116 Petty Building • 336-334-5836 • **www.uncg.edu/mat**

**Administration**

Ratnasingham Shivaji, Department Head

Maya Chhetri, Director of Graduate Study

**About **

The department offers a variety of outstanding graduate programs. Our faculty and staff serve nearly 4,000 students every year. The faculty consists of nationally and internationally recognized researchers in diverse areas of mathematics, statistics and mathematics education. They are also outstanding professionals committed to teaching excellence, and they take great pride in guiding our students to enjoy the beauty of mathematics.

The department has also been hosting various professional conferences and special events, lecture series, colloquia and seminars. These activities have greatly enhanced our students’ learning experience at UNCG. Most of our graduate students are supported via attractive graduate assistantships.

**Mission statement **

The mission of the Department of Mathematics and Statistics at the University of North Carolina at Greensboro is to provide intellectual leadership in the mathematical sciences that is of direct benefit to the State of North Carolina and that commands national and international respect for the quality of its educational programs and for its depth of scholarship.

**Graduate Programs**

- Post-Baccalaureate Certificate in Statistics, (12)
- Master of Arts (MA) in Mathematics, Mathematics, Applied Statistics, Actuarial Mathematics, and Data Analytics concentrations, (30-33)
- Doctor of Philosophy (PhD) in Computational Mathematics, (60 hours minimum)
- Doctoral Minor in Statistics, (18)

__Professors__**Maya Chhetri**, Nonlinear elliptic PDE’s, nonlinear functional analysis, applied mathematics (Director of Graduate Study). (E)**Richard H. Fabiano**, Analysis, applied mathematics, differential equations, and control theory. (E)**Sat N. Gupta**, Sampling designs, time series forecasting, biostatistics (Associate Head). (E)**Scott J. Richter**, Nonparametric methods, equivalence testing, statistical consulting. (E)**Jan Rychta**r, Functional analysis, game theory. (E)**Ratnasingham Shivaji**, Partial differential equations (Head of the Department). (E)**Jerry E. Vaughan**, General topology and set theory. (E)

__Associate Professors__

**Gregory Bell**, Geometric group theory, geometric topology, asymptotic invariants of groups. (E)**Igor Erovenko**, Combinatorial properties of linear groups, bounded generation of S-arithmetic groups.**Talia Fernos**, Group theory.**Xiaoli Gao**, Statistics.**Sebastian Pauli**, Computational number theory, algebraic number theory, computer algebra. (E)**Filip Saidak**, Analytic and probablistic number theory, mathematical biology.**Carol Seaman**, Undergraduate mathematics education.**Clifford Smyth**, Combinatorics. (E)**Brett A. Tangedal**, Number theory. (E)**Dan Yasaki**, Number Theory.**Haimeng Zhang**, Spatial statistics, survival analysis, computational statistics, applied probability. (E)

__Assistant Professors__

**Thomas Lewis**, Computational mathematics, applied math.**Jonathan Rowell**, Mathematical biology, applied math.**Dohyoung Ryang**, Mathematics education, efficacy beliefs, learning community, lesson study, geometric group theory.

**Statistics, PBC, (12)**

The purpose of the 12-hour Post-Baccalaureate Certificate in Statistics is to provide statistical training for persons who wish to enhance their knowledge of statistics but do not wish to pursue a formal degree and for professionals whose interests require a knowledge of statistics beyond the undergraduate level. The objective of the certificate is to offer a structured introduction to the basic ideas of graduate level statistical analysis.

**Application and Admission**

For information regarding deadlines and requirements for admission, please see the **Guide to Graduate Admissions**.

**Degree Requirements**

**Required Courses (6)**

STA 661 Advanced Statistics in the Behavioral and Biological Sciences I (3)

STA 662 Advanced Statistics in the Behavioral and Biological Sciences II (3)

**Electives (6)**

Students must complete two additional three-hour STA courses at the 500 level or above, excluding:

STA 571 Statistical Methods for Research I (3)

STA 572 Statistical Methods for Research II (3)

STA 580 Biostatistical Methods (3)

**Mathematics, MA, (30-33)**

The MA in Mathematics is offered in four areas of concentration: mathematics (30-33), applied statistics (33), actuarial mathematics (30), and data analytics (30). Course work must be approved by the Department of Mathematics and Statistics and must include certain courses as explained in the discussion of the concentrations.

Students who plan to continue to the PhD program in computational mathematics are urged to elect the concentration in mathematics. They may then use the doctoral qualifying examinations to satisfy the comprehensive examination requirement in the non-thesis option for the MA degree.

**Application and Admission**

For information regarding deadlines and requirements for admission, please see the **Guide to Graduate Admissions**.

In addition to the application materials required by The Graduate School, applicants must submit a 500-700 word Personal Statement to be considered for admission.

*Mathematics Concentration (30-33)*

The mathematics concentration offers a 30-hour thesis or project option and a 33-hour coursework option. At least half the work credited towards the degree must be in 600-level courses: 15 hours for the 30-hour program, and 18 hours for the 33-hour program.

**Algebra or Analysis (3)**

Each candidate must complete any one of the following courses:

MAT 517 Theory of Groups (3)

MAT 545 Differential Equations and Orthogonal Systems (3)

MAT 591 Advanced Abstract Algebra (3)

MAT 592 Advanced Abstract Algebra (3)

MAT 595 Mathematical Analysis (3)

MAT 596 Mathematical Analysis (3)

*Note*: Students who have had appropriate algebra or analysis courses as undergraduates may be exempted from this requirement upon approval by the Director of Graduate Study. In this case, these 3 hours must be replaced by 3 hours chosen in consultation with the Director of Graduate Study.)

**Core Courses (9)**

At least 9 hours of course work must be chosen from the following list. At least 6 of these hours must constitute a complete year-long sequence.

