Mathematics and Statistics
College of Arts and Sciences
116 Petty Building
336-334-5836
https://mathstats.uncg.edu/
Ratnasingham Shivaji, Head of Department
Dan Yasaki, Associate Head of Department
Maya Chhetri, Director of Graduate Study
Sebastian Pauli, Director of Undergraduate Study
The Department of Mathematics and Statistics offers undergraduate and graduate degrees. The goal of all of the Department’s programs is to produce students who are both technically competent and sufficiently well grounded in theory that they can contribute to fundamental research in their chosen specialty. There are many opportunities for graduates of mathematics programs in industry, government, business, research, and teaching.
The faculty consists of nationally and internationally recognized researchers in diverse areas of mathematics, statistics, and mathematics education. They are outstanding professionals committed to teaching excellence, and they take great pride in guiding students to enjoy the beauty of mathematics. The department has been hosting various professional conferences and special events, lecture series, colloquia, and seminars. These activities have greatly enhanced the student learning experience at UNC Greensboro.
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.
Undergraduate
The Department of Mathematics and Statistics offers undergraduate programs leading to the B.A. and B.S. degrees in Mathematics, as well as a minor in Mathematics and a minor in Statistics. To give a professional direction to the student’s liberal arts education, the mathematics major may choose a concentration in mathematics, statistics or high school teaching licensure. There are many opportunities for math majors in industry, actuarial sciences, government, business, and secondary school teaching. The mathematics programs also provide excellent preparation for graduate studies in many areas, including computer science, economics, engineering, law, mathematics, operations research, and statistics.
Graduate
The department offers a variety of outstanding graduate programs. A graduate degree in Mathematics is not only an excellent choice for students who pursue a career in teaching and/or research, there are also many opportunities in banking, consulting, government, and the IT industry. Most of our graduate students are supported via attractive graduate assistantships.
The Department of Mathematics and Statistics offers a Ph.D. in Computational Mathematics, a Masters in Mathematics, and a Post-Baccalaureate Certificate in Statistics. Additionally, students pursuing a doctoral degree from another department at UNCG may obtain a doctoral minor in statistics.
Professor
Maya Chhetri^{G}
Richard H Fabiano^{G}
Sat N Gupta^{G}
Scott J Richter^{G}
Ratnasingham Shivaji, Helen Barton Excellence Professor^{G}
John Stufken, Bank of America Excellence Professor, Professor
Haimeng Zhang^{G}
Associate Professor
Gregory C Bell^{G}
Igor Erovenko^{G}
Talia Fernos^{G}
Xiaoli Gao^{G}
Tom Lewis^{G}
Sebastian G Pauli^{G}
Jonathan T Rowell^{G}
Filip Saidak^{G}
Clifford D Smyth^{G}
Brett A Tangedal^{G}
Dan Yasaki^{G}
Assistant Professor
Yu-Min Chung^{G}
Michael B Hull
Jianping Sun^{G}
Yi Zhang^{G}
Visiting Assistant Professor
Elizabeth Fowler Lewis
Donald Robertson
Lecturer
Monika Goel
Matt Winston Jester
Senior Academic Professional
Tracey H Howell
G | Graduate-level faculty |
Mathematics Disciplinary Honors
Requirements
- A minimum of 12 credit hours as detailed below.
- UNC Greensboro cumulative GPA of 3.30 or better or, for transfer students, cumulative GPA of 3.30 or better from all prior institutions.
- A grade of B or higher in all course work used to satisfy the Honors requirement in Mathematics
Code | Title | Credit Hours |
---|---|---|
Required | 6-9 | |
Honors Work ^{*} | ||
Senior Honors Project | ||
Select two courses from the following: | 6 | |
Elementary Linear Algebra | ||
Introduction to Abstract Algebra | ||
Ordinary Differential Equations | ||
Introduction to Mathematical Analysis |
* | To be taken before HSS 490 |
Recognition
Receive a Certificate of Disciplinary Honors in Mathematics; have that accomplishment, along with the title of the Senior Honors Project, noted on the official transcript; and be recognized at a banquet held at the end of the spring semester.
Honors Advisor
Contact Richard Fabiano at fabiano@uncg.edu for further information and guidance about Honors in Mathematics. To apply: http://honorscollege.uncg.edu/forms/disc-application.pdf
Mathematics (MAT)
MAT 112 Contemporary Topics in Mathematics 3
Practical mathematical topics including set theory, properties and operations of number systems, algebra, geometry and consumer mathematics. Additional topics may be selected from logic, systems of numeration, and mathematical systems.
