Admissions | Program Requirements | Graduate Courses |

**Dickinson Hall, Room 622, (501) 569-8100, Website**

The Master of Science in Mathematical Sciences program provides advanced preparation for careers in private industry and government or for doctoral study. It is designed to accommodate full-time employees and can be completed in two years by including summer classes. Concentrations are offered in applied mathematics, applied statistics, computational sciences, and interdisciplinary mathematics. Computer labs are available with research-quality mathematical and scientific software.

The program is continually adding to and updating its software and a number of courses in the program require computer use. Applied mathematics is critical to most areas of today’s highly technological workforce, and the master’s program is a passport to this exciting and expanding career field. For more information visit the mathematical sciences program website.

### Admission Requirements

- Baccalaureate degree from an accredited institution with a cumulative grade point average of 2.75 (4.0 scale) or 3.0 in the last 60 hours.
- Courses with a grade of C or greater in matrix algebra, differential equations, an advanced calculus sequence, statistical methods, and a scientific programming language.
- Six appropriate advanced mathematics hours with grades of C or greater (i.e., Analysis, Topology, Numerical Analysis, Mathematical Statistics)
- Official Graduate Record Examination score.
- Letters of Recommendation.
- Writing Sample.

Applicants lacking prerequisite classes must complete specified preparatory courses. Contact the program coordinator for details.

### Program Requirements

The mathematical sciences degree requires 33 graduate semester credit hours with a master’s research project or 36 graduate credit hours without the project, including 12 core hours; 3 research project hours or 6 alternate hours; 9 hours of mathematical emphasis courses; 9 hours from specialization; and written and oral comprehensive examination. In addition, the Graduate Record Examination general and mathematics sections must be taken during the first semester.

The written comprehensive examination covers material from the four core courses – MATH 7323 Advanced Numerical Analysis I, MATH 7350 Mathematical Statistics I, MATH 7311 Advanced Linear Algebra, and MATH 7322 Advanced Differential Equations. The oral comprehensive examination consists of a presentation from the student’s area of specialization and a question and answer session derived from the student’s course work.

#### Core Courses

**MATH 7311 Advanced Linear Algebra**

MATH 7322 Advanced Differential Equations

MATH 7323 Advanced Numerical Analysis I

MATH 7350 Mathematical Statistics I

MATH 7322 Advanced Differential Equations

MATH 7323 Advanced Numerical Analysis I

MATH 7350 Mathematical Statistics I

### Graduate Assistantships

A limited number of graduate assistantships are available. Contact the program coordinator for information.

### Specializations

There are two areas of specialization: applied mathematics and applied statistics.

#### Applied Mathematics

This specialization requires 33 semester credit hours, the research project, or 36 semester hours without the research project. In addition to the 12 hours of core courses listed above, the degree requires 9 hours of mathematical emphasis courses, 9 hours of elective courses, MATH 8300, and written and oral comprehensive examinations.

#### Emphasis Courses

MATH 7312 Computational Linear Algebra

MATH 7324 Advanced Numerical Analysis II

MATH 7325 Partial Differential Equations

#### Approved Electives

MATH 5302 Complex Analysis

MATH 5308 Integral Transforms

MATH 7351 Mathematical Statistics II

MATH 7352 Mathematical Statistics III

MATH 7353 Linear and Nonlinear Regression

MATH 7354 Experimental Design

MATH 7355 Sampling Techniques

MATH 7399 Selected Topics

MATH 5305 Financial Math

#### Applied Statistics

This program is designed to place students into an industry working as a statistician. In addition to the 12 hours of core courses listed above, the degree requires MATH 7351, 7352, and 7353, 9 hours of courses in an area of emphasis, MATH 8300 or 6 hours of approved electives, and written and oral comprehensive examinations.

#### Approved Electives

MATH 7354 Experimental Design

MATH 7355 Sampling Techniques

MATH 7312 Computational Linear Algebra

MATH 7399 Selected Topics

MATH 5305 Financial Math

#### Emphasis Areas

MATH 7399 Special Topics

MATH 7354 Experimental Design

MATH 7355 Sampling Techniques

#### Examples of elective courses include:

STAT 7343 Programming in SAS

MATH 7350 Mathematical Statistics I

MATH 7351 Mathematical Statistics II

MATH 7352 Mathematical Statistics III

MATH 7353 Linear and Nonlinear Regression Models

MATH 7354 Experimental Design

#### Graduation Requirements

- Successful completion of an approved program of study.
- Pass both the written and oral comprehensive exams.

### Courses in Mathematics

**MATH 5199, 5299, 5399 Selected Topics**

Prerequisites: graduate standing, consent of instructor. Content varies; see semester schedule. One hour lecture per week for each hour of credit. Offered on demand.

**MATH 5301 Analysis I**

Prerequisites: MATH 2307, 3312. Real number system, Euclidean n-space, complex numbers, topology of general metric spaces, continuous functions, point-wise and uniform convergence, series, the derivative. Offered on demand.

**MATH 5302 Complex Analysis**

Prerequisite: grade of C or greater in MATH 5303. Algebra of complex numbers, analytic functions, integration, power series, Laurent series, elementary conformal mappings. Three hours lecture per week.

**MATH 5303 Advanced Calculus I**

Prerequisites: MATH 2307, 3312. Real number system, sequences, limits, continuity, metric spaces, convexity, derivatives, linear analysis, implicit function theorem.

**MATH 5304 Advanced Calculus II**

Prerequisite: MATH 4303/5303. Measure theory, geometry of curves and surfaces, differential forms, Stoke’s theorem, and Green’s theorem.