MAT 723 Numerical Mathematics (3)

MAT 724 Numerical Mathematics (3)

MAT 731 Combinatorics (3)

MAT 732 Graph Theory (3)

MAT 727 Linear Algebra and Matrix Theory (3)

MAT 728 Linear Algebra and Matrix Theory (3)

CSC 653 Advanced Theory of Computation (3)

CSC 656 Foundations of Computer Science (3)

CSC 653 Advanced Theory of Computation (3)

CSC 656 Foundations of Computer Science (3)

MAT 688 Mathematical Logic and Axiomatic Set Theory (3)

MAT 689 Mathematical Logic and Axiomatic Set Theory (3)

MAT 741 Modern Abstract Algebra (3)

MAT 742 Modern Abstract Algebra (3)

MAT 743 Complex Analysis (3)

MAT 744 Complex Analysis (3)

MAT 745 Real Analysis (3)

MAT 746 Real Analysis (3)

MAT 737 General Topology (3)

MAT 738 General Topology (3)

MAT 645 Approximation Theory (3)

MAT 646 Approximation Theory (3)

STA 651 Mathematical Statistics (3)

STA 652 Mathematical Statistics (3)

**Electives (12-21)**

With prior approval of the Director of Graduate Study a student will select 12-21 hours of other 500-or 600-level mathematical sciences courses.

**Thesis, Project, or Comprehensive Examination (Capstone Experience)**

Each candidate may elect to prepare a thesis or project, or pass a written comprehensive examination on his/her program of course work. The thesis or project option is a 30 hour program; the coursework option with a comprehensive exam is a 33 hour program.

**Thesis (6)**

The candidate may prepare a thesis based on the investigation of a topic in mathematics. A thesis director will be appointed by the Department Head after consultation with the student and the Director of Graduate Study. Candidates may include up to 6 hours of thesis (MAT 699) in the required 30 hours. An oral examination on the thesis is required.

**Project in Mathematics (3)**

The candidate may prepare a project in mathematics based on in-depth investigation of a topic in mathematics. A project director will be appointed by the Department Head after consultation with the student and the Director of Graduate Study. Candidates may include 3 hours of project (MAT 687) in the required 30 hours. A written report and an oral examination on the project are required.

**Comprehensive Examination**

A candidate who does not prepare a thesis must take 33 hours of course work and pass a written comprehensive examination of his/her program. Please consult with the Director of Graduate Study for information concerning the comprehensive examination.

*Applied Statistics Concentration (33)*

Undergraduate prerequisites: Baccalaureate degree and the following courses or their equivalents: STA 290, 291; MAT 191, 292; and CSC 130 or 230 or 231.

**Foundation Courses (7)**

STA 551 Introduction to Probability (3)

STA 552 Introduction to Mathematical Statistics (3)

STA 581 SAS System for Statistical Analysis (1)

Students who have completed these courses as part of another degree prior to being accepted in the master’s program will choose replacement courses.

**Core Courses (8)**

STA 661 Advanced Statistics in the Behavioral and Biological Sciences I (3)

STA 662 Advanced Statistics in the Behavioral and Biological Sciences II (3)

STA 668 Consulting Experience (1)

STA 690 Graduate Seminar (1)

**Statistics Electives (6-9)**

At least two courses chosen from the following:

STA 670 Categorical Data Analysis (3)

STA 671 Multivariate Analysis (3)

STA 673 Statistical Linear Models I (3)

STA 674 Statistical Linear Models II (3)

STA 675 Advanced Experimental Design (3)

STA 676 Sample Survey Methods (3)

STA 677 Advanced Topics in Data Analysis and Quantitative Methods (3)

STA 711 Experimental Course

**Interdisciplinary Electives (3-6)**

Student can earn the remaining credits required for the degree either by taking any STA courses at the 500 level or above (except STA 571) or by taking a maximum of six (6) hours of approved graduate courses outside of statistics. Pre-approved interdisciplinary electives are:

CSC 523 Numerical Analysis and Computing (3)

CSC 524 Numerical Analysis and Computing (3)

CSC 526 Bioinformatics (3)

ECO 663 Predictive Data Mining (3)

ECO 664 Time Series and Forecasting (3)

ERM 669 Item Response Theory (3)

ERM 728 Exploratory and Confirmatory Factor Analytic Methods for Scale Construction (3)

ERM 729 Advanced Item Response Theory (3)

ERM 731 Structural Equation Modeling in Education (3)

HEA 602 Epidemiology (3)

MAT 531 Combinatorial Analysis (3)

MAT 541 Stochastic Processes (3)

MAT 542 Stochastic Processes (3)

**Thesis or Project (Capstone Experience)**

Each candidate must elect to prepare a thesis or project. Both options require 33 hours.

**Thesis (6)**

The candidate may prepare a thesis based on the investigation of a topic in statistics. A thesis director will be appointed by the Department Head after consultation with the student and the Director of Graduate Study. Candidates will include 6 hours of thesis (STA 699) or 3 hours of STA 698 and 3 hours of STA 699 in the required 33 hours. An oral examination on the thesis is required.

**Project (3)**

A candidate who does not prepare a thesis must complete a project under the direction of an advisor chosen by the Director of Graduate Study in consultation with the student. Three hours of STA 698 will be included in the 33 hour program.

*Actuarial Mathematics Concentration (30)*

The MA in Mathematics with concentration in Actuarial Mathematics provides students wishing to pursue a career in actuarial science a solid foundation in Applied Probability and Statistical Models and their applications in the area of actuarial science. It is designed to help students pass the preliminary actuarial exams while providing educational experiences related to the actuarial field. Students will be encouraged to seek internship opportunities during the summer. The concentration requires 30 credit hours and is offered with an optional project. At least 15 hours must be at the 600-level or above.

The target student population for this program will be students with a bachelor’s degree in mathematics, statistics, economics, finance, or a related field who want to pursue an actuarial industry who want to advance their career.

**Required Foundations and Methods (12)**

STA 551 Introduction to Probability (3)

STA 552 Introduction to Mathematical Statistics (3)

STA 655 Applied Probability Models (3)

MAT 586 Financial Mathematics for Actuaries (3)

**Elective Courses (15-18)**

Actuarial exam and Applied Statistics models (at least 9 credits)

STA 686 Actuarial Models I (3)

STA 687 Actuarial Models II (3)

STA 591 Actuarial Exam Preparation Seminar (1)

STA 573 Theory of Linear Regression (3)

STA 682 Theory of Time Series (3)

STA 565 Analysis of Survival Data (3)

**Other Applied Statistics Courses (at most 6 credits)**

Any other STA 600 level courses, excluding those listed above and STA 651, STA 652, STA 667, STA 668, STA 690, STA 699 Actuarial Educational Experiences Courses (at most 6 credits)

ECO 641 Microeconomics I (3)

ECO 646 Macroeconomics (3)

ISM 671 Data Management (3)

ISM 675 Models and Methods in Business Analytics (3)

MBA 702 Financial and Managerial Accounting (3)

MBA 707 Financial Management (3)

**Capstone Course (at most 3 credits)**

STA 698 Project in Statistics (3)

*Data Analytics Concentration (30)*

The concentration in Data Analytics provides students with advanced analytical training to develop their ability to draw insights from big data, including: data collection, preparation and integration, statistical methods and modeling, and other techniques for analyzing complex data. The program is highly applied in nature, integrating project-based learning, simulations, case studies, and specific electives addressing the analytical needs of various industry sectors. The concentration requires a minimum of 30 hours including either a project (3) or thesis (6) option.