GE Core: GMT
Notes: Students may not receive credit for both MAT 112 and RCO 112.
MAT 115 College Algebra 3
Algebraic expressions, exponents, radicals, factoring, solving equations and inequalities, graphing, polynomial and rational functions.
GE Core: GMT
Notes: Credit can be earned for only one of MAT 115 or MAT 150.
MAT 120 Calculus with Business Applications 3
Introductory survey of differential calculus with emphasis on techniques and applications related to business and the social sciences.
GE Core: GMT
Prerequisites: An acceptable score on the mathematics placement test or a minimum grade of C (2.0) in at least one of: MAT 115, MAT 150, MAT 151, and/or MAT 190.
Notes: This course does not serve as a prerequisite for MAT 292 (Calculus II). This is a terminal course and not adequate preparation for MAT 292.
MAT 150 Precalculus I 3
Review of elementary algebra, equations, inequalities, relations, functions, transformations, graphing, complex numbers, polynomial and rational functions.
GE Core: GMT
Notes: Credit can be earned for only one of MAT 115 or MAT 150.
MAT 151 Precalculus II 3
Properties, graphs, and applications of exponential, logarithmic, trigonometric functions.
GE Core: GMT
Prerequisites: An acceptable score on the mathematics placement test. or a grade of C or better in MAT 115 or MAT 150.
MAT 190 Precalculus 3
This course covers essential prerequisites for calculus. Topics include functions and graphs, equations and inequalities, polynomial and rational functions, trigonometry, functions of trigonometric, exponential, and logarithmic type.
GE Core: GMT
Prerequisites: Acceptable score on the mathematics placement test.
MAT 191 Calculus I 3
Limits and introductory differential calculus of the algebraic and transcendental functions of one variable.
GE Core: GMT
Prerequisites: An acceptable score on the mathematics placement test. or a grade of C or better in MAT 151 (or MAT 190).
MAT 220 Plane and Solid Analytic Geometry 3
Study of conic sections (including rotation of axes), graphing with polar coordinates, quadric surfaces, and vectors.
Prerequisites: Grade of C or better in MAT 151 (or equivalent).
Notes: Hours do not count toward degree requirements for MATH major.
MAT 253 Discrete Mathematical Structures 3
A rigorous introduction to discrete mathematical structures, proof techniques, and programming. Topics include sets, functions, sequences, relations, induction, propositional and predicate logic, modular arithmetic, and mathematical programming.
Notes: Only one of MAT 253 or MAT 295 can count toward degree requirements for MATH major.
MAT 292 Calculus II 3
Introductory integral calculus of the algebraic and transcendental functions of one variable, techniques of integration.
GE Core: GMT
Prerequisites: Grade of C or better in MAT 191.
MAT 293 Calculus III 3
Infinite sequences and series, conic sections, polar coordinates, vectors in dimensions two and three, vector-valued functions.
Prerequisites: Grade of C or better in MAT 292.
MAT 310 Elementary Linear Algebra 3
Linear systems, matrices, determinants, eigenvalues and eigenvectors, finite-dimensional vector spaces, linear transformations.
Prerequisites: Grade of C or better in MAT 292.
MAT 311 Introduction to Abstract Algebra 3
Sets and mappings, equivalence relations, mathematical induction, introduction to theory of groups, rings, and fields.
MAT 320 Introduction to Topology 3
Metric spaces, continuity, equivalence of various types of definitions of continuity, convergence, compactness, connectedness, topological spaces.
Prerequisites: Minimum grade of C in MAT 293 and a minimum grade of C in one of MAT 253 or MAT 310 or CSC 250.
MAT 322 Linear Programming 3
Covers simplex computational procedure, minimum feasible solutions, artificial-basis technique, slack variables, perturbation techniques, cycling, parametric objective and dual problems, sensitivity analysis, and decomposition algorithms.
Prerequisites: Grade of C or better in MAT 310.
MAT 330 Axiomatic Foundations of Geometry 3
Axiomatic systems, logic and proof, incidence geometries, absolute geometries, Euclidean geometry, and an introduction to non-Euclidean geometries and transformational geometry.
Prerequisites: Grade of C or better in MAT 292.
Notes: Required for students seeking secondary licensure in mathematics.
