The Graduate School Bulletin
Department of Mathematics and Statistics
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Department of Mathematics and Statistics Homepage
Admissions Information
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Faculty
Requirements for the Post-Baccalaureate Certificate in Statistics
Requirements for the Master of Arts in Mathematics
Applied Mathematics Concentration
Applied Statistics Concentration
Pure Mathematics Concentration
Requirements for the Doctor of Philosophy in Computational Mathematics
Doctoral Minor in Statistics
MAT Mathematics Courses
STA Statistics Courses
Faculty
Professors
Alexander Chigogidze, D.Sc.
Geometric topology, functional analysis (Head of Department).
Paul F. Duvall, Jr., Ph.D.
Geometric topology, combinatorics, dynamics (Director of Graduate Study).
Sat N. Gupta, Ph.D.
Sampling designs, time series forecasting, biostatistics.
Jerry E. Vaughan, Ph.D.
General topology and set theory.
Associate Professors
Maya Chhetri, Ph.D.
Nonlinear elliptic PDE’s, nonlinear functional analysis, applied mathematics.
Igor Erovenko, Ph.D.
Combinatorial properties of linear groups, bounded generation of S-arithmetic groups.
Richard H. Fabiano, Ph.D.
Analysis, applied mathematics, differential equations, and control theory.
Scott J. Richter, Ph.D.
Nonparametric methods, equivalence testing, statistical consulting.
Carol Seaman, Ph.D.
Undergraduate mathematics education.
Brett A. Tangedal, Ph.D.
Number theory.
Assistant Professors
Gregory Bell, Ph.D.
Geometric group theory, geometric topology, asymptotic invariants of groups.
Roland Deutsch, Ph.D.
Environmetrics, computational statistics, multivariate statistics and nonparametric statistics.
Carlos Nicolas, Ph.D.
Combinatorial and computational geometry, enumerative combinatorics.
Sebastian Pauli, Ph.D.
Computational number theory, algebraic number theory, computer algebra.
Jan Rychtar, Ph.D.
Functional analysis, game theory.
Filip Saidak, Ph.D.
Analytic and probabilistic number theory, mathematical biology.
Clifford Smyth, Ph.D.
Combinatorics.
Dan Yasaki, Ph.D.
Computational number theory, modular forms.
Requirements for the Post-Baccalaureate Certificate in Statistics
The Department of Mathematics and Statistics offers a graduate program of study leading to a 12 hour Post-Baccalaureate Certificate in statistics. The purpose of the certificate 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.
Required Courses (6 hours)
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 hours)
Students must complete two additional three- hour STA courses at the 500-level or above, excluding STA 571/571L, STA 572/572L, and STA 580.
Requirements for the Master of Arts in Mathematics
The Department of Mathematics and Statistics offers a graduate program of study leading to a Master of Arts degree in three areas of concentration: applied mathematics (30-33 hours), applied statistics (33 hours), and pure mathematics (30-33 hours). In the applied mathematics and pure mathematics concentrations, there is a thesis option (30 hours) and a non-thesis option (33 hours). 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. 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 Ph.D. program in computational mathematics are urged to elect the concentration in pure mathematics. They may then use the doctoral qualifying examinations to satisfy the comprehensive examination requirement in the non-thesis option for the M.A. degree.
Applied Mathematics Concentration (30-33 Hours)
Algebra or Analysis (3 hours)
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 Modern Algebra (3)
MAT 595 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 hours)
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 623, 624 Numerical Mathematics (3) (3)
MAT 631, 632 Combinatorics and Graph Theory (3) (3)
MAT 647, 648 Linear Algebra and Matrix Theory (3) (3)
MAT 615, CSC 653 Symbolic Logic and Advanced Theory of Computation (3) (3)
MAT 615, CSC 656 Symbolic Logic and Foundations of Computer Science (3) (3)
CSC 653, 656 Advanced Theory of Computation and Foundations of Computer Science (3) (3)
MAT 695, 696 Real Analysis (3) (3)
MAT 645, 646 Approximation Theory (3) (3)
STA 651, 652 Mathematical Statistics (3) (3)
Electives (12-21 hours)
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 or Comprehensive Examination
Each candidate may elect to prepare a thesis or pass a written comprehensive examination on his/her program of course work. The thesis option is a 30 hour program; the non-thesis option is a 33 hour program.
