# Mathematics (MATH)

**MATH 1314 College Algebra**

The fundamentals of algebra; polynomials and graphs; conic sections; systems of linear equations, matrices; sequences and series; mathematical induction and the binomial theorem.

Prerequisites: Completion of Texas Success Initiative (TSI) mathematics requirements, appropriate level developmental course sequence, an minimum ACT Mathematics score of 19 with an ACT Composite score of 23 or above, a minimum SAT Mathematics score of 500 with a SAT Total score of 1,070 or above, or a Redesigned SAT Mathematics score of 530 or above.

TCCN: MATH 1314

**MATH 1316 Plane Trigonometry**

Trigonometry, analytic trigonometry, applications of trigonometry, complex numbers, polar coordinates and parametric equations.

Prerequisites: ACT Mathematics score of 27 or above, an SAT Mathematics score of 630 or above, a Redesigned SAT Mathematics score of 650 or above, or MATH 1314.

TCCN: MATH 1316

**MATH 1324 Business Math I**

Systems of linear equations and matrices; linear programming; mathematics of finance; limits, continuity, derivatives.

Prerequisites: ACT Mathematics score of 25 or above, an SAT Mathematics score of 600 or above, a Redesigned SAT Mathematics score of 620 or above, or MATH 1314.

TCCN: MATH 1324

**MATH 1325 Business Math II**

Applications of the derivative, anti-derivatives, and techniques of integration; functions and calculus of several variables.

Prerequisites: MATH 1324.

TCCN: MATH 1325

**MATH 1332 Mathematics for Liberal Arts I**

This course is designed to enhance mathematical literacy and to stimulate interest in appreciation for mathematics and quantitative reasoning as valuable tools for addressing issues in a constantly changing society. Topics may include, at an introductory level, logical reasoning and problem solving through mathematical games and puzzles; sets, relations, and functions; counting and number concepts (number theory and infinity).

Prerequisites: Completion of Texas Success Initiative (TSI) Mathematics requirements or appropriate level developmental course sequence.

TCCN: MATH 1332

**MATH 1333 Math for Liberal Arts II**

This course is designed to enhance mathematical literacy and to stimulate interest in appreciation for mathematics and quantitative reasoning as valuable tools for addressing issues in a constantly changing society. Topics may include, at an introductory level, logical reasoning and problem solving through mathematical games and puzzles; sets, relations, and functions; counting and number concepts (number theory and infinity).

Prerequisites: Completion of Texas Success Initiative (TSI) Mathematics requirements or appropriate level developmental course sequence.

TCCN: MATH 1333

**MATH 1342 Introductory Statistics**

Topics include organization of data; probability; random variables; the normal distribution; inferences; chi-square; regression and correlation; analysis of variance; and non-parametric statistics.

Prerequisites: Completion of Texas Success Initiative (TSI) Mathematics requirements or appropriate level developmental course sequence.

TCCN: MATH 1342

**MATH 1348 Analytic Geometry**

Study of the equations of lines, circles and conics. Vectors in two and three dimensions. Dot and cross product. Introduction to quadrics.

**MATH 1350 Fundamentals of Mathematics I**

Sets, relations, functions, number system, and elementary number theory. This course cannot be used to fulfill Core Curriculum requirements.

Prerequisites: MATH 1332, MATH 1333, MATH 1342, or MATH 1314.

TCCN: MATH 1350

**MATH 1351 Fundamentals of Mathematics II**

Probability, statistics, and geometry. This course cannot be used to fulfill Core Curriculum requirement.

Prerequisites: MATH 1350.

TCCN: MATH 1351

**MATH 2330 Elementary Geometry**

Introduction to classical Euclidean Geometry. Postulates, congruency, similarity and classical construction. Introduction to solid geometry and transformations in the plane. (Formerly MATH 3320)

**MATH 2412 Pre-Calculus**

Topics include: Analytic geometry, complex numbers, and systems of algebraic equations; algebraic, exponential, logarithmic and trigonometric functions and applications; sequences and applications. Students will receive credits for at most two courses from MATH 1314, 1316 and 2412.

