calculus of variations, dynamic programming, integral equations, optimal control, perturbation methods, and library research in applied mathematics. This course may be repeated for credit as the topic changes. Prerequisite(s): Permission of department chair.

MATH 5381. Research Analysis. 1 Credit Hour.

An overview of the components of research in the main areas of mathematics. These areas will include pure mathematics and statics, applied mathematics and statistics, and mathematics education. The course will culminate with a study of what is a proper literary review and how to submit an article for publication. Prerequisite(s): Graduate standing in the mathematics department or permission of department chair.

MATH 5389. Advanced Special Problems. 1-3 Credit Hours.

Special problems in mathematics. Work may be either theory or laboratory. May be repeated with permission of the department chair for additional credit when fewer than four credits have been earned. Prerequisite(s): Permission of department chair.