Thesis (6 hours)
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.
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 Hours)
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 hours)
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 hours)
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 hours)
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 hours)
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 523/524 Numerical Analysis and Computing (3) (3)
CSC 526 Bioinformatics (3)
ECO 553 Economic Forecasting (3)
ECO 722 Time Series and Forecasting (1-4)
ECO 723 Predictive Data Mining (1-4)
ERM 669 Item Response Theory (3)
ERM 728 Factor Analysis and Multidimensional Scaling (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 541/542 Stochastic Processes (3) (3)
Thesis or Project (Capstone Experience)
Each candidate must elect to prepare a thesis or project. Both options require 33 hours.
Thesis (6 hours)
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 hours)
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.
Pure Mathematics Concentration (30-33 Hours)
Algebra and Analysis (9 hours)
Each candidate must complete any three of the following four courses:
MAT 591 Advanced Modern Algebra (3)
MAT 592 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, 6, or 9 hours must be replaced by the same number of hours chosen in consultation with the Director of Graduate Study.)
Students who intend to continue in the doctoral program in computational mathematics are strongly advised to complete all four of the above courses.
Core Courses (9 hours)
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 631, 632 Combinatorics and Graph Theory (3) (3)
MAT 647, 648 Linear Algebra and Matrix Theory (3) (3)
MAT 688, 689 Mathematical Logic and Axiomatic Set Theory (3) (3)
MAT 691, 692 Modern Abstract Algebra (3) (3)
MAT 693, 694 Complex Analysis (3) (3)
MAT 695, 696 Real Analysis (3) (3)
MAT 697, 698 General Topology (3) (3)
Electives (6-15 hours)
With prior approval of the Director of Graduate Study, a student will select 6-15 hours of other 500-600 level mathematics courses.
Thesis or Comprehensive Examination (Capstone Experience)
Each candidate may elect to (1) prepare a thesis or (2) pass a written comprehensive examination on his/her program of course work. The thesis option is a 30 hour program, and the non-thesis option is a 33 hour program.
Thesis (6 hours)
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.
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. This requirement can be met by passing three of the department’s doctoral qualifying examinations. Please consult with the Director of Graduate Study for further details.
Requirements for the Doctor of Philosophy in Computational Mathematics
The Department of Mathematics and Statistics offers a graduate program of study leading to the Ph.D. in computational mathematics. The program requires a minimum of 60 hours, including 48 hours of course work in mathematics or related area and 12 hours of dissertation.
Course Work (48 hours)
The student selects 48 hours of course work in mathematics and related areas with the approval of the Director of Graduate Study.
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 and should be taken prior to the beginning of the fifth semester. These examinations each cover the material of two courses. The student must pass examinations in three of the following five areas.
Algebra—MAT 591 Advanced Modern Algebra, MAT 592 Abstract Algebra
Analysis—MAT 595 Mathematical Analysis, MAT 596 – Mathematical Analysis
Topology—MAT 697 General Topology, MAT 698 General Topology
Combinatorics—MAT 631 Combinatorics, MAT 632 Graph Theory
Numerical Mathematics—MAT 623 Numerical Mathematics, MAT 624 Numerical Mathematics
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.
Other Reviews and Examinations
When a student has passed the comprehensive examination, and completed the programming project successfully, the student submits a dissertation research proposal, which is defended before the dissertation advisor and the advisory committee in an oral examination. After passing this examination, the student may then make a formal application to the Graduate School for admission for candidacy for a doctoral degree.