MAT 349 Preparation for Industrial Careers in Mathematical Sciences 3
This course prepares mathematical sciences students for industrial careers by engaging them in research problems that come directly from industry.
Prerequisites: Permission of instructor.
MAT 353 Introduction to Discrete Mathematics 3
Elementary graph theory, combinatorics, partially ordered sets.
MAT 390 Ordinary Differential Equations 3
First order differential equations and linear equations of finite order, Laplace transforms, undetermined coefficients, variation of parameters, applications, numerical methods.
Prerequisites: Grade of C or better in MAT 292.
MAT 394 Calculus IV 3
Multivariable functions, partial differentiation, multiple integrals, vector calculus.
Prerequisites: Grade of C or better in MAT 293.
MAT 395 Introduction to Mathematical Analysis 3
Properties of real numbers, sequences, limits of sequences and functions, continuity, differentiation, Riemann integral.
Prerequisites: Grade of C or better in MAT 253, MAT 293, and MAT 310.
MAT 405 Foundations of Mathematics for Teaching I 3
Capstone survey of real and complex numbers; polynomial, rational, exponential, logarithmic, and trigonometric functions; calculus concepts. Special teaching problems and procedures for secondary topics in relation to their mathematical foundations.
Prerequisites: Grade of C (2.0) or better in MAT 310.
MAT 406 Foundations of Mathematics for Teaching II 4
Capstone survey of geometry, probability, data analysis, and discrete mathematics. Special teaching problems and procedures for secondary topics related to their mathematical foundations, including 50-hour internship in secondary math classroom.
Prerequisites: Minimum grade of C (2.0) in MAT 405 and minimum grade of C (2.0) in one of either MAT 311 or MAT 395. Admission to the Teacher Education Program.
MAT 413 Historical Development of Mathematics 3
Study of the historical development of mathematics, not a history of persons involved in development.
Prerequisites: Grade of C or better in MAT 292.
Notes: Hours do not count toward degree requirements for MATH major nor for the M.A. degree in Mathematics.
MAT 414 Theory of Numbers 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.
Prerequisites: Grade of C or better in either MAT 311 or MAT 395.
MAT 415 Mathematical Logic 3
Formal languages, recursion, compactness, and effectiveness. First-order languages, truth, and models. Soundness and completeness theorems. Models of theories.
Prerequisites: Grade of C or better in MAT 311 (or MAT 353).
MAT 416 Intermediate Abstract Algebra 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.
Prerequisites: Grade of C or better in MAT 311.
MAT 417 Theory of Groups 3
Elementary properties of groups and homomorphisms, quotients and products of groups, the Sylow theorems, structure theory for finitely generated abelian groups.
MAT 419 Intuitive Concepts in Topology 3
Basic concepts, vector fields, the Jordan curve theorem, surfaces, homology of complexes, continuity.
Prerequisites: Grade of C or better in MAT 311 (or MAT 395).
MAT 420 Non-Euclidean Geometry 3
Fifth postulate, hyperbolic geometries, elliptic geometries, consistency of non-Euclidean geometries, models for geometries, elements of inversion.
Prerequisites: Grade of C or better in MAT 311 (or MAT 395).
MAT 421 Projective Geometry 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 specializations.
Prerequisites: Permission of instructor.
MAT 422 Introductory Functional Analysis 3
Basic concepts in Banach spaces, Hilbert spaces, linear operators, and their applications.
Prerequisites: Grade of C or better in MAT 395.
MAT 423 Numerical Methods 3
Number systems and errors, solutions of non-linear and linear systems, interpolation, numerical differentiation and integration, solution of differential equations. Implementation of numerical methods using a high-level programming language.
Prerequisites: A grade of at least C in MAT 293.
MAT 425 Intermediate Mathematical Analysis 3
Integration, infinite series, sequences and series of functions.
Prerequisites: Grade of C or better in MAT 395.
MAT 431 Combinatorial Analysis 3
he pigeon-hole principle, permutations, combinations, generating functions, principle of inclusion and exclusion, distributions, partitions, recurrence relations.
Prerequisites: Grade of C or better in MAT 253 (or MAT 295 or MAT 311 or MAT 395). or permission of instructor.
MAT 432 Introductory Graph Theory 3
Basic concepts, graph coloring, trees, planar graphs, networks.