Prerequisites: ACT Mathematics score of 25 or above, an SAT Mathematics score of 600 or above, a Redesigned SAT Mathematics score of 620 or above, or MATH 1314.

TCCN: MATH 2412

**MATH 2413 Calculus I**

Limits, continuity, differentiation, applications to optimization; integration and the Fundamental Theorem of Calculus.

Prerequisites: ACT Mathematics score of 29 or above, an SAT Mathematics score of 660 or above, a Redesigned SAT Mathematics score of 690 or above, MATH 1316, or MATH 2412.

TCCN: MATH 2413

**MATH 2414 Calculus II**

Techniques and applications of integration: area between curves, volumes of solids of revolution, work, areas of surfaces of revolution, arc-length, introduction to differential equations, parametric equations and polar coordinates, sequences and series.

Prerequisites: MATH 2413.

TCCN: MATH 2414

**MATH 2415 Calculus III**

Vector operations in R2, R3, lines, planes; vector-functions, space curves, curvature; multivariable calculus, optimization, Lagrange multipliers; multiple integrals; vector fields, theorems of Green, Gauss and Stokes.

Prerequisites: MATH 2414.

TCCN: MATH 2415

**MATH 3195 Seminar**

Seminar on various topics in mathematics. May be repeated for credit with departmental approval.

**MATH 3295 Seminar**

Seminar on various topics in mathematics. May be repeated for credit with departmental approval.

**MATH 3310 Introduction to Linear Algebra**

Introduction to linear transformations and matrices; vector spaces, vector operations.

Prerequisites: MATH 2415.

**MATH 3318 Advanced Linear Algebra**

A continuation of MATH 3310. Focuses on more abstract aspects as well as computational aspects. Topics include inner product spaces, spectral theorems, diagonalization, Hermitian matrices, quadratic forms, numerical linear and Jordan canonical.

Prerequisites: MATH 3310.

**MATH 3320 Modern Geometry**

This course will treat topics from plane geometry. A brief introduction to spherical and hyperbolic geometries will also be given. Intended primarily for students seeking middle school (grades 4-8) certification.

**MATH 3325 Geometry**

Selected topics from the foundations of Euclidean and non-Euclidean geometries. Includes the study of spherical and hyperbolic geometries, as well as transformational geometry, with techniques from linear algebra. Intended primarily for students seeking secondary certification.

Prerequisites: MATH 3310.

**MATH 3328 Advanced Geometry**

Study of Neutral, Euclidean and Hyperbolic geometrics from an axiomatic perspective.

Prerequisites: MATH 3365.

**MATH 3330 Ordinary Differential Equation**

Solution of first order differential equations. Study of second and higher order equations with constant coefficients. Power series solutions. Laplace Transform and Linear Systems. A brief introduction to numerical methods.

Prerequisites: MATH 2414.

**MATH 3360 Statistical Analysis**

Fundamentals of probability, distribution theory, random variables, law of large numbers, central limit theorems, statistical inequalities.

Prerequisites: MATH 2414.

**MATH 3365 Discrete Mathematics**

This course is a study of elements of discrete mathematics. Topics covered: logic; counting techniques; mathematical induction; the binomial theorem; number theory; sets, relations and functions.

Prerequisites: MATH 2413.

**MATH 3371 Communications in Mathematics**

This course is designated to enhance students' communication skills in mathematics. Emphasis will be placed in writing proofs. Topics include set theory, logic and properties of numbers at an elementary level. Substantial writing in mathematics using LaTeX is required.