The advisory committee shall examine the dissertation, and no dissertation shall be accepted unless it secures unanimous approval of the advisory committee. The doctoral candidate who has successfully completed all other requirements for the degree will be scheduled by the chair of the advisory committee to take a final oral examination.
Schedule for Examinations and Projects
| Semester | Examination or Project |
|---|---|
| 1-5 | 3 written comprehensive examinations |
| 2-6 | Programming project |
| 3-7 | Dissertation proposal (oral examination) |
| 6-14 | Dissertation defense (oral examination) |
Dissertation (12 hours)
MAT 799 Dissertation (12)
Requirements for the Doctoral Minor in Statistics
Students pursuing a doctorate from other departments may obtain a statistics minor by completing 18 semester hours of graduate level statistics courses.
Required Courses (6 hours)
STA 661 Advanced Statistics in the Behavioral and Biological Sciences I
STA 662 Advanced Statistics in the Behavioral and Biological Sciences II
Electives (12 hours)
Four additional three-hour STA courses, excluding 571, 572, and 580.
MAT Mathematics Courses
| 503 | Problem Solving in Mathematics (3:3) |
| Pr. grade of at least C in 191 and 303 or permission of instructor 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. This course can not be applied toward the requirements for the M.A. degree in mathematics. | |
| 504 | Foundations of Geometry (3:3) |
| Pr. grade of at least C in 292 or permission of instructor 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. This course can not be applied toward the requirements for the M.A. degree in mathematics. | |
| 505 | Foundations of Mathematics (3:3) |
| Pr. grade of at least C in 292 or 303 or permission of instructor 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. This course can not be applied toward the requirements for the M.A. degree in mathematics. | |
| 513 | Historical Development of Mathematics (3:3) |
| Pr. grade of at least C in 292 Study of the historical development of mathematics—not a history of the persons involved in this development. This course can not be applied toward the requirements for the M.A. degree in mathematics. | |
| 514 | Theory of Numbers (3:3) |
| Pr. grade of at least C in 311, or permission of instructor Introduction to multiplicative and additive number theory. Divisibility, prime numbers, congruences, linear and non-linear Diophantine equations (including Pell’s equation), quadratic residues, number-theoretic functions, and other topics. | |
| 515 | Mathematical Logic (3:3) |
| Pr. grade of at least C in 253 or 311, or permission of instructor Formal languages, recursion, compactness, and effectiveness. First-order languages, truth, and models. Soundness and completeness theorems. Models of theories. | |
| 516 | Polynomial Rings (3:3) |
| Pr. grade of at least C in 311 or permission of instructor Rings, integral domains, fields, division algorithm, factorization theorems, zeros of polynomials, greatest common divisor, relation between the zeros and the coefficients of a polynomial, formal derivatives, prime polynomials, Euclidean rings, the Fundamental Theorem of Algebra. | |
| 517 | Theory of Groups (3:3) |
| Pr. grade of at least C in 311 or permission of instructor Elementary properties of groups and homomorphisms, quotients and products of groups, the Sylow theorems, structure theory for finitely generated Abelian groups. | |
| 518 | Set Theory and Transfinite Arithmetic (3:3) |
| Pr. grade of at least C in 311 or 395 or permission of instructor The axioms of set theory, operations on sets, relations and functions, ordinal and cardinal numbers. | |
| 519 | Intuitive Concepts in Topology (3:3) |
| Pr. grade of at least C in 311 or 395 or permission of instructor Basic concepts, vector fields, the Jordan curve theorem, surfaces, homology of complexes, continuity. | |
| 520 | Non-Euclidean Geometry (3:3) |
| Pr. grade of at least C in 311 or 395 or permission of instructor The fifth postulate, hyperbolic geometries, elliptic geometries, the consistency of the non-Euclidean geometries, models for Euclidean and non-Euclidean geometries, elements of inversion. | |