**Analytics Methods and Foundations (15)**

STA 551 Introduction to Probability (3)

STA 552 Introduction to Mathematical Statistics (3)

STA 562 Statistical Computing (3)

STA 673 Statistical Linear Models I (3)

STA 703 Topics in High Dimensional Data Analysis (3)

**Analytics Applications (9-12)**

At least two courses chosen from

STA 565 Analysis of Survival Data (3)

STA 575 Nonparametric Statistics (3)

STA 661 Advanced Statistics in the Behavioral and Biological Sciences I (3)

STA 662 Advanced Statistics in the Behavioral and Biological Sciences II (3)

STA 670 Categorical Data Analysis (3)

STA 671 Multivariate Analysis (3)

STA 674 Statistical Linear Models II (3)

STA 677 Advanced Topics in Data Analysis and Quantitative Methods (3)

**At most two courses chosen from**

ECO 663 Predictive Data Mining (3)

ECO 664 Time Series and Forecasting (3)

ECO 725 Data Methods in Economics (3)

CSC 510 Big Data and Machine Learning (3)

CSC 655 Advanced Topics in Algorithms (3)

CSC 671 Advanced Database Systems (3)

CSC 676 Topics in Database Systems (3)

ISM 671 Data Management (3)

ISM 675 Models and Methods in Business Analytics (3)

ISM 685 Business Analytics for Competitive Advantage (3)

**Analytics Capstone (3-6)**

STA 698 Project in Statistics (3)

or

STA 699 Thesis (1-6)

**Computational Mathematics, PhD, (60 hours minimum)**

The PhD in Computational Mathematics requires a minimum of 60 semester hours, including 39-42 hours of course work in mathematics or related area and 18-21 hours of dissertation.

**Application and Admission**

For information regarding deadlines and requirements for admission, please see the **Guide to Graduate Admissions**.

In addition to the application materials required by The Graduate School, applicants must submit a 500-700 word Personal Statement to be considered for Fall admission.

Students with a master’s degree in mathematics, computer science or statistics may apply directly to the PhD program. In exceptional cases well-qualified applicants will be considered for admission directly after completing an undergraduate degree in mathematics, computer science or statistics.

**Degree Requirements**

**Course Work (39-42)**

The student selects 39-42 hours of course work in mathematics and related areas with the approval of the Director of Graduate Study. With the approval of the Director of Graduate Study, up to 18 of the 39-42 hours may be accepted from UNCG’s MA in mathematics program or from a comparable master’s program.

**Qualifying Examinations**

Qualifying examinations, covering a student’s chosen field of research and related advanced course work, must be taken after the student has removed any provisions or special conditions attached to admission; two exams should be passed prior to the beginning of the fifth semester. These examinations each cover the material of one of the following two-course sequences:

*Analysis*

MAT 595 Mathematical Analysis (3)

MAT 596 Mathematical Analysis (3)

*Linear Algebra*

MAT 727 Linear Algebra and Matrix Theory (3)

MAT 728 Linear Algebra and Matrix Theory (3)

*Mathematical Statistics*

STA 651 Mathematical Statistics (3)

STA 652 Mathematical Statistics (3)

**Preliminary Examination**

The preliminary exam is held in two parts: written and oral. The exam is constructed by a committee appointed by the Graduate Director in consultation with the student’s advisor and the Department Head. The exam covers material from at least three courses in addition to the qualifying exam courses. Students have at most two attempts to pass the preliminary exam. Students must have unanimous support of the committee to pass the exam.

**Programming Project**

The student must complete a programming project of such quality that it can become part of a computer algebra system, could be distributed as a package for a computer algebra system, or yields new mathematical data.

**Dissertation (18-21)**

MAT 799 Dissertation (1-12)

**Other Reviews and Examinations**

After the student has passed both qualifying examinations, has chosen a dissertation supervisor, and passed the preliminary exam, they form the dissertation committee in consultation with the Graduate Director. With the help of the supervisor, the student proposes a dissertation topic in a public oral presentation. In this presentation, the student explains his or her dissertation topic in sufficient detail to demonstrate capability to begin research.

At the conclusion of the presentation, the dissertation committee will administer an oral exam to determine the student’s competence to begin work on the dissertation. A part of the exam is the computational/programming project. This project should clearly demonstrate that the student is fully capable of handling computational aspects of the intended dissertation topic. After passing this examination, the student may then make a formal application to the Graduate School for admission to candidacy. The dissertation proposal and oral exam can be attempted at most twice.

**Schedule for Examinations and Projects**

Semester | Examination or Project |

1-4 | 2 written qualifying examinations |

4-7 | Preliminary exam, dissertation proposal, computational/programming project, (oral examination) |

6-14 | Dissertation work and defense (oral examination) |

**Statistics, Doctoral Minor, (18)**

Students pursuing a doctorate from other departments may obtain a statistics minor by completing 18 semester hours of graduate level statistics courses.

**Requirements**

**Required Courses (6)**

STA 661 Advanced Statistics in the Behavioral and Biological Sciences I (3)

STA 662 Advanced Statistics in the Behavioral and Biological Sciences II (3)

**Electives (12)**

Four additional three-hour STA courses, excluding:

STA 571 Statistical Methods for Research I (3)

STA 572 Statistical Methods for Research II (3)

STA 580 Biostatistical Methods (3)

**MAT 503 Problem Solving in Mathematics (3:3)**

Investigates the nature of problem solving, covers procedures involved in problem solving, develops individual problem solving skills, and collects a set of appropriate problems. Required for middle grades mathematics concentration.