Prerequisites: Grade of C or better in MAT 310 and any one of the courses MAT 253, MAT 295, MAT 311, MAT 395, MAT 431.
MAT 435 Differential Equations and Orthogonal Systems 3
An introduction to Fourier series and orthogonal sets of functions, with applications to boundary value problems.
Prerequisites: Grade of C or better in MAT 293 and MAT 390. or permission of instructor.
MAT 436 Partial Differential Equations with Applications 3
Fourier integrals, Bessel functions, Legendre polynomials and their applications. Existence and uniqueness of solutions to boundary value problems.
Prerequisites: Grade of C or better in MAT 435.
MAT 439 Topics in Applied Mathematics 3
Selected topics of current interest in applied mathematics.
Prerequisites: Grade of C or better in MAT 293 and MAT 390. or permission of instructor;
Notes: May be repeated for credit with approval of the Department Head.
MAT 440 Introductory Complex Analysis 3
The complex number system, holomorphic functions, power series, complex integration, representation theorems, the calculus of residues.
Prerequisites: Grade of C or better in MAT 394.
MAT 441 Stochastic Processes 3
Markov processes, Markov reward processes, queuing, decision making, graphs, and networks. Applications to performance, reliability, and availability modeling.
Prerequisites: Grade of C or better in MAT 394 and MAT 353. or equivalents.
MAT 442 Stochastic Processes 3
Markov processes, Markov reward processes, queuing, decision making, graphs, and networks. Applications to performance, reliability, and availability modeling.
Prerequisites: Grade of C or better in MAT 394 and MAT 353. or equivalents.
MAT 465 Student Teaching and Seminar-Secondary Mathematics 12
Supervised student teaching in senior high school under direction of university supervisor. Observation, participation, and appropriate classroom teaching experience on full-time teaching assignment for full semester with weekly seminar.
Prerequisites: MAT 406. Admission to the Teacher Education Program.
MAT 486 Financial Mathematics for Actuaries 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.
Prerequisites: Minimum grade of C (2.0) in MAT 394 or permission of instructor. Graduate students in MA in Mathematics, Ph.D. students in Computational Mathematics, or undergraduate students in the accelerated BS to MA in Mathematics.
MAT 488 Directed Study in Mathematics 1-3
MAT 490 Senior Seminar in Mathematics 3
Oral presentations on topics in mathematics, including current mathematics literature.
Prerequisites: Senior standing and mathematics major, or permission of instructor.
MAT 493 Honors Work 3-6
Prerequisite: Permission of instructor; 3.30 GPA in the major, 12 s.h. in the major;
Notes: May be repeated for credit if the topic of study changes.
MAT 494 Directed Study in Mathematics 1-3
MAT 503 Problem Solving in Mathematics 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.
Prerequisites: 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 513 Historical Development of Mathematics 3
Study of the historical development of mathematics, not a history of persons involved in development.
Prerequisites: Grade of C or better in MAT 292.
Notes: Hours do not count toward degree requirements for MATH major nor for the M.A. degree in Mathematics.
MAT 591 Advanced Abstract Algebra 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.
Prerequisites: Grade of C or better in MAT 516.
MAT 593 Directed Study in Mathematics 1-3
MAT 594 Directed Study in Mathematics 1-3
MAT 601 Seminar in the Teaching of Mathematics I 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 602 Seminar in Mathematical Software 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.
Prerequisites: Knowledge of a programming language.
MAT 603 Practicum in the Teaching of Mathematics 2
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.
Corequisites: MAT 601.
MAT 614 Theory of Numbers 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.
Prerequisites: Grade of C or better in either MAT 311 or MAT 395.
MAT 617 Theory of Groups 3
Elementary properties of groups and homomorphisms, quotients and products of groups, the Sylow theorems, structure theory for finitely generated abelian groups.
MAT 619 Intuitive Concepts in Topology 3
Basic concepts, vector fields, the Jordan curve theorem, surfaces, homology of complexes, continuity.
Prerequisites: Grade of C or better in MAT 311 (or MAT 395).
MAT 620 Non-Euclidean Geometry 3
Fifth postulate, hyperbolic geometries, elliptic geometries, consistency of non-Euclidean geometries, models for geometries, elements of inversion.
Prerequisites: Grade of C or better in MAT 311 (or MAT 395).
MAT 621 Projective Geometry 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 specializations.
Prerequisites: Permission of instructor.