| 521 | Projective Geometry (3:3) |
| Pr. permission of instructor 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, ideal and imaginary elements, models, and Euclidean specifications. | |
| 522 | Hilbert Spaces and Spectral Theory (3:3) |
| Pr. grade of at least C in 395 or permission of instructor Vector-spaces: basis, dimension, Hilbert spaces; pre-Hilbert spaces, norms, metrics, orthogonality, infinite sums. Linear subspaces; annihilators, closed and complete subspaces, convex sets. Continuous linear mappings; normed spaces. Banach spaces, Banach algebras, dual spaces. Reisz-Frechet theorem. Completion. Bilinear and sesquilinear maps. Adjoints. Operators in Hilbert space: isometric, unitary, self-adjoint, projection, and normal operations. Invariant subspaces. Continuous operators. Spectral theorems for a normal co-operator. | |
| 531 | Combinatorial Analysis (3:3) |
| Pr. grade of at least C in 253 or 295 or 311 or 395, or permission of instructor The pigeon-hole principle, permutations, combinations, generating functions, principle of inclusion and exclusion, distributions, partitions, recurrence relations. | |
| 532 | Introductory Graph Theory (3:3) |
| Pr. grade of at least C in 310 and any one of the following courses: 253, 295, 311, 395, 531 Basic concepts, graph coloring, trees, planar graphs, networks. | |
| 540 | Complex Functions with Applications (3:3) |
| Pr. grade of at least C in 293 The complex number system, holomorphic functions, power series, complex integration, representation theorems, the calculus of residues. | |
| 541, 542 | Stochastic Processes (3:3), (3:3) |
| Pr. grade of at least C in 394 and either 353 or STA 351 Markov processes, Markov reward processes, queuing, decision making, graphs and networks. Applications to performance, reliability, and availability modeling. | |
| 545 | Differential Equations and Orthogonal Systems (3:3) |
| Pr. grade of at least C in 293 and 390 or permission of instructor An introduction to Fourier series and orthogonal sets of functions, with applications to boundary value problems. | |
| 546 | Partial Differential Equations with Applications (3:3) |
| Pr. grade of at least C in 545 Fourier integrals, Bessel functions, Legendre polynomials and their applications. Existence and uniqueness of solutions to boundary value problems. | |
| 549 | Topics in Applied Mathematics (3:3) |
| Pr. grade of at least C in 293 and 390 or permission of instructor Selected topics of current interest in applied mathematics. May be repeated for credit with approval of department head. | |
| 556 | Advanced Discrete Mathematics (3:3) |
| Pr. grade of at least C in 253 or permission of instructor Advanced topics in discrete mathematics and their uses in studying computer science. | |
| 589 | Experimental Course |
| This number reserved for experimental courses. Refer to the Course Schedule for current offerings. | |
| 591 | Advanced Modern Algebra (3:3) |
| Pr. grade of at least C in 311 Set theory: sets, mapping, integers. Group theory: normal subgroups, quotient groups, permutation groups. Sylow theorems. Ring theory: homomorphisms, ideals, quotient rings, integral domains, fields, Euclidean rings, polynomial rings. | |
| 592 | Abstract Algebra (3:3) |
| Pr. grade of at least C in 591 or 311 with permission of instructor Fields: extensions, transcendental elements, roots of polynomials, Euclidean construction, Galois theory, solvability of radicals. Linear transformations: characteristic roots, canonical forms of matrices, trace and transpose. Hermitian, unitary, and normal transformations. | |
| 593, 594 | Directed Study in Mathematics (1-3), (1-3) |
| 595, 596 | Mathematical Analysis (3:3), (3:3) |
| Pr. 395 or permission of instructor Real number axioms, basic topology, sequences, series, continuity, differentiation. Riemann-Stieltjes integral. | |
| 601 | Seminar in the Teaching of Mathematics I (1:1) |
| Seminar on practices and principles of undergraduate teaching in mathematics and statistics. Required for all teaching assistants. (Graded on S-U basis) | |
| 602 | Seminar on Mathematical Software (3:3) |