*Prerequisite*

Grade of at least C in MAT 191 and MAT 303 or permission of instructor

*Notes*

Hours do not count toward degree requirements for Mathematics majors. This course cannot be applied toward the requirements for the M.A. degree in Mathematics.

**MAT 504 Foundations of Geometry for Teachers (3:3)**

Primarily for students seeking teacher certification. Includes logic and axiom systems, history, plane and solid Euclidean geometry, proof strategies, introduction to non-Euclidean geometries, and transformational geometry.

*Prerequisite*

Grade of at least C in MAT 292 or permission of instructor

*Offered*

Fall

*Notes*

Hours do not count toward degree requirements for Mathematics majors. This course cannot be applied toward the requirements for the M.A. degree in Mathematics.

**MAT 505 Foundations of Mathematics for Teachers (3:3)**

Primarily for students seeking teacher certification. Includes properties and algebra of real numbers; analytic geometry; polynomial, rational, exponential, logarithmic, and trigonometric functions; complex numbers; concept of limits of functions.

*Prerequisite*

Grade of at least C in MAT 292 or MAT 303 or permission of instructor

*Offered*

Spring

*Notes*

Hours do not count toward degree requirements for Mathematics majors. This course cannot be applied toward the requirements for the M.A. degree in Mathematics.

**MAT 513 Historical Development of Mathematics (3:3)**

Study of the historical development of mathematics, not a history of persons involved in development.

*Prerequisite*

Grade of at least C in MAT 292

*Offered*

Fall

*Notes*

Hours do not count toward degree requirements for a mathematics major. This course cannot be applied toward the requirements for the M.A. degree in Mathematics.

**MAT 514 Theory of Numbers (3:3)**

An introductory course to both multiplicative and additive number theory. Divisibility, prime numbers, congruencies, linear and nonlinear Diophantine equations (including Pell’s equation), quadratic residues, number-theoretic functions, and other topics.

*Prerequisite*

Grade of at least C in MAT 311

**MAT 515 Mathematical Logic (3:3)**

Formal languages, recursion, compactness, and effectiveness. First-order languages, truth, and models. Soundness and completeness theorems. Models of theories.

*Prerequisite*

Grade of at least C in MAT 311 or MAT 353

**MAT 516 Intermediate Abstract Algebra (3:3)**

Rings, integral domains, fields, division algorithm, factorization theorems, zeros of polynomials, greatest common divisor, formal derivatives, prime polynomials, Euclidean domains, the fundamental theorem of algebra.

*Prerequisite*

Grade of at least C in MAT 311

**MAT 517 Theory of Groups (3:3)**

Elementary properties of groups and homomorphisms, quotients and products of groups, the Sylow theorems, structure theory for finitely generated abelian groups.

*Prerequisite*

Grade of at least C in MAT 311

**MAT 518 Set Theory and Transfinite Arithmetic (3:3)**

The axioms of set theory, operations on sets, relations and function, ordinal and cardinal numbers.

*Prerequisite*

Grade of at least C in MAT 311 or MAT 395

**MAT 519 Intuitive Concepts in Topology (3:3)**

Basic concepts, vector fields, the Jordan curve theorem, surfaces, homology of complexes, continuity.

*Prerequisite*

Grade of at least C in MAT 311 or MAT 395

**MAT 520 Non-Euclidean Geometry (3:3)**

Fifth postulate, hyperbolic geometries, elliptic geometries, consistency of non-Euclidean geometries, models for geometries, elements of inversion.

*Prerequisite*

Grade of at least C in MAT 311 or MAT 395

**MAT 521 Projective Geometry (3:3)**

Transformation groups and projective, affine and metric geometries of the line, plane, and space. Homogeneous coordinates, principles of duality, involutions, cross-ratio, collineations, fixed points, conics, models, and Euclidean specifications.

*Prerequisite*

Permission of instructor

**MAT 522 Introductory Functional Analysis (3:3)**

Basic concepts in Banach spaces, Hilbert spaces, linear operators, and their applications.

*Prerequisite*

Grade of at least C in MAT 395

**MAT 525 Intermediate Mathematical Analysis (3:3)**

Integration, infinite series, sequences and series of functions.

*Prerequisite*

Grade of at least C in MAT 395

**MAT 531 Combinatorial Analysis (3:3)**

The pigeon-hole principle, permutations, combinations, generating functions, principle of inclusion and exclusion, distributions, partitions, recurrence relations.

*Prerequisite*

Grade of at least C in MAT 253 or MAT 295 or MAT 311 or MAT 395, or permission of instructor

**MAT 532 Introductory Graph Theory (3:3)**

Basic concepts, graph coloring, trees, planar graphs, networks.

*Prerequisite*

Grade of at least C in MAT 310 and any one of the courses MAT 253, MAT 295, MAT 311, MAT 395, MAT 531

**MAT 540 Introductory Complex Analysis (3:3)**

The complex number system, holomorphic functions, power series, complex integration, representation theorems, the calculus of residues.

*Prerequisite*

Grade of at least C in MAT 394; grade of at least C in MAT 395 for Mathematics majors

**MAT 541 Stochastic Processes (3:3)**

Markov processes, Markov reward processes, queuing, decision making, graphs, and networks. Applications to performance, reliability, and availability modeling.

*Prerequisite*

Grade of at least C in MAT 394 and either MAT 353 or STA 351, or equivalents

**MAT 542 Stochastic Processes (3:3)**

Markov processes, Markov reward processes, queuing, decision making, graphs, and networks. Applications to performance, reliability, and availability modeling.

*Prerequisite*

Grade of at least C in MAT 394 and either MAT 353 or STA 351, or equivalents

**MAT 545 Differential Equations and Orthogonal Systems (3:3)**

An introduction to Fourier series and orthogonal sets of functions, with applications to boundary value problems.

*Prerequisite*

Grade of at least C in MAT 293 and MAT 390 or permission of instructor

**MAT 546 Partial Differential Equations with Applications (3:3)**

Fourier integrals, Bessel functions, Legendre polynomials and their applications. Existence and uniqueness of solutions to boundary value problems.

*Prerequisite*

Grade of at least C in MAT 545

**MAT 549 Topics in Applied Mathematics (3:3)**

Selected topics of current interest in applied mathematics.

*Prerequisite*

Grade of at least C in MAT 293 and MAT 390 or permission of instructor

*Notes*

May be repeated for credit with approval of the Department Head.

