Admissions | Program Requirements | Graduate Courses |

**ETAS, Room 405, (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

Students may be admitted to the program for **regular admission** with the following:

- Baccalaureate degree from a regionally accredited institution with a cumulative grade point average of 2.70 (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.

Students with an undergraduate cumulative GPA between 2.0 and 2.69, or a a GPA between 2.7 and 3.0 in their last 60 hours may petition the department for consideration for **special conditional admission**. Applicants must discuss and provide evidence regarding two or more of the following criteria as part of their petition:

- GPA in previous mathematics/statistics courses
- Amount of time elapsed since the previous degree (5+ years preferred)
- Professional experience in mathematics, statistics, or teaching
- Professional accomplishments that demonstrate the applicant’s abilities with respect to time management or focused, intensive study
- Extraordinary circumstances related to the overall low GPA

Applicants whose petitions are approved by the department must maintain a GPA of 3.0 or higher in their first 9 hours of coursework in order to remain in the program. Special conditionally admitted students may also be subject to other conditions for enrollment, such as required courses in the first 9 hours of study as specified by the admissions committee. Special conditionally admitted students completing their M.S. coursework with a GPA of 3.0 or higher after their first 9 credit hours will become regularly admitted.

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

## Early Entry B.S./B.A. to M.S.

The Early Entry B.S./B.A. to M.S. for Mathematics majors interested in pursuing a M.S. in Mathematics after graduation is intended to serve as a fast path for completing the Master’s degree following completion of an undergraduate degree in mathematics.

### Admissions

Students are strongly encouraged to apply to the Early Entry program before the end of their junior year to help ensure that they have the full subsequent year to begin taking appropriate courses for graduate credit.

Undergraduate students may apply and be accepted provisionally into the M.S. Mathematics graduate program any time after completing 75 or more hours of undergraduate course work. However, at least 90 hours of undergraduate course work must have been completed by the time the first graduate Mathematics course is taken.

All applicants must have at least a 3.2 overall GPA and at least a 3.5 major GPA to be considered. Students who have transferred to our program can participate provided their relevant transfer course work (i.e. courses taken at other institutions that are being used to meet our B.S./B.A. requirements) also meets the 3.2 minimum GPA criteria and 3.5 minimum major GPA criteria. The GRE requirement is waived for students with an overall 3.5 GPA or higher. Students with an overall GPA between 3.2 and 3.49 must apply using the GRE option.

All applicants must complete an application for and be admitted into the M.S. in Mathematics program and the Graduate School.

All applicants must complete an Early-Entry Program form and be approved for admission by the M.S. Mathematics graduate coordinator. The graduate coordinator’s decision is final and cannot be appealed. The form must be approved by the graduate coordinator before the student begins graduate course work. Failure to obtain prior approval negates the ability to “double count” courses.

If, at the end of the student’s baccalaureate degree, an Early Entry B.S./B.A. to M.S. student has failed to meet the Graduate School admission requirement of 2.7 overall undergraduate GPA, the student will be dismissed from the M.S. Mathematics program.

Once a completed application has been received by the Department of Mathematics and Statistics, the student will be notified quickly, generally within 30 days, whether they have been accepted into the program.

Acceptance into the Early Entry B.A./B.S. to M.S. program indicates a commitment by the student to pursue the M.S. degree in mathematics after the completion of the baccalaureate degree in mathematics.

A completed application consists of:

- A completed graduate application for for the UA Little Rock Graduate School
- Completed Early-Entry Program form
- Two letters of recommendation, one of which must be from an university faculty member in the Department of Mathematics and Statistics (letters are to be submitted directly by recommenders)
- Portfolio of work in mathematics courses (optional)

Submit your application to the Early Entry B.A./B.S. to M.S. Program Coordinator.

### Program Restrictions

To ensure that they follow the proper degree plan, students must meet with the M.S. Mathematics graduate coordinator upon acceptance to the Early Entry B.A./B.S. to M.S. program to map out and approve the graduate courses they will take. Accepted students will have provisional status in the graduate program, pending the award of the baccalaureate degree. Students accepted into the Early Entry B.A./B.S. to M.S. program will be subject to the same policies as traditionally matriculated M.S. Mathematics students.

The Early Entry B.A./B.S. to M.S. program may not be used in conjunction with the credit reservation program; therefore, no graduate courses taken before admission to the program may be applied to the M.S. Mathematics degree.

### Program Requirements for M.S.

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; three research project hours or six alternate hours; nine hours of mathematical emphasis courses; nine hours from specialization; and written and oral comprehensive examination.