| Pr. knowledge of a programming language Variety of issues in the design of mathematical software, i.e., type systems, user interfaces, and memory managment. Each student investigates one computer algebra system more closely. | |
| 606 | Calculus for Middle Grade Teachers (3:3) |
| Pr. 505 or permission of instructor History, developments, major concepts, and applications of differential and integral calculus covering functions of several variables. No credit toward mathematics degrees. | |
| 607 | Abstract Algebra for Middle Grade Teachers (3:3) |
| Pr. 303 and 505; or permission of instructor Development and major concepts of abstract algebraic structures including groups, rings, fields, vector spaces, and matrix algebra. No credit toward mathematics degrees. | |
| 623, 624 | Numerical Mathematics (3:3), (3:3) |
| Pr. MAT 390, MAT 595, MAT 596, or equivalents Functional analytic treatment of computation, approximation, optimization, interpolation, smoothing equations, linear systems, differential equations. Emphasis on the mathematical development and analysis of numerical techniques. | |
| 631 | Combinatorics (3:3) |
| Pr. 311 or permission of instructor Topics include selections, arrangements, theory of generating functions, inclusion-exclusion principle, recurrences, Polya’s theory, block designs, stirling numbers, coding theory. | |
| 632 | Graph Theory (3:3) |
| Pr. 631 or permission of instructor 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. | |
| 645, 646 | Approximation Theory (3:3), (3:3) |
| Pr. 390, 595, 596 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. | |
| 647, 648 | Linear Algebra and Matrix Theory (3:3), (3:3) |
| Pr. 310, 311 or permission of instructor 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. | |
| 649 | Topics in Operations Research (3:3) |
| Pr. permission of instructor 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. | |
| 650 | Management Decision-Making Under Uncertainty (3:3) |
| Pr. permission of instructor Models and techniques to be used in making decisions under uncertainty. Markov Chains, Linear Programming Under Uncertainty, and Chance-Constrained programming. | |
| 659 | Advanced Topics in Mathematics (3:3) |
| Pr. permission of instructor Topics vary according to interest and demand, and include algebra, applied mathematics, combinatorics, dynamics, mathematical logic, topology, and other topics. May be repeated for credit when topic varies. | |
| 659 | Computational Algebra (3:3) |
| Pr. 591, 592, and knowledge of a programming language. or permission of instructor Variety of basic subjects in computational algebra: fast arithmetic, algorithms for finite fields, matrix normal forms over rings, polynomial factorization, and Groebner bases. | |
| 671 | Computational Algebra (3:3) |
| Pr. 591, 592, and knowledge of a programming language. or permission of instructor Variety of basic subjects in computational algebra: fast arithmetic, algorithms for finite fields, matrix normal forms over rings, polynomial factorization, and Groebner bases. |
|
| 688, 689 | Mathematical Logic and Axiomatic Set Theory (3:3), (3:3) |
| Pr. 311, 394, or equivalents 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. | |
| 690 | Mathematics Seminar (2:2) |
| Pr. admission to candidacy for master’s degree Topics in mathematics suitable for development into a master’s thesis. Current mathematical literature. | |
| 691, 692 | Modern Abstract Algebra (3:3), (3:3) |
| Pr. bachelor’s degree with a major in mathematics. Credits equivalent to credits for mathematics 310, 311, 595, and 596, or permission of instructor and department head 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. | |
| 693, 694 | Complex Analysis (3:3), (3:3) |
| Pr. bachelor’s degree with a major in mathematics. Credits equivalent to credits for mathematics 310, 311, 595, and 596, or permission of instructor and department head The complex number system, holomorphic functions, power series, complex integration, representation theorems, the calculus of residues. | |
| 695, 696 | Real Analysis (3:3), (3:3) |