MAT 622 Introductory Functional Analysis 3
Basic concepts in Banach spaces, Hilbert spaces, linear operators, and their applications.
Prerequisites: Grade of C or better in MAT 395.
MAT 623 Numerical Methods 3
Number systems and errors, solutions of non-linear and linear systems, interpolation, numerical differentiation and integration, solution of differential equations. Implementation of numerical methods using a high-level programming language.
Prerequisites: A grade of at least C in MAT 293.
MAT 625 Intermediate Mathematical Analysis 3
Integration, infinite series, sequences and series of functions.
Prerequisites: Grade of C or better in MAT 395.
MAT 631 Combinatorial Analysis 3
The pigeon-hole principle, permutations, combinations, generating functions, principle of inclusion and exclusion, distributions, partitions, recurrence relations.
Prerequisites: Grade of C or better in MAT 253 (or MAT 295 or MAT 311 or MAT 395) or permission of instructor.
MAT 632 Introductory Graph Theory 3
Basic concepts, graph coloring, trees, planar graphs, networks.
Prerequisites: Grade of C or better in MAT 310 and any one of the courses MAT 253, MAT 295, MAT 311, MAT 395, MAT 531.
MAT 635 Differential Equations and Orthogonal Systems 3
An introduction to Fourier series and orthogonal sets of functions, with applications to boundary value problems.
Prerequisites: Grade of C or better in MAT 293 and MAT 390. or permission of instructor.
MAT 636 Partial Differential Equations with Applications 3
Fourier integrals, Bessel functions, Legendre polynomials and their applications. Existence and uniqueness of solutions to boundary value problems.
Prerequisites: Grade of C or better in MAT 545.
MAT 639 Topics in Applied Mathematics 3
Selected topics of current interest in applied mathematics.
Prerequisites: Grade of C or better in MAT 293 and MAT 390. or permission of instructor;
Notes: May be repeated for credit with approval of the Department Head.
MAT 640 Introductory Complex Analysis 3
The complex number system, holomorphic functions, power series, complex integration, representation theorems, the calculus of residues.
Prerequisites: Grade of C or better in MAT 394.
MAT 641 Stochastic Processes 3
Markov processes, Markov reward processes, queuing, decision making, graphs, and networks. Applications to performance, reliability, and availability modeling.
Prerequisites: Grade of C or better in MAT 394 and MAT 353. or equivalents.
MAT 642 Stochastic Processes 3
Markov processes, Markov reward processes, queuing, decision making, graphs, and networks. Applications to performance, reliability, and availability modeling.
Prerequisites: Grade of C or better in MAT 394 and MAT 353. or equivalents.
MAT 659 Advanced Topics in Mathematics 3
Topics vary according to interest and demand, and include algebra, applied mathematics, combinatorics, dynamics, mathematical logic, topology, and other topics.
Prerequisites: Permission of instructor.
Notes: May be repeated for credit when topic varies.
MAT 686 Financial Mathematics for Actuaries 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.
Prerequisites: Minimum grade of C (2.0) in MAT 394 or permission of instructor. Graduate students in MA in Mathematics, Ph.D. students in Computational Mathematics, or undergraduate students in the accelerated BS to MA in Mathematics.
MAT 687 Project in Mathematics 3
Directed research project in Mathematics.
Prerequisites: Admission to the MA in Mathematics and Permission of Instructor.
MAT 691 Advanced Abstract Algebra 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.
Prerequisites: Grade of C or better in MAT 516.
MAT 692 Advanced Abstract Algebra 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.
Prerequisites: Grade of C or better in MAT 516.
MAT 695 Mathematical Analysis 3
Real number axioms, metric spaces, sequences, series, continuity, differentiation, the Riemann-Stieltjes integral.
Prerequisites: MAT 395 or permission of instructor.
MAT 696 Mathematical Analysis 3
Real number axioms, metric spaces, sequences, series, continuity, differentiation, the Riemann-Stieltjes integral.
Prerequisites: MAT 395 or permission of instructor.
MAT 699 Thesis 1-6
MAT 701 Graduate Seminar in Computational Mathematics 3
Readings from the literature of computational mathematics.
Prerequisites: MAT 748 or permission of instructor.
Notes: May be repeated for credit when topic varies.
MAT 709 Topics in Computational Mathematics 3
Advanced study in special topics in computational mathematics.
Prerequisites: MAT 748 or permission of instructor.