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

### 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

In addition to the 12 hours of core courses listed above, the degree requires 9 hours of emphasis courses, 9 hours of elective courses, a master’s research project or 6 more hours of electives, 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 5305 Financial Math

MATH 5306 Topology

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 7390 Teaching Collegiate Math

##### Applied Statistics

In addition to the 12 hours of core courses listed above, the degree requires 9 hours of emphasis courses, 9 hours of elective courses, a master’s research project or 6 more hours of electives, and written and oral comprehensive examinations.

###### Emphasis Areas

MATH 7351 Mathematical Statistics II

MATH 7352 Mathematical Statistics III

MATH 7353 Linear and Nonlinear Regression

###### Approved Electives

STAT 5342 Introduction to SAS

STAT 7343 Programming in SAS

STAT 7340 Advanced Statistical Methods I

STAT 7341 Advanced Statistical Methods II

MATH 5305 Financial Math

MATH 5306 Topology

MATH 7354 Experimental Design

MATH 7355 Sampling Techniques

MATH 7312 Computational Linear Algebra

MATH 7390 Teaching Collegiate Math

MATH 7399 Selected Topics

#### 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 5306 Topology**

Prerequisities: a grade of C or greater in MA TH 2350 and MATH 2453 Topological spaces, connectedness, compactness, separation axioms, metric spaces, sequences, completeness, Urysohn’s metrization theorm, homotopy, the fundamental group. Additional topics selected from The Tychonofftheorem, compactifications. Dual-listed in the UALR Undergraduate Catalog as MATH 4306. This course is not open to students with credit for MATH 4306. 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 5361 History of Mathematics I**

This course will provide an overview of aspects of the history of mathematics from the early beginnings to the sixteenth century. This survey/seminar course is organized to focus on discussion, group work, inquiry-based learning approaches, and less lecture. Attention will be on how the history of mathematics is important in the teaching of mathematics. This course gives historical perspectives of number systems, numbers and operations, algebra, geometry, trigonometry, calculus, discrete mathematics, probability, statistics/data analysis, and measurement.

**MATH 5362 History of Mathematics II**

This course will provide an overview of aspects of the history of mathematics from the sixteenth century to the present. This survey/seminar course is organized to focus on discussion, group work, inquiry-based learning approaches, and less lecture. Attention will be on how the history of mathematics is important in the teaching of mathematics. This course gives historical perspectives of number systems, numbers and operations, algebra, geometry, trigonometry, calculus, discrete mathematics, probability, statistics/data analysis, and measurement.

**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 7390 Teaching Collegiate Math**

Research-based investigation of teaching college-level mathematics courses: placement, prerequisites, remedial courses, service courses, preparing syllabi, grading, technology, pedagogical strategies. Three credit hours.

**MATH 7395 Master Research Project**

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

**MATH 7396 Master Research Project in Collegiate Math Education**

This course is built on a research project that explores the nature of students’ understanding and misconception of collegiate mathematics. This course will introduce techniques for assessing students’ skills and understanding, and develop teaching interventions to improve students’ learning. Three credit 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.

### Courses in Statistics

**STAT 7340 Advanced Statistical Methods I**

Prerequisite: A grade of C or greater in MATH 1451 and STAT 3352 or equivalent. This course is designed to cover the more common advanced statistical concepts and methods. Probability theory, collecting data, sampling, inference, interval estimation, tests of hypotheses for single mean, two means, proportions, and the use of computer packages.

**STAT 7341 Advanced Statistical Methods II**

Prerequisite: A grade of B or greater in STAT 7340. This course is designed to cover the more common and advanced statistical concepts and methods. Simple linear regression, multiple linear regression, ANOVA of single factor experiments, ANOVA of multi-factor experiments, non-parametric methods, categorical data analysis, Bayesian decision theory and methods, and the use of computer packages.

**STAT 7342 Introduction to SAS**

This course is designed to introduce students in all disciplines to conducting data analyses and managing data using the SAS system and SAS programming language. The basics of the SAS language and SAS data sets, reading SAS logs, viewing and printing output, inputting data into SAS, manipulating data and creating new variables using SAS procedures, generating descriptive statistics and frequency distributions using SAS Insight. Performing hypothesise tests and constructing confidence intervals, building categorical models, building and interpreting simple and multiple linear regression models, constructing ANOVA models using SAS procedures and Analyst. Three credit hours.

**STAT 7343 Programming in SAS**

Prerequisite: A grade of B or greater in STAT 7342. This course is designed to introduce students in all disciplines to conducting a deep SAS programming on topics in statistical simulation and computation using the SAS system and SAS programming language. Pseudo-random-variate generation, optimization, Monte Carlo simulation, Bootstrap, and Jackknife methods.