**MAT 556 Topics in Discrete Mathematics (3:3)**

Selected topics of current interest in discrete mathematics.

*Prerequisite*

Grade of at least C in MAT 353

**MAT 586 Financial Mathematics for Actuaries (3:3)**

Measurement of interest, present and accumulated value, amortization, sinking funds, bonds, duration, immunization, and an introductory analysis of financial derivatives. Intended to help prepare for the FM/2 actuarial exam.

*Prerequisite*

Grade of at least C in MAT 394, or permission of instructor

**MAT 589 Experimental Course**

This number reserved for experimental courses. Refer to the Course Schedule for current offerings.

**MAT 590 Mathematical Models in Biology (3:3)**

Exploration of research and methodology at the interface of mathematics and biology, with an overview of relevant fields and in-depth case studies. Focus will be on mathematical models in biology.

*Cross Listed Courses*

Same as BIO 590.

*Prerequisite*

B-or higher in BIO 112 and either MAT 191 or STA 271; or instructor’s permission

**MAT 591 Advanced Abstract Algebra (3:3)**

Groups: homomorphisms, quotient groups, Sylow theorems, finitely generated abelian groups. Rings: homomorphisms, ideals, quotient rings, integral domains, Euclidean domains, factorization. Fields: algebraic extensions of fields, Galois theory.

*Prerequisite*

Grade of at least C in MAT 516

**MAT 592 Advanced Abstract Algebra (3:3)**

Groups: homomorphisms, quotient groups, Sylow theorems, finitely generated abelian groups. Rings: homomorphisms, ideals, quotient rings, integral domains, Euclidean domains, factorization. Fields: algebraic extensions of fields, Galois theory.

*Prerequisite*

Grade of at least C in MAT 516

**MAT 593 Directed Study in Mathematics (1–3)**

*Offered*

Fall & Spring

**MAT 594 Directed Study in Mathematics (1–3)**

*Offered*

Fall & Spring

**MAT 595 Mathematical Analysis (3:3)**

Real number axioms, metric spaces, sequences, series, continuity, differentiation, the Riemann-Stieltjes integral.

*Prerequisite*

MAT 395 or permission of instructor

**MAT 596 Mathematical Analysis (3:3)**

Real number axioms, metric spaces, sequences, series, continuity, differentiation, the Riemann-Stieltjes integral.

*Prerequisite*

MAT 395 or permission of instructor

**MAT 601 Seminar in the Teaching of Mathematics I (1:1)**

Seminar on practices and principles of undergraduate teaching in mathematics and statistics.

*Notes*

Required for all teaching assistants. Grade: Satisfactory/Unsatisfactory, S/U

**MAT 603 Practicum in the Teaching of Mathematics (2:0:6)**

Practicum in teaching mathematics at the college/university level. Topics include course design, class materials, exams, grading, syllabus, choosing textbooks, dealing with difficult matters, and mathematical typesetting.

*Corequisite*

MAT-601

**MAT 602 Seminar on Mathematical Software (3:3)**

Variety of issues in the design of mathematical software, i.e., type systems, user interfaces, and memory management. Each student investigates one computer algebra system more closely.

*Prerequisite*

Knowledge of a programming language

**MAT 606 Calculus for Middle Grade Teachers (3:3)**

History, developments, major concepts, and applications of differential and integral calculus covering functions of several variables.

*Prerequisite*

MAT 505 or permission of instructor

*Notes*

No credit toward mathematics degrees.

**MAT 607 Abstract Algebra for Middle Grade Teachers (3:3)**

Development and major concepts of abstract algebraic structures including groups, rings, fields, vector spaces, and matrix algebra.

*Prerequisite*

MAT 303 and MAT 505; or permission of instructor

*Notes*

No credit toward mathematics degrees.

**MAT 645 Approximation Theory (3:3)**

Normed linear spaces. Convexity. Existence and unicity of best approximations. Tchebycheff approximation by polynomials and other linear families. Least-squares approximation and related topics. Rational approximation. The characterization of best approximations. The Stone Approximation Theorem. The Muntz Theorem. Polygonal approximation and bases. Approximation in the mean.

*Prerequisite*

MAT 390, MAT 595, MAT 596

**MAT 646 Approximation Theory (3:3)**

Normed linear spaces. Convexity. Existence and unicity of best approximations. Tchebycheff approximation by polynomials and other linear families. Least-squares approximation and related topics. Rational approximation. The characterization of best approximations. The Stone Approximation Theorem. The Muntz Theorem. Polygonal approximation and bases. Approximation in the mean.

*Prerequisite*

MAT 390, MAT 595, MAT 596

**MAT 649 Topics in Operations Research (3:3)**

Advanced linear programming. Integer programming, nonlinear programming, inventory models and queueing models. Application of these optimization techniques in the general area of administration are demonstrated through examples via the digital computer.

*Prerequisite*

Permission of instructor

**MAT 650 Management Decision-Making Under Uncertainty (3:3)**

Models and techniques to be used in making decisions under uncertainty. Markov Chains, Linear Programming Under Uncertainty, and Chance-Constrained programming.

*Prerequisite*

Permission of instructor

**MAT 659 Advanced Topics in Mathematics (3:3)**

Topics vary according to interest and demand, and include algebra, applied mathematics, combinatorics, dynamics, mathematical logic, topology, and other topics.

*Prerequisite*

Permission of instructor

*Notes*

May be repeated for credit when topic varies.

**MAT 687 Project in Mathematics (3:0)**

Directed research projects in Mathematics.

**MAT 688 Mathematical Logic and Axiomatic Set Theory (3:3)**

Quantification theory, completeness theorems, prenex normal forms, categoricity. The characterization problem, consistency, the theory of models, isomorphisms and substructures, cardinality of models, joint consistency. Incompleteness and undecidability, recursive functions, Church’s thesis, Recursion theory, Set theory, the axiom of constructibility, forcing, the independence proofs.

*Prerequisite*

MAT 311, MAT 394, or equivalents

**MAT 689 Mathematical Logic and Axiomatic Set Theory (3:3)**

Quantification theory, completeness theorems, prenex normal forms, categoricity. The characterization problem, consistency, the theory of models, isomorphisms and substructures, cardinality of models, joint consistency. Incompleteness and undecidability, recursive functions, Church’s thesis, Recursion theory, Set theory, the axiom of constructibility, forcing, the independence proofs.