**MATH 3390 Principles of Math for Elem Ed**

An in-depth study of the mathematical principles and concepts underlying the traditionally computational techniques for the teaching of mathematics at early childhood and elementary school levels. The course content includes problem solving; arithmetic, algebra, geometry, probability, logic, counting, numeration and number systems (including natural, integer, rational, and real number systems), and their historical development; content based teaching; integrating various areas of mathematics; and examining connections of college-level mathematics course contents with the mathematics content of and its effective teaching at the early childhood and elementary school levels. In addition, TExES Mathematics Standards V-IX covering Mathematical Processes, Mathematical Perspectives, Mathematical Learning and Instruction, Mathematical Assessment and Professional Development will be emphasized. Students must earn a “C" or better to successfully complete the course. The course may not be counted toward a major or minor in Mathematics or for certification in secondary mathematics. Open only to early childhood/elementary education majors. It is strongly recommended to take this course concurrently with Block II.

Prerequisites: Completion of Block I and a grade of at least “C" in MATH 1350 and 1351.

**MATH 3395 Seminar**

Seminar on various topics in mathematics. May be repeated for credit with departmental approval.

**MATH 4152 Internship In Mathematics**

A directed internship in a public/private organization that is appropriate to the student's career objective or desire in a mathematical science setting. Students will apply mathematical knowledge in a real world setting and receive on-the-job training experience. Seminar and training will be held to discuss field experience from theoretical and applied perspectives.

Prerequisites: Permission of the instructor and advisor.

**MATH 4252 Internship in Mathematics**

A directed internship in a public/private organization that is appropriate to the student's career objective or desire in a mathematical science setting. Students will apply mathematical knowledge in a real world setting and receive on-the-job training experience. Seminar and training will be held to discuss field experience from theoretical and applied perspectives.

Prerequisites: Permission of the instructor and advisor.

**MATH 4305 Number Theory**

Divisibility, congruence, power residues, quadratic reciprocity, Diophantine equations, Euler's function, Fermat's theorem, primitive roots, Legendre and Jacobi symbols.

**MATH 4310 Abstract Algebra I**

Introduction to abstract algebra. Topics include Introduction to Ring theory: arithmetic in integers, modular arithmetic, fields, arithmetic in the Ring of polynomials. Unique factorization in integers and polynomials. Introduction to Group theory: definition and examples, subgroups, quotient groups, symmetry groups and permutation groups.

Prerequisites: MATH 3365.

**MATH 4315 Abstract Algebra II**

Continuation of MATH 4310. Topics in group theory: group actions, Sylow theorems, fundamental theorem of Abelian groups, and finite simple groups. Topics in Ring theory: ideals and quotient rings, Euclidean domain, principal ideal domain and unique factorization domain. Topics in Field theory: vector spaces, field extensions, finite field, and Galois Theory.

Prerequisites: MATH 4310.

**MATH 4330 Numerical Linear Algebra**

Numerical methods for problems of linear algebra, including the solution of large systems, eigenvalues and eigenvectors.

Prerequisites: MATH 3310

**MATH 4335 Advanced Calculus**

A course in real analysis. It will include topology, continuity, differentiation, integration, sequences, series and power series.

**MATH 4340 Numerical Analysis I**

Error analysis, solutions of non-linear functions, systems of linear equations, eigenvalue problems, interpolation theory, numerical differentiation and integration, numerical methods for ordinary differential equations.

**MATH 4341 Numerical Analysis II**

Finite difference methods and finite element methods for elliptic, parabolic and hyperbolic equations.

**MATH 4345 Complex Variables**

This is a course in complex variables which will include analytic functions, power series, the theory of residues and conformal mappings.

Prerequisites: MATH 4335 or permission of instructor.

**MATH 4350 Partial Differential Equations**

Theory of partial differential equations and boundary value problems with applications to the physical sciences and engineering. Detailed analysis of the wave equation, the heat equation, and the potential equation. Numerical methods to solving partial differential equations will also be discussed.

Prerequisites: MATH 3330.

**MATH 4352 Internship in Mathematics**

A directed internship in a public/private organization that is appropriate to the student's career objective or desire in a mathematical science setting. Students will apply mathematical knowledge in a real world setting and receive on-the-job training experience. Seminar and training will be held to discuss field experience from theoretical and applied perspectives.

Prerequisites: Permission of the instructor and advisor.