Notes: May be repeated for credit when topic varies.
MAT 721 Mathematical Cryptography 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.
Prerequisites: MAT 748 or permission of instructor.
MAT 723 Numerical Mathematics 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.
Prerequisites: MAT 390, MAT 595, MAT 596, or equivalents.
MAT 726 Finite Element Methods 3
Introduce the fundamental concepts of the finite element method for approximating solutions to boundary and initial boundary value problems. Topics include modeling, mathematical formulations, convergence analysis, and computer implementation.
Prerequisites: A grade of B or better in MAT 727.
MAT 727 Linear Algebra and Matrix Theory 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.
Prerequisites: MAT 310, MAT 311 or permission of instructor.
MAT 728 Linear Algebra and Matrix Theory 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.
Prerequisites: MAT 310, MAT 311 or permission of instructor.
MAT 735 Ordinary Differential Equations 3
Existence and uniqueness theorems for initial value problems, theory of linear equations, nonlinear equations, stability theory, boundary value problems.
Prerequisites: MAT 390 and MAT 595 or permission of instructor.
MAT 736 Partial Differential Equations 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.
Prerequisites: MAT 735 or permission of instructor.
MAT 737 General Topology 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.
Prerequisites: 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 740 Modern Abstract Algebra 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.
MAT 741 Modern Abstract Algebra 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.
Prerequisites: 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
Main algorithms used to compute basic information about algebraic number fields, including integral bases, ideal factorization, system of fundamental units, and class group structure.
Prerequisites: MAT 748 or permission of instructor.
MAT 743 Complex Analysis 3
The complex number system, holomorphic functions, power series, complex integration, representation theorems, the calculus of residues.
Prerequisites: 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
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.
Prerequisites: 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
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.
Prerequisites: 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
Triangulations and WRAP. Computing homology algorithmically. Morse theory and persistent homology. Computations on knots, braids, and links.
Prerequisites: MAT 748 or permission of instructor.
MAT 748 Computational Algebra 3
Variety of basic subjects in computational algebra: fast arithmetic, algorithms for finite fields, matrix normal forms over rings, polynomial factorization, and Groebner bases.
Prerequisites: MAT 591, MAT 592, and knowledge of a programming language. or permission of instructor.
MAT 790 Directed Doctoral Research 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.
Prerequisites: Permission of Director of Graduate Study.
MAT 799 Dissertation 1-12
MAT 801 Thesis Extension 1-3
Thesis Extension.
MAT 802 Dissertation Extension 1-3
Dissertation Extension.
Statistics (STA)
STA 108 Elementary Introduction to Probability and Statistics 3
Survey of statistics intended for undergraduates in any discipline. Graphical displays, numerical measures, relationships between variables, elements of good data collection. Basic probability, introduction to inferential techniques including confidence intervals and significance testing. Emphasis on statistical literacy.
GE Core: GMT
Notes: May not be taken for credit by students who have received credit for ECO 250 or ECO 350 or who are concurrently enrolled in ECO 250. Students may not earn credit for both RCO 114 and STA 108.
STA 271 Fundamental Concepts of Statistics 3
Survey of basic descriptive and inferential statistics. Graphs and descriptive measures, simple linear regression and correlation, data collection, basic probability and probability models, interval estimation and significance testing, analysis of variance, use of statistical software. An appropriate preparation for more advanced statistics courses in any discipline.
Prerequisites: Minimum grade of C in MAT 115 or MAT 150 or MAT 151 or MAT 190 or MAT 191 or STA 108. or permission of department.
STA 290 Introduction to Probability and Statistical Inference 3
Introduction to probability models and statistical inference. Descriptive statistics, basic probability laws, discrete and continuous probability models, sampling distributions, central limit theorem, estimation, hypothesis testing, simple regression, and correlation.
Prerequisites: Minimum grade of C (2.0) or concurrent registration in MAT 292. or permission of instructor .
STA 301 Statistical Methods 3
Two-group comparisons, simple and multiple regression, one and two factor ANOVA, categorical data analysis, nonparametric methods.
Prerequisites: Minimum grade of C (2.0) in either STA 271 or STA 290. or permission of instructor.
STA 352 Statistical Inference 3
Descriptive and inferential statistics. Emphasis on sampling distributions; theory of estimation and tests of hypotheses, linear hypothesis theory, regression, correlation and analysis of variance.
Prerequisites: Grade of at least C in STA 290 or permission of instructor .