*Prerequisite*

MAT 311, MAT 394, or equivalents

**MAT 690 Mathematics Seminar (2:2)**

Topics in mathematics suitable for development into a master’s thesis. Current mathematical literature.

*Prerequisite*

Admission to candidacy for master’s degree

**MAT 699 Thesis (1–6)**

**MAT 701 Graduate Seminar in Computational Mathematics (3:3)**

Readings from the literature of computational mathematics.

*Prerequisite*

MAT 671 or permission of instructor

*Notes*

May be repeated for credit when topic varies.

**MAT 709 Topics in Computational Mathematics (3:3)**

Advanced study in special topics in computational mathematics.

*Prerequisite*

MAT 671 or permission of instructor

*Notes*

May be repeated for credit when topic varies.

**MAT 711 Experimental Course**

This number reserved for experimental courses. Refer to the Course Schedule for current offerings.

**MAT 721 Mathematical Cryptography (3:3)**

Mathematics of cryptography with emphasis on public key systems. Applications of elliptic and hyperelliptic curves and lattice theory in attacking and evaluating the security of cryptographic systems.

*Prerequisite*

MAT 671 or permission of instructor

**MAT 723 Numerical Mathematics (3:3)**

Functional analytic treatment of computation, approximation, optimization, interpolation, smoothing equations, linear systems, differential equations. Emphasis on the mathematical development and analysis of numerical techniques.

*Prerequisite*

MAT 390, MAT 595, MAT 596, or equivalents

**MAT 724 Numerical Mathematics (3:3)**

Functional analytic treatment of computation, approximation, optimization, interpolation, smoothing equations, linear systems, differential equations. Emphasis on the mathematical development and analysis of numerical techniques.

*Prerequisite*

MAT 390, MAT 595, MAT 596, or equivalents

**MAT 727 Linear Algebra and Matrix Theory (3:3)**

Vector spaces. Linear operators and similarity. The eigenvalue problem and a special decomposition theorem. Normal forms: Smith form for matrices, rational and Jordan forms. Spectral resolution of matrix functions. Special topics.

*Prerequisite*

MAT 310, MAT 311 or permission of instructor

**MAT 728 Linear Algebra and Matrix Theory (3:3)**

Vector spaces. Linear operators and similarity. The eigenvalue problem and a special decomposition theorem. Normal forms: Smith form for matrices, rational and Jordan forms. Spectral resolution of matrix functions. Special topics.

*Prerequisite*

MAT 310, MAT 311 or permission of instructor

**MAT 731 Combinatorics (3:3)**

Topics include selections, arrangements, theory of generating functions, inclusion-exclusion principle, recurrences, Polya’s theory, block designs, stirling numbers, coding theory.

*Prerequisite*

MAT 311 or permission of instructor

**MAT 732 Graph Theory (3:3)**

Topics include graphs, paths, trees, directed trees, networks, cycles and circuits, planarity, matching theory, independence, chromatic polynomials, Ramsey theory, extremal theory, the vector spaces associated with a graph.

*Prerequisite*

MAT 631 or permission of instructor

**MAT 735 Ordinary Differential Equations (3:3)**

Existence and uniqueness theorems for initial value problems, theory of linear equations, nonlinear equations, stability theory, boundary value problems.

*Prerequisite*

MAT 390 and MAT 595 or permission of instructor

**MAT 736 Partial Differential Equations (3:3)**

Derivation of partial differential equations (PDE) models and applications, linear first order PDE’s, elliptic equations and Green’s function, PDE’s of parabolic and hyperbolic type.

*Prerequisite*

MAT 735 or permission of instructor

**MAT 737 General Topology (3:3)**

Topological spaces, point set topology, product and quotient spaces, embedding and metrization, uniform spaces, function spaces, homotopy theory, simplicial complexes and homology, more algebraic topology, general homology theories.

*Prerequisite*

Bachelor’s degree with a major in mathematics. Credits equivalent to credits for mathematics MAT 310, MAT 311, MAT 595, and MAT 596, or permission of instructor and department head

**MAT 738 General Topology (3:3)**

Topological spaces, point set topology, product and quotient spaces, embedding and metrization, uniform spaces, function spaces, homotopy theory, simplicial complexes and homology, more algebraic topology, general homology theories.

*Prerequisite*

Bachelor’s degree with a major in mathematics. Credits equivalent to credits for mathematics MAT 310, MAT 311, MAT 595, and MAT 596, or permission of instructor and department head

**MAT 741 Modern Abstract Algebra (3:3)**

Real and complex number fields; rings, integral domains and fields; polynomial rings; extensions of rings and fields; elementary factorization theory; ideals; topics in linear algebra.

*Prerequisite*

Bachelor’s degree with a major in mathematics. Credits equivalent to credits for mathematics MAT 310, MAT 311, MAT 595, and MAT 596, or permission of instructor and department head

**MAT 742 Computational Number Theory (3:3)**

Main algorithms used to compute basic information about algebraic number fields, including integral bases, ideal factorization, system of fundamental units, and class group structure.

*Prerequisite*

MAT 671 or permission of instructor

**MAT 743 Complex Analysis (3:3)**

The complex number system, holomorphic functions, power series, complex integration, representation theorems, the calculus of residues.

*Prerequisite*

Bachelor’s degree with a major in mathematics. Credits equivalent to credits for mathematics MAT 310, MAT 311, MAT 595, and MAT 596, or permission of instructor and department head

**MAT 744 Complex Analysis (3:3)**

The complex number system, holomorphic functions, power series, complex integration, representation theorems, the calculus of residues.

*Prerequisite*

Bachelor’s degree with a major in mathematics. Credits equivalent to credits for mathematics MAT 310, MAT 311, MAT 595, and MAT 596, or permission of instructor and department head

**MAT 745 Real Analysis (3:3)**

Lebesque measure; the Lebesque integral; differentiation and integration, the classical Banach spaces; metric spaces, topological spaces, compact spaces; Banach spaces, measure and integration, measure and outer measure; the Daniell integral; mappings of measure spaces.