**MATH 4355 Selected Topics in Math**

Topics selected from the fields of pure or applied mathematics. May be repeated when topic changes.

Prerequisites: Senior standing and permission of instructor.

**MATH 4360 Introduction to Topology**

Basic concepts of point-set topology including connectedness, compactness, etc. and metric spaces.

**MATH 4365 Geometry of Curves&Surfaces**

This course will present geometry of curves and surfaces in three dimensional Euclidean space. Topics include 1) From Curve Theory: Parametized Curves, Arc Length, Frenet-Serret Frame, Singularities, Theory of Contact, Curvature, Torsion, Intrinsic Equation of Curves, Global Properties of Curves; 2) From Surface Theory: Parametrized Surfaces, Tangent Plane and Normal Line, First and Second Fundamental Forms, Curvature of Surfaces.

**MATH 4380 Undergraduate Research in Math**

Students work on a theoretical or applied research project. The plan of study is negotiated by the faculty member and the student. Course may be repeated under different topic for credit. Evaluation of performance in this course is on a Pass/Fail basis.

Prerequisites: Consent of the instructor and the department.

**MATH 4385 History of Mathematics**

Topics from arithmetic and computation, algebra, geometry, trigonometry, calculus, number theory, linear algebra, etc. from ancient recorded history to modern times intertwined with historical perspectives, biographies of several mathematicians from different cultures and times, their contributions, and that of their cultures, to mathematics and society.

Prerequisites: Nine semester hours of advanced mathematics.

**MATH 4390 Math in Middle&High School**

Selected topics from secondary school mathematics. Content, materials, and contemporary issues specific to teaching of mathematics at the secondary school level. In addition, TExES Mathematics Standards V-VIII covering Mathematical Processes, Mathematical Perspectives, Mathematical Learning and Instruction, and Mathematical Assessment will be emphasized. Concurrent enrollment in Block II is strongly recommended.

Prerequisites: Completion of Block I and at least twelve upper-level mathematic SCH.

**MATH 4395 Senior Mathematics Project**

A study project under the direction of a member of the mathematics faculty. Required will be a written report, oral presentation and approval by both the advisor and one additional mathematics faculty member.

Prerequisites: Senior standing and permission of instructor.

**MATH 4452 Internship in Mathematics**

Prerequisites: Permission of the instructor and advisor.

**MATH 5191 Mathematics Seminar**

A seminar presents diverse topics from pure and applied mathematics. Students are encouraged to present a series of articles, journals and portions of monograms during the class meetings. May be repeated once when topics vary. (Formerly MATH 5190)

Prerequisites: Graduate standing and permission of instructor.

**MATH 5252 Internship in Mathematics**

Students are encouraged to have directed internships in a public or private organization appropriate to the student's career objective/desire. Taken during the last year of the student's program of study, student has to provide that the nature of the assignment undertaken in the organization has relevant mathematics components.

Prerequisites: Graduate standing and permission of the department and instructor.

**MATH 5290 Research Mthds in Mathematics**

This course deals with the basic tools of the mathematics to better understand mathematical research. Analytical concepts, survey research, in some cases, statistical/computational software and their methods will be the basis of this course.

Prerequisites: Graduate standing and permission of the instructor.

**MATH 5303 Number Theory I**

This first course in number theory introduces algebraic number theory as well as the analytic methods. Topics include: Number fields, algebraic integers, ideals and units, ideal class groups, ramification theory, quadratic and cyclotomic fields, zeta-functions and L-series.

Prerequisites: Graduate standing and permission of instructor.

**MATH 5304 Number Theory II**

Topics include: Artin reciprocity law, topics from field theory; modular functions and elliptic curves, Diophantine equations, distribution of prime numbers, computations applications of algebraic curves over finite fields such as elliptic curve cryptography and coding.

Prerequisites: MATH 5303.

**MATH 5305 Real Analysis I**

This is a course on Lebesgue measure and integration. The classical Lp spaces will be defined and basic results established, such as the Holder and Minkowski inequalities and completeness of the spaces.