STA 382 Introduction to Sampling Methods 3
Designing survey instruments; estimation of population mean, total, and proportion using simple random, stratified, systematic, and cluster sampling; other sampling techniques such as pps sampling and randomized response methods.
Prerequisites: Minimum grade of C (2.0) in STA 301. or permission of instructor .
STA 431 Introduction to Probability 3
Events and probabilities (sample spaces), dependent and independent events, random variables and probability distribution, expectation, moment generating functions, multivariate normal distribution, sampling distributions.
Prerequisites: Grade of at least C in STA 290 and MAT 293 or permission of instructor.
STA 432 Introduction to Mathematical Statistics 3
Point estimation, hypothesis testing, confidence intervals, correlation and regression, small sample distributions.
Prerequisites: Grade of at least C in STA 431 or permission of instructor.
STA 435 Theory of Linear Regression 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.
Prerequisites: Grade of at least C in STA 352 and MAT 310, or STA 662, or permission of instructor.
STA 440 SAS System for Statistical Analysis 1
Creating, importing, and working with SAS data sets. Using SAS procedures for elementary statistical analysis, graphical displays, and report generation.
Prerequisites: STA 271 or STA 290 or similar introductory statistics course.
STA 442 Statistical Computing 3
Statistical methods requiring significant computing or specialized software. Simulation, randomization, bootstrap, Monte Carlo techniques; numerical optimization. Extensive computer programming involved. This course does not cover the use of statistical software packages.
Prerequisites: Minimum grade of C (2.0) in STA 301. knowledge of a scientific programming language.
STA 445 Nonparametric Statistics 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.
Prerequisites: Grade of at least C in STA 352 or STA 662. or permission of instructor.
STA 465 Analysis of Survival Data 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.
Prerequisites: STA 301 or STA 352. or permission of instructor.
STA 481 Introduction to Design of Experiments 3
Planning and analysis of experimental and observational studies. Completely randomized, blocked, split-plot, and repeated measures designs. Factorial arrangements and interaction. Power and sample size calculation.
Prerequisites: Minimum grade of C (2.0) in STA 301. or permission of instructor.
STA 482 Introduction to Time Series Models 3
Estimation/removal of trend and seasonality, introduction to stationary stochastic processes, fitting ARMA/ARIMA models, forecasting techniques, miscellaneous topics, and introduction to a time series modeling software package.
Prerequisites: STA 352 or permission of instructor.
STA 489 Experimental Course 3
This number reserved for experimental courses. Refer to the Course Schedule for current offerings.
STA 491 Actuarial Exam Preparation Seminar 1
Topics vary according to interest and demand. Intended to help prepare for the P/1, FM/2, or MLC exam.
Prerequisites: STA 431 or STA 687 or permission of instructor.
Notes: One credit maximum. May be repeated; Grade: Pass/Not Pass (P/NP).
STA 493 Directed Study in Statistics 1-3
STA 494 Directed Study in Statistics 1-3
STA 571 Statistical Methods for Research I 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
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.
Prerequisites: STA 571 or permission of instructor.
STA 593 Directed Study in Statistics 1-3
STA 631 Introduction to Probability 3
Events and probabilities (sample spaces), dependent and independent events, random variables and probability distribution, expectation, moment generating functions, multivariate normal distribution, sampling distributions.
Prerequisites: Grade of at least C in STA 290 and MAT 293 or permission of instructor.
STA 632 Introduction to Mathematical Statistics 3
Point estimation, hypothesis testing, confidence intervals, correlation and regression, small sample distributions.
Prerequisites: Grade of at least C in STA 551 or permission of instructor.
STA 635 Theory of Linear Regression 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.
Prerequisites: Grade of at least C in STA 352 and MAT 310, or STA 662, or permission of instructor.
STA 640 SAS System for Statistical Analysis 1
Creating, importing, and working with SAS data sets. Using SAS procedures for elementary statistical analysis, graphical displays, and report generation.
Prerequisites: STA 271 or STA 290 or similar introductory statistics course.
STA 642 Statistical Computing 3
Statistical methods requiring significant computing or specialized software. Simulation, randomization, bootstrap, Monte Carlo techniques; numerical optimization. Extensive computer programming involved. This course does not cover the use of statistical software packages.
Prerequisites: Minimum grade of C (2.0) in STA 301. knowledge of a scientific programming language.