*Prerequisite*

Bachelor’s degree with a major in mathematics. Credits equivalent to credits for mathematics MAT 310, MAT 311, MAT 595, and MAT 596, or permission of instructor and department head

**MAT 746 Real Analysis (3:3)**

Lebesque measure; the Lebesque integral; differentiation and integration, the classical Banach spaces; metric spaces, topological spaces, compact spaces; Banach spaces, measure and integration, measure and outer measure; the Daniell integral; mappings of measure spaces.

*Prerequisite*

Bachelor’s degree with a major in mathematics. Credits equivalent to credits for mathematics MAT 310, MAT 311, MAT 595, and MAT 596, or permission of instructor and department head

**MAT 747 Computational Topology (3:3)**

Triangulations and WRAP. Computing homology algorithmically. Morse theory and persistent homology. Computations on knots, braids, and links.

*Prerequisite*

MAT 671 or permission of instructor

**MAT 748 Computational Algebra (3:3)**

Variety of basic subjects in computational algebra: fast arithmetic, algorithms for finite fields, matrix normal forms over rings, polynomial factorization, and Groebner bases.

*Prerequisite*

MAT 591, MAT 592, and knowledge of a programming language. or permission of instructor

**MAT 790 Directed Doctoral Research (1–6:1–6)**

Individual work on a dissertation research problem, which could also include original research or a review of current literature leading to a dissertation proposal.

*Prerequisite*

Permission of Director of Graduate Study

**MAT 799 Dissertation (1–12)**

MAT 801 Thesis Extension (1–3)

MAT 802 Dissertation Extension (1–3)

**MAT 803 Research Extension (1–3)**

**STA 551 Introduction to Probability (3:3)**

Events and probabilities (sample spaces), dependent and independent events, random variables and probability distribution, expectation, moment generating functions, multivariate normal distribution, sampling distributions.

*Prerequisite*

Grade of at least C in STA 290 and MAT 293 or permission of instructor

*Offered*

Fall

**STA 552 Introduction to Mathematical Statistics (3:3)**

Point estimation, hypothesis testing, confidence intervals, correlation and regression, small sample distributions.

*Prerequisite*

Grade of at least C in STA 551 or permission of instructor

*Offered*

Spring

**STA 562 Statistical Computing (3:3)**

Statistical methods requiring significant computing or specialized software. Simulation, randomization, bootstrap, Monte Carlo techniques; numerical optimization. Extensive computer programming involved. Extensive computer programming involved. This course does not cover the use of statistical software packages.

*Prerequisite*

Grade of at least a C in STA 291 or STA 580 and knowledge of a scientific programming language

*Offered*

Alt Fall

**STA 565 Analysis of Survival Data (3:3)**

Methods for comparing time-to-event data, including parametric and nonparametric procedures for censored or truncated data, regression model diagnostics, group comparisons, and the use of relevant statistical computing packages.

*Prerequisite*

STA 291 or STA 352 or permission of instructor

**STA 571 Statistical Methods for Research I (3:3)**

Introduction to statistical concepts. Basic probability, random variables, the binomial, normal and Student’s t distributions, hypothesis tests, confidence intervals, chi-square tests, introduction to regression, and analysis of variance.

*Notes*

Hours do not count toward degree requirements for a mathematics major.

**STA 572 Statistical Methods for Research II (3:3)**

Statistical methodology in research and use of statistical software. Regression, confidence intervals, hypothesis testing, design and analysis of experiments, one-and two-factor analysis of variance, multiple comparisons, hypothesis tests.

*Prerequisite*

STA 571 or permission of instructor

*Offered*

Spring

**STA 573 Theory of Linear Regression (3:3)**

Linear regression, least squares, inference, hypothesis testing, matrix approach to multiple regression. Estimation, Gauss-Markov Theorem, confidence bounds, model testing, analysis of residuals, polynomial regression, indicator variables.

*Prerequisite*

Grade of at least C in STA 352 and MAT 310, or MAT 662, or permission of instructor

*Offered*

Fall

**STA 574 Theory of the Analysis of Variance (3:3)**

Multivariate normal distribution, one-way analysis of variance, balanced and unbalanced two-way analysis of variance, empty cells, multiple comparisons, special designs, selected topics from random effects models.

*Prerequisite*

Grade of at least C in STA 573 or permission of instructor

*Offered*

Spring

**STA 575 Nonparametric Statistics (3:3)**

Introduction to nonparametric statistical methods for the analysis of qualitative and rank data. Binomial test, sign test, tests based on ranks, nonparametric analysis of variance, nonparametric correlation and measures of association.

*Prerequisite*

Grade of at least C in STA 352 or STA 572 or STA 662, or permission of instructor

*Offered*

Fall

**STA 580 Biostatistical Methods (3:3)**

Statistical methods for biological research including: descriptive statistics; probability distributions; parametric and nonparametric tests; ANOVA; regression; correlation; contingency table analysis.

*Prerequisite*

Grade of at least C in STA 271 or STA 290 or permission of instructor

*Offered*

Fall

**STA 581 SAS System for Statistical Analysis (1:1)**

Creating, importing, and working with SAS data sets. Using SAS procedures for elementary statistical analysis, graphical displays, and report generation.

*Prerequisite*

STA 271, STA 290, or similar introductory statistics course

*Offered*

Fall & Spring

**STA 589 Experimental Course**

This number reserved for experimental courses. Refer to the Course Schedule for current offerings.

**STA 591 Actuarial Exam Preparation Seminar (1:0)**

Topics vary according to interest and demand. Intended to help prepare for the P/1, FM/2, or MLC exam.

*Prerequisite*

STA 551, MAT 586, or STA 687, or permission of instructor

*Notes*

The course can be repeated. Students can only earn one credit for the first enrollment, after which no credit hour will be given.

**STA 593 Directed Study in Statistics (1–3)**

*Offered*

Fall & Spring

**STA 594 Directed Study in Statistics (1–3)**

*Offered*

Fall & Spring

**STA 651 Mathematical Statistics (3:3)**

Requisite mathematics; distribution and integration with respect to a distribution. Theory of random variable and probability distributions. Sampling distributions, statistical estimation, and tests of significance. Random processes. Numerical examples.

*Prerequisite*

STA 352 and either MAT 394 or MAT 395 or MAT 595

**STA 652 Mathematical Statistics (3:3)**

Requisite mathematics; distribution and integration with respect to a distribution. Theory of random variable and probability distributions. Sampling distributions, statistical estimation, and tests of significance. Random processes. Numerical examples.