| Pr. bachelor’s degree with a major in mathematics. Credits equivalent to credits for mathematics 310, 311, 595, and 596, or permission of instructor and department head 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. | |
| 697, 698 | General Topology (3:3), (3:3) |
| Pr. bachelor’s degree with a major in mathematics. Credits equivalent to credit for mathematics 310, 311, 595, and 596, or permission of instructor and department head 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. | |
| 699 | Thesis (1-6) |
| 701 | Graduate Seminar in Computational Mathematics (3:3) |
| Pr. 671 or permission of instructor Readings from the literature of computational mathematics. May be repeated for credit when topic varies. | |
| 709 | Topics in Computational Mathematics (3:3) |
| Pr. 671 or permission of instructor Advanced study in special topics in computational mathematics. May be repeated for credit when topic varies. | |
| 711 | Experimental Course |
| This number reserved for experimental courses. Refer to the Course Schedule for current offerings. | |
| 721 | Mathematical Cryptography (3:3) |
| Pr. 671 or permission of instructor 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. | |
| 742 | Computational Number Theory (3:3) |
| Pr. 671 or permission of instructor Main algorithms used to compute basic information about algebraic number fields, including integral bases, ideal factorization, system of fundamental units, and class group structure. | |
| 747 | Computational Topology (3:3) |
| Pr. 671 or permission of instructor Triangulations and WRAP. Computing homology algorithmically. Morse theory and persistent homology. Computations on knots, braids, and links. | |
| 799 | Dissertation (1-12) |
| 801 | Thesis Extension (1-3) |
| 803 | Research Extension (1-3) |
Courses Planned Primarily for Mathematics Teachers
The courses below are planned primarily for teachers who have a bachelor’s degree with a major in mathematics. They are offered by special arrangement.
Prerequisites: The student is expected to have credits in courses equivalent to 191, 292, 293, 310, 311, or 390.
| 613 | Development of Mathematics (3:3) |
| 614 | Advanced Number Theory (3:3) |
| 615 | Symbolic Logic (3:3) |
| 616 | Polynomials over General Rings (3:3) |
| 617 | Algebraic Theory of Semigroups (3:3) |
| 618 | Transfinite Ordinal and Cardinal Numbers (3:3) |
| 619 | Conceptual Topology (3:3) |
| 620 | A Survey of Geometry (3:3) |
| 621 | Advanced Linear Geometry (3:3) |
STA Statistics Courses
| 551 | Introduction to Probability (3:3) |
| Pr. grade of at least C in 290 and MAT 293 or permission of instructor Events and probabilities (sample spaces), dependent and independent events, random variables and probability distributions, expectation, moment generating functions, multivariate normal distribution, sampling distributions. (Fall) | |
| 552 | Introduction to Mathematical Statistics (3:3) |
| Pr. grade of at least C in 551 or permission of instructor Point estimation, hypothesis testing, confidence intervals, correlation and regression, small sample distributions. (Spring) | |
| 562 | Statistical Computing (3:3) |
| Pr. 291 or 580 and knowledge of a scientific programming language Statistical methods requiring significant computing or specialized software. Simulation, randomization, bootstrap, Monte Carlo techniques, numerical optimization. Extensive computer programming involved. NOT a course in the use of statistical software packages. | |
| 565 | Analysis of Survival Data (3:3) |
| Pr. 291 or 352 or permission of instructor 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. | |
| 571 | Statistical Methods for Research I (3:3) |
| Coreq. 571L 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. | |
| 571L | Statistical Methods Laboratory I (1:0:2) |
| Coreq. 571 Using statistical software packages for data analysis. Problems parallel assignments in 571. | |
| 572 | Statistical Methods for Research II (3:3) |
| Pr. 571 and 571L or permission of instructor. Coreq. 572L 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. | |
| 572L | Statistical Methods Laboratory II (1:0:2) |
| Pr. 571 and 571L or permission of instructor. Coreq. 572 Using statistical software packages for data analysis. Problems parallel assignments in 572. | |