STA 645 Nonparametric Statistics 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.
Prerequisites: Grade of at least C in STA 352 or STA 662. or permission of instructor.
STA 651 Mathematical Statistics 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.
Prerequisites: STA 352 and either MAT 394 or MAT 395 or MAT 595.
STA 652 Mathematical Statistics 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.
Prerequisites: STA 352 and either MAT 394 or MAT 395 or MAT 595.
STA 655 Applied Probability Models 3
An introduction to Markov chains, Poisson processes, renewal processes, Brownian motion, and survival models. Examples drawn from applied field such as engineering, management, finance, and sciences.
Prerequisites: STA 551, or permission of instructor.
STA 661 Advanced Statistics in the Behavioral and Biological Sciences I 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.
Prerequisites: STA 271 or an equivalent introductory statistics course.
STA 662 Advanced Statistics in the Behavioral and Biological Sciences II 3
Continuation of STA 661. Multiple regression and correlation, analysis of covariance, factorial ANOVAs, randomized block designs, multiple comparisons, split-plot designs, repeated measures.
Prerequisites: STA 661 or permission of instructor.
STA 665 Analysis of Survival Data 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.
Prerequisites: STA 301 or STA 352. or permission of instructor.
STA 667 Statistical Consulting 1
Statistical consultation on a 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.
Prerequisites: Permission of instructor.
Notes: Credit is not applicable to a graduate plan of study. Grade: Satisfactory/Unsatisfactory (S/U).
STA 668 Consulting Experience 1
Development of consulting skills through reading and discussion of literature on statistical consulting and participation in statistical consulting sessions.
Prerequisites: STA 662 or permission of instructor.
Notes: Grade: Satisfactory/Unsatisfactory (S/U).
STA 670 Categorical Data Analysis 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.
Prerequisites: STA 662 or permission of instructor.
STA 671 Multivariate Analysis 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.
Prerequisites: ERM 680 and ERM 681, or STA 573, or STA 662, or permission of instructor.
STA 673 Statistical Linear Models I 3
Abstract vector spaces, inner product spaces, projections, the Spectral Theorem, least squares, multiple regression, ANOVA, multiple comparisons, data analysis.
Prerequisites: STA 352 and MAT 310 or permission of instructor.
STA 674 Statistical Linear Models II 3
Abstract vector spaces, inner product spaces, projections, the Spectral Theorem, least squares, multiple regression, ANOVA, multiple comparisons, data analysis.
Prerequisites: STA 352 and MAT 310 or permission of instructor.
STA 675 Advanced Experimental Design 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.
Prerequisites: STA 662 or permission of instructor.
STA 676 Sample Survey Methods 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.
Prerequisites: STA 352 or STA 572 or STA 662 or permission of instructor.
STA 677 Advanced Topics in Data Analysis and Quantitative Methods 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.
Prerequisites: STA 662.
STA 682 Theory of Time Series 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.
Prerequisites: STA 551 or STA 651, or permission of instructor.
STA 689 Experimental Course 3
This number reserved for experimental courses. Refer to the Course Schedule for current offerings.
STA 690 Graduate Seminar 1
Development of presentation skills through reading, discussions, and presentation of current research topics in applied statistics.
Prerequisites: STA 662 or permission of instructor.
Notes: Grade: Satisfactory/Unsatisfactory (S/U).
STA 691 Actuarial Exam Preparation Seminar 1
Topics vary according to interest and demand. Intended to help prepare for the P/1, FM/2, or MLC exam.
Prerequisites: STA 551 or STA 687 or permission of instructor.
Notes: One credit maximum. May be repeated; Grade: Pass/Not Pass (P/NP).
STA 698 Project in Statistics 3
Directed research project in statistics.
Prerequisites: Permission of instructor.
Notes: Grade: Satisfactory/Unsatisfactory (S/U).
STA 699 Thesis 1-6
STA 701 Seminar in Computational Statistics 3
Readings from the literature in Computational Statistics.
Prerequisites: 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
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.
Prerequisites: STA 562, STA 673, or permission of instructor.
Corequisites: STA 674.
STA 709 Topics in Computational Statistics 3
Advanced study in special topics in Computational Statistics.
Prerequisites: STA 552 or STA 652 or permission of instructor.
Notes: May be repeated for credit.
STA 801 Thesis Extension 1-3
Thesis Extension.
STA 803 Research Extension 1-3