*Prerequisite*

STA 352 and either MAT 394 or MAT 395 or MAT 595

**STA 655 Applied Probability Models (3:3)**

An introduction to Markov chains, Poisson processes, renewal processes, Brownian motion, and survival models. Examples drawn from applied fields such as engineering, management, finance, and sciences.

*Prerequisite*

STA 551, or consent of instructor

**STA 661 Advanced Statistics in the Behavioral and Biological Sciences I (3:3)**

Statistical techniques and design considerations for controlled experiments and observational studies. Exploratory data analysis, elementary probability theory, principles of statistical inference, contingency tables, one-way ANOVA, bivariate regression and correlation.

*Prerequisite*

STA 271 or an equivalent introductory statistics course

**STA 662 Advanced Statistics in the Behavioral and Biological Sciences II (3:3)**

Continuation of STA 661. Multiple regression and correlation, analysis of covariance, factorial ANOVAs, randomized block designs, multiple comparisons, split-plot designs, repeated measures.

*Prerequisite*

STA 661 or permission of instructor

**STA 667 Statistical Consulting (1:1)**

Statistical consultation on doctoral or master’s research. Access to the Statistical Consulting Center. Students are required to attend the initial class meeting during the beginning of the semester.

*Prerequisite*

Permission of instructor

*Notes*

Credit is not applicable to a graduate plan of study. Grade: Satisfactory/Unsatisfactory, S/U

**STA 668 Consulting Experience (1:0:1)**

Development of consulting skills through reading and discussion of literature on statistical consulting and participation in statistical consulting sessions.

*Prerequisite*

STA 662 or permission of instructor

*Notes*

Grade: Satisfactory/Unsatisfactory, S/U

**STA 670 Categorical Data Analysis (3:3)**

Methods for analyzing dichotomous, multinomial and ordinal responses. Measures of association; inference for proportions and contingency tables; generalized linear models including logistic regression and loglinear models.

*Prerequisite*

STA 662 or permission of instructor

**STA 671 Multivariate Analysis (3:3)**

Multivariate normal distribution. Cluster analysis, discriminant analysis, canonical correlation, principal component analysis, factor analysis, multivariate analysis of variance. Use and interpretation of relevant statistical software.

*Prerequisite*

STA 573 or STA 662 or permission of instructor

**STA 672 Applied Statistical Computing (3:3)**

Limitations and advantages of statistical packages (SAS, SPSSX, BMDP, Minitab). Evaluation in terms of statistical methods, utility, availability, sophistication, data base manipulation, and programming capabilities. Applications from various disciplines.

*Prerequisite*

STA 572 or STA 662

**STA 673 Statistical Linear Models I (3:3)**

Abstract vector spaces, inner product spaces, projections, the Spectral Theorem, least squares, multiple regression, ANOVA, multiple comparisons, data analysis.

*Prerequisite*

STA 352 and MAT 310 or permission of instructor

**STA 674 Statistical Linear Models II (3:3)**

Abstract vector spaces, inner product spaces, projections, the Spectral Theorem, least squares, multiple regression, ANOVA, multiple comparisons, data analysis.

*Prerequisite*

STA 352 and MAT 310 or permission of instructor

**STA 675 Advanced Experimental Design (3:3)**

Topics include factorials and fractional factorials, incomplete block designs, split-plot and repeated measures, random and mixed effects models, crossover designs, response surface designs, power analysis.

*Prerequisite*

STA 662 or permission of instructor

**STA 676 Sample Survey Methods (3:3)**

Survey methods for students from any discipline. Random, stratified, cluster, multi-stage and other sampling schemes. Estimation of population means, variances, and proportions. Questionnaire design and analysis.

*Prerequisite*

STA 352 or STA 572 or STA 662 or permission of instructor

**STA 677 Advanced Topics in Data Analysis and Quantitative Methods (3:3)**

Topics vary according to interest and demand. Quantitative methods not normally covered in detail in other statistics courses. Topics may be selected from psychometrics, econometrics, biometrics, sociometrics, quantitative epidemiology.

*Prerequisite*

STA 662

**STA 682 Theory of Time Series (3:3)**

Examples of time series; objectives in time series modeling; theory and applications of linear and non-linear time series models; ARMA/ARIMA/ARCH/GARCH models; time series modeling using computer packages.

*Prerequisite*

STA 551 or STA 651, or permission of instructor

**STA 686 Actuarial Models I (3:3)**

Actuarial models for life contingencies; single and multiple lives models, present values, premium, reserves, pension plans, and retirement benefits. Intended for the MLC actuarial exam.

*Prerequisite*

STA 551 and MAT 586, or consent of instructor

**STA 687 Actuarial Models II (3:3)**

Actuarial models for life contingencies; single and multiple lives models, present values, premium, reserves,

pension plans and retirement benefits. Intended for the MLC actuarial exam.

*Prerequisite*

STA 686, or consent of instructor

**STA 690 Graduate Seminar (1:0:1)**

Development of presentation skills though reading, discussions, and presentation of current research topics in applied statistics.

*Prerequisite*

STA 662 or permission of instructor

*Notes*

Grade: Satisfactory/Unsatisfactory, S/U

**STA 698 Project in Statistics (3)**

Directed research project in statistics.

*Prerequisite*

Permission of instructor

*Notes*

Grade: Satisfactory/Unsatisfactory, S/U

**STA 699 Thesis (1–6)**

**STA 701 Seminar in Computational Statistics (3:3)**

Readings from the literature in Computational Statistics.

*Prerequisite*

Either STA 651 and STA 652; or STA 676; or permission of instructor

*Notes*

May be repeated up to 9 hours as topics vary.

**STA 703 Topics in High Dimensional Data Analysis (3:3)**

Advanced study in special topics in statistical data analysis with large scale data sets. The course may be repeated up to 9 hours as topics vary.

*Prerequisite*

STA 562, STA 673, or permission of instructor

*Corequisite*

STA 674

**STA 709 Topics in Computational Statistics (3:3)**

Advanced study in special topics in Computational Statistics.

*Prerequisite*

STA 552 or STA 652 or permission of instructor

*Notes*

May be repeated for credit.

**STA 711 Experimental Course**

This number reserved for experimental courses. Refer to the Course Schedule for current offerings.

**STA 801 Thesis Extension (1–3)**

**STA 803 Research Extension (1–3)**