Prerequisites: Graduate standing and permission of instructor.

**MATH 5306 Linear Algebra**

Topics include: Canonical structure theorems, diagonalization, the spectral theorem, inner-product spaces, and their applications and extensions.

Prerequisites: Graduate standing and permission of instructor.

**MATH 5311 Real Analysis II**

Topics include: Fourier series, introduction to Hilbert Spaces, the spectral theorem for compact linear operators on Hilbert spaces with applications to differential equations. Prerequiste: MATH 5305, and knowldege equivalent to MATH 3310.

**MATH 5312 Functional Analysis I**

This is the first course in Functional Analysis. Topics include: Topological vector spaces, Banach spaces, the open mapping and closed graph theorems, the Hahn-Banach theorem, duality and weak topologies.

Prerequisites: MATH 5305 and knowledge equivalent to MATH 3310.

**MATH 5315 Combinatorics**

This course discusses discrete mathematical structures, especially the enumeration and the optimization problems related to them. Algorithmic (constructive) aspects will be emphasized. Course work involves computer programming projects. Topics include: basic tools of combinatorics, graphs and networks, relations, the counting problems, the existence problems, the combinatorial optimization.

Prerequisites: Graduate standing and permission of instructor.

**MATH 5316 Graph Theory**

This is a basic course in graph theory. Fundamental concepts of graph theory will be investigated. Topics include: directed graphs, trees and distance, spanning trees, coloring of graphs, planar graphs, edges and cycles.

Prerequisites: Graduate standing and permission of instructor.

**MATH 5320 Complex Variables I**

This is the first course on functions of one complex variable. It will begin with the complex number system and will treat topics such as power series, analytic functions, Mobius transformations, complex integrations, residue calculus, singularities, and Schwarz's Lemma.

Prerequisites: Graduate standing and consent of instructor.

**MATH 5321 Complex Variables II**

This is the second course on functions of one complex variable. Topics include: conformal mappings, convex functions, the Hadamard Three Circles Theorem, compactness, convergence in the space of analytic functions, Runge's theorem, analytic continuation and Riemann surfaces, harmonic functions, entire functions, and Picard's Theorems.

Prerequisites: MATH 5320.

**MATH 5330 Abstract Algebra I**

This is the first course in Abstract Algebra. The main topics in this course will be groups, rings, fields, subgroups, quotient groups, ideals, homomorphisms and introduction to field extensions. There will be classical examples of permutation groups, polynomial rings and integral domains, questions of factorization, ideals and fundamental homomorphism theorems.

Prerequisites: Graduate standing and consent of instructor.

**MATH 5331 Abstract Algebra II**

Topics include modules, finite fields, Fundamental Theorem of Field Theory, algebraic extensions, the classification of finite fields, Fundamental Theorem of Galois Theory, and the cyclotomic extension.

Prerequisites: MATH 5330.

**MATH 5340 Differential Geometry**

This course is an introduction to the differential geometry of n-dimensional manifolds. Topics include: Riemannian manifolds, differential forms and Stokes Theorem. (Note that differential geometry is relevant to differential equations, mathematical physics, as well as other areas of sciences.)

Prerequisites: MATH 5365 and knowledge equivalent to MATH 2415 and MATH 4335.

**MATH 5350 Ordinary Diff Equations I**

This is the first course in ordinary differential equations. The course will include systems of linear differential equations, two dimensional autonomous systems, existence, uniqueness and continuation of solutions, dependence of solutions on initial conditions and parameters.

Prerequisites: Graduate standing and permission of instructor.

**MATH 5355 Advanced Topics in Mathematics**

Advanced topics selected from the fields of pure or applied mathematics. May be repeated when topic changes.

Prerequisites: Graduate standing and permission of instructor.