| 573 | Theory of Linear Regression (3:3) |
| Pr. grade of at least C in 352 and MAT 310, or 662, or permission of instructor 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. | |
| 574 | Theory of the Analysis of Variance (3:3) |
| Pr. 573 or permission of instructor 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. | |
| 575 | Nonparametric Statistics (3:3) |
| Pr. grade of at least C in 352 or 572 or 662 or permission of instructor 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. | |
| 580 | Biostatistical Methods (3:3) |
| Pr. grade of at least C in 271 or 290, or permission of instructor Statistical methods for biological research including: descriptive statistics, probability distributions, parametric and nonparametric tests, ANOVA, regression, correlation, contingency table analysis. | |
| 581 | SAS System for Statistical Analysis (1:1) |
| Pr. 271, 290 or similar introductory statistics course Creating, importing, and working with SAS data sets. Using SAS procedures for elementary statistical analysis, graphical displays, and report generation. | |
| 589 | Experimental Course |
| This number reserved for experimental courses. Refer to the Course Schedule for current offerings. | |
| 593, 594 | Directed Study in Statistics (1-3), (1-3) |
| 651, 652 | Mathematical Statistics (3:3), (3:3) |
| Pr. 352 and either MAT 394 or MAT 395 or MAT 595 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. | |
| 661 | Advanced Statistics in the Behavioral and Biological Sciences I (3:3) |
| Pr. 271 or an equivalent introductory statistics course 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. | |
| 662 | Advanced Statistics in the Behavioral and Biological Sciences II (3:3) |
| Pr. 661 or permission of instructor Continuation of STA 661. Multiple regression and correlation, analysis of covariance, factorial ANOVAs, randomized block designs, multiple comparisons, split-plot designs, repeated measures. | |
| 667 | Statistical Consulting (1:1) |
| Pr. permission of instructor 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. (Graded on S-U basis. Credit is not applicable to a graduate plan of study.) | |
| 668 | Consulting Experience (1:0:1) |
| Pr. 662 or permission of instructor Development of consulting skills through reading and discussion of literature on statistical consulting and participation in statistical consulting sessions. (Graded on S-U basis). | |
| 670 | Categorical Data Analysis (3:3) |
| Pr. 662 or permission of instructor 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. | |
| 671 | Multivariate Analysis (3:3) |
| Pr. 573 or 662 or permission of instructor 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. | |
| 672 | Applied Statistical Computing (3:3) |
| Pr. 572 or 662 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. | |
| 673, 674 | Statistical Linear Models I, II (3:3), (3:3) |
| Pr. 352 and MAT 310 or permission of instructor Abstract vector spaces, inner product spaces, projections, the Spectral Theorem, least squares, multiple regression, ANOVA, multiple comparisons, data analysis. | |
| 675 | Advanced Experimental Design (3:3) |
| Pr. 662 or permission of instructor 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. | |
| 676 | Sample Survey Methods (3:3) |
| Pr. 352 or 572 or 662 or permission of instructor 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. | |
| 677 | Advanced Topics in Data Analysis and Quantitative Methods (3:3) |
| Pr. 662 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. | |
| 690 | Graduate Seminar (1:0:1) |
| Pr. 662 or permission of instructor Development of presentation skills though reading, discussions, and presentation of current research topics in applied statistics. (Graded on S-U basis) | |
| 698 | Project in Statistics (3) |
| Pr. permission of instructor Directed research project in statistics. (Graded on S-U basis) | |
| 699 | Thesis (1-6) |
| 711 | Experimental Course |
| This number reserved for experimental courses. Refer to the Course Schedule for current offerings. | |
| 801 | Thesis Extension (1-3) |
| 803 | Research Extension (1-3) |