**MATH 5305 Financial Mathematics**

Prerequisites: Math 1451 or equivalent. Determining equivalent measures of interest; discounting; accumulating; determining yield rates; estimating the rate of return on a fund; amortization. Three credit hours.

**MATH 5308 Integral Transform Theory**

Prerequisite: MATH 3322. Linear differential equations; Laplace transform; functions of complex variable, integration by method of residues, Laplace transform inversion integral; Z- transform, Z-transform inversion integral, difference equations; Fourier series, Fourier transform.

**MATH 5323 Numerical Analysis**

Prerequisites: MATH 2307 or equivalent, 3312 or equivalent; scientific programming language. Error analysis, solutions of equations, interpolation, approximations, numerical differentiation and integration, linear systems.

**MATH 7311 Advanced Linear Algebra**

Prerequisite: MATH 3312. Vector spaces, subspaces, linear independence and dependence, basis and dimensions; linear transformations, null space, rank, isomorphism, inner product spaces, norms, inner products, orthogonal sets, orthogonal projections, bilinear and quadratic forms; eigen values and eigen vectors, similar matrices, diagonalization, symmetric and Hermitian matrices. Jordan canonical form. Three lecture hours per week.

**MATH 7312 Computational Linear Algebra**

Prerequisites; MATH 3312 and MATH 4323. LU decomposition; QR factorization; Iterative techniques for solving systems of equations, Gauss-Seidel; Eigen value problem, iterative and direct techniques, The Condition Number; Lanczos Algorithm. Three lecture hours per week.

**MATH 7322 Advanced Differential Equations**

Prerequisite: MATH 3322. Power series solutions, systems of differential equations, nonlinear ordinary differential equations, phase plane analysis, stability, differential equations and applications.

**MATH 7323 Advanced Numerical Analysis I**

Prerequisites: MATH 4323, 7311. Numerical solutions of linear operator equations, some nonlinear systems, optimization methods.

**MATH 7324 Advanced Numerical Analysis II**

Prerequisites: MATH 7323 and 7325. Numerical analysis of ordinary and partial differential equations. Three lecture hours per week.

**MATH 7325 Partial Differential Equations**

Prerequisites: MATH 3322 or equivalent course. First order equations in two independent variables, the method of characteristics, discontinuous and weak solutions; Linear second order equations, elliptic equations, hyperbolic equations, parabolic equations; Fourier series. Three lecture hours per week.

**MATH 7326 Optimization**

Prerequisites: MATH 3312 and 3322 or equivalent courses. Linear and nonlinear programming. Three lecture hours.

**MATH 7327 Graph Theory**

Prerequisites: MATH 3312 or equivalent course. Graphs and subgraphs; trees; connectivity; Euler tours and Hamiltionian cycles; matchings; planar graphs; directed graphs; networks. Three lecture hours per week.

**MATH 7330 Theory of Finite Element Methods**

Prerequisites: Math 2453 and Math 3322 or equivalent. Finite element method is a numerical technique for finding approximate

solutions of partial differential equations. It has strong applications in engineering. This course will provide mathematical foundation for finite element method. Three lecture hours per week. Three credit hours.

**MATH 7350 Mathematical Statistics I**

Probability measures, combinatorial theory, random variables, continuous and discrete distributions, expectations, moments,

jointly distributed random variables, independence, functions of a random variable, limit theorems.

**MATH 7351 Mathematical Statistics II**

Sampling, sampling distributions, order statistics, point estimators and their properties, interval estimators and their properties, tests of hypotheses, linear models, nonparametric methods.

**MATH 7352 Mathematical Statistics III**

Prerequisites: MATH 7350. Multivariate distribution theory and quadratic forms; Linear models and least squares; Analysis of

categorical data; Non-parametric statistics; Decision theory and Baysian inference. Three lecture hours per week.

**MATH 7353 Linear/Non-Linear Regression**

Prerequisites: MATH 7350. Differentiation of vectors and matrices; random vectors and matrices; distribution theory; full rank linear regression models; non-linear regression models. Three lecture hours per week.

**MATH 7354 Experimental Design**

Prerequisites: MATH 7350 (may be taken as a corequisite with the consent of the instructor). Single factor experiments; Randomized blocks and Latin square designs; factorial designs; repeated measures; nested designs; response surfaces. Three lecture hours per week.

**MATH 7313 Real Analysis**

Prerequisites: A grade of C or greater in MATH 4302/5302. Set theory and axioms, functions of a real variable, Lévesque measure, differentiation and integration, Branch Spaces

**MATH 7355 Sampling Techniques**

Prerequisites: MATH 7350 (may be taken as a corequisite with the consent of the instructor). Simple random sampling; sampling

for proportions; stratified random sampling; ratio estimators; systematic random sampling; cluster sampling; acceptance sampling. Three lecture hours.

**MATH 7399 Selected Topics in Applied Mathematics**

Prerequisite: consent of instructor. Topics in mathematics, applied mathematics, and numerical analysis may include discrete

mathematics; ordinary, partial differential equations; integral transforms; complex variables; optimization techniques, linear algebra; approximation theory; topology; geometry; abstract algebra; number theory. Topics in statistics may include statistical inference, sampling, linear models, biostatistics, stochastic processes, statistical computing. May be repeated for credit when topic changes. Offered on demand.

**MATH 8300 Master Research Project**

Prerequisite: 18 graduate hours. Research and individual investigation on a topic in applied mathematics.