**MATH 5360 Partial Differential Equations**

This is a basic course in partial differential equations. The course will cover the following: first order linear partial differential equations, classification of second order equations and canonical forms, Fourier series and integrals, the wave equation, the Cauchy problem for hyperbolic equations, the heat equation, the weak maximum principle, the strong maximum principle, the Laplace equation, Green's function and Poisson's formula.

Prerequisites: MATH 5350.

**MATH 5365 Topology**

This is an introductory course in point-set topology. The course will include topological spaces, continuous functions, connectedness, separation axioms. Tychonoff's theorems, para-compactness, complete metric spaces and function spaces will also be discussed.

Prerequisites: Graduate standing and permission of instructor.

**MATH 5367 Numerical Methods for PDE I**

A study of algorithms for the numerical solution of hyperbolic and parabolic partial differential equations using the finite difference method; stability and convergence of methods and error bounds. Applications from physics and engineering will be emphasized.

Prerequisites: Graduate standing and permission of instructor.

**MATH 5368 Numerical Methods for PDE II**

A study of algorithms for the numerical solution of elliptic partial differential equations using the finite difference method; stability and convergence of methods and error bounds. Applications from physics and engineering will be emphasized.

Prerequisites: Graduate standing and permission of instructor.

**MATH 5370 Mathematical Modeling**

This is the first course in mathematical modeling. Topics include: linear equations and models, non-linear equations and models, modeling with linear systems, modeling with non-linear systems, mathematical modeling and dynamical systems, non-homogeneous systems, empirical models and linear regression, bifurcation and chaos. Working knowledge of a computer programming language is preferred.

Prerequisites: Graduate standing and permission of instructor.

**MATH 5375 Probability**

Topics include: distribution functions, random variables, expectation, independence, convergence concepts, law of large numbers, characteristic functions, the central limit theorem, conditional expectation, martingales and Brownian.

Prerequisites: MATH 5305.

**MATH 5395 Graduate Research in Math**

Students work on a theoretical or applied research project. The plan of study is negotiated by the faculty member and the student. Course may be repeated under different topic for credit. Offer only “Pass/Fail” grades.

Prerequisites: Consent of the instructor and the department.

**MATH 5398 Thesis I**

This course is designed to be the first step towards the successful completion of the Mathematics thesis. Students schedule the coursework in consultation with their advisor. Evaluation of performance is CR/NC. Students will receive credit for the class when they have a proposal approved by their thesis committee and the required evidence of progress on a draft. If the grade of IP is received, the student must enroll again for credit. Approval of the major professor and the depa1tment chair. All core courses should be completed prior to beginning thesis work, preferably during the last year of the student's program of study.

Prerequisites: Graduate standing and permission from the student's thesis advisory committee.

**MATH 5399 Thesis II**

This course is designed to be the final step towards the successful completion of the Mathematics thesis. Students schedule the coursework in consultation with their advisor. Evaluation of performance is CR/NC. Students will receive credit for the class when they have success fully written and defended their thesis to their thesis committee. If the grade of IP is received, the student must enroll again for credit.

Prerequisites: Graduate standing, MATH 5398: Thesis I, permission from the student's thesis advisory committee and approval of the major professor and the department chair.

**MATH 5699 Thesis II**

This course is designed to be the final step towards the successful completion of the Mathematics thesis. Students schedule the coursework in consultation with their advisor. Evaluation of performance is CR/NC. Students will receive credit for the class when they have success fully written and defended their thesis to their thesis committee. If the grade of IP is received, the student must enroll again for credit.

Prerequisites: Graduate standing, MATH 5398: Thesis I, permission from the student's thesis advisory committee and approval of the major professor and the department chair.

**MATH 5999 Thesis II**

This course is designed to be the final step towards the successful completion of the Mathematics thesis. Students schedule the coursework in consultation with their advisor. Evaluation of performance is CR/NC. Students will receive credit for the class when they have success fully written and defended their thesis to their thesis committee. If the grade of IP is received, the student must enroll again for credit.

Prerequisites: Graduate standing, MATH 5398: Thesis I, permission from the student's thesis advisory committee and approval of the major professor and the department chair.