Professors. Donald M. Davis, Ph.D. (Stanford), chairperson; Bennett Eisenberg, Ph.D. (M.I.T.); B. K. Ghosh, Ph.D. (London); Wei-Min Huang, Ph.D. (Rochester); Samir A. Khabbaz, Ph.D. (Kansas); Jerry P. King, Ph.D. (Kentucky); Nelson G. Markley, Ph.D. (yale), Provost; Gregory T. McAllister, Ph.D. (Berkeley), head of the Division of Applied Mathematics and Statistics; George E. McCluskey, Ph.D. (Pennsylvania), head of the Division of Astronomy; Eric P. Salathe, Ph.D. (Brown), director of the Institute for Biomedical Engineering and Mathematical Biology; Murray Schechter, Ph.D. (N.Y.U.); Andrew K. Snyder, Ph.D. (Lehigh); Lee J. Stanley, Ph.D. (Berkeley); Gilbert A. Stengle, Ph.D. (Wisconsin); Joseph E. Yukich, Ph.D. (M.I.T.).
Associate professors. Bruce A. Dodson, Ph.D. (S.U.N.Y. at Stony Brook); Vladimir Dobric, Ph.D. (Zagreb, Croatia); David L. Johnson, Ph.D. (M.I.T.); Clifford S. Queen, Ph.D. (Ohio State); Penny D. Smith, Ph.D. (Polytechnic Institute of Brooklyn); Susan Szczepanski, Ph.D. (Rutgers); Ramamirtham Venkataraman, Ph.D. (Brown).
Assistant professors. Garth Isaak, Ph.D. (Rutgers); Terrence Napier, Ph.D. (University of Chicago).
Adjunct professor. Howard Fegan, Ph.D. (Oxford).
Mathematics is the universal language of science, and is essential for a clear and complete understanding of virtually all phenomena. Mathematical training prepares a student to express and analyze problems and relationships in a logical manner in a wide variety of disciplines including the physical, engineering, social, biological, and medical sciences, business, and pure mathematics itself. This is a principal reason behind the perpetual need and demand for mathematicians in education, research centers, government, and industry.
The department offers three major programs leading to the degrees of bachelor of arts in mathematics, bachelor of science in mathematics, and bachelor of science in statistics. It also offers five minor programs for undergraduates.
The Division of Astronomy and the Division of Applied Mathematics and Statistics are parts of the Department of Mathematics. Details on these divisions may be found in separate listings in the catalog.
The program involves a total of 121 credit hours, 42 of which are in required major courses listed below. The remaining 79 credit hours are for college and university requirements, general electives, and additional mathematics courses that a student may wish to take.
Required Major Courses (42 credit hours) Math 21, 22, 23 Calculus I, II and III (12) or Math 31, 32, 33 Honors Calculus I, II, III Math 205 Linear Methods (3) or Math 320 Ordinary Differential Equations (4) Math 219 Principles of Analysis I (4) Math 243 Algebra (4) Math 244 Linear Algebra (4) Math 220 Principles of Analysis II (4) or Math 316 Complex Analysis (4) or Math 208 Complex Variables (3) Math Electives (12)Note: The twelve hours of electives must be approved by the student's major advisor. A student must achieve an average of 2.0 or higher in major courses.
Each student is assigned a faculty advisor to guide an individual program and supervise the choice of electives.
Required Major Courses (39 credit hours) Math 21, 22, 23 Calculus (12) or Math 31, 32, 33 Honors Calculus (12) Math 12 Basic Statistics (4) or Math 231 Probability and Statistics (3) Math 205 Linear Methods (3) Math 219 Principles of Analysis I (4) Math 220 Principles of Analysis II (4) or Math 208 Complex Variables (3) or Math 316 Complex Analysis (4) Math 243 Algebra (4) Math 244 Linear Algebra (4) two CSc courses or one CSc course and Eng 1.Major Electives (12 credit hours) Four courses with specific mathematical content chosen with the approval of the faculty advisor.
Electives (33 credit hours) These are to be selected with the approval of the faculty advisor to include at least 15 credit hours from at least two fields of application.
Required Major Courses (45 credit hours) Math 21, 22, 23 Calculus (12) or Math 31, 32, 33 Honors Calculus (12) Math 12 Basic Statistics (4) or Math 231 Probability and Statistics (3) Math 205 Linear Methods (3) Math 208 Complex Variables or Math 316 Complex Analysis (4) Math 219 Principles of Analysis I (4) Math 230 Numerical Methods (3) Math 243 Algebra (4) or Math 261 Discrete Structures (3) or Math 244 Linear Algebra (4) Math 320 Ordinary Differential Equations (4) Math 322 Methods of Applied Analysis I (3) two CSc courses or one CSc course and Eng 1.Major Electives (12 credit hours)
Four courses with specific mathematical content chosen with the approval of the faculty advisor.
Electives (27 credit hours)
These are to be selected to include a field of application with the approval of the faculty advisor.
The program involves a total of 121 credit hours, which are divided into four parts.
College and University Requirements (37 credit hours) See page 33.
Required Major Courses (42 credit hours) Math 21, 22, 23 Calculus I, II and III (12) or Math 31, 32, 33 Honors Calculus I, II, III (12) Math 12 Basic Statistics (4) Math 205 Linear Methods (3) Math 309 Theory of Probability (3) Math 310 Probability and Its Applications (3) Math 312 Applied Statistics (3) Math 334 Mathematical Statistics (4) Math 338 Regression Analysis (4) Math 374 Statistical Project (3) CSc 11 Introduction to Computing (4) CSc 17 Data Structures (4)Note: Math 12 may be replaced by Math 231. A student must achieve an average of 2.0 or higher in major courses.
Major Electives (12 credit hours)
Four courses chosen from: Math 208, 219, 230, 244, 320, 322, IE 221, 222, 316, 332, 339.
Professional Electives (30 credit hours)
These are to be selected from at least two fields of application of statistics and probability, such as biology, psychology, social relations, computer science, engineering, economics, and management.
The major and professional electives must be approved by the faculty advisor.
Each program requires twelve credit hours of work shown below, and Math 23 or 33. For substitutions, the student should consult the chairperson.
Minor in Pure Mathematics
Math 219, 243, 244
Math 220 or 303 or 307 or 316 or 342
Minor in Applied Mathematics
Two of Math 205, 208, 230, 231, 244, 320
Math 322
Math 323 or 341
*Minor in Probability and Statistics
Math 12 or 231
Math 309
Two of Math 310, 312, 334, 338
Minor in Actuarial Science
Math 202, 205, 230, 231
Math 309 or 334
For information on examinations of actuarial societies,
students may consult their minor advisor.
Minor in Astronomy
Phys 21, Astr 2
Astr 211 or 221
Astr 332 or 342
Intensive review of fundamental concepts in mathematics utilized in calculus, including functions and graphs, exponentials and logarithms, and trigonometry. This course is for students who need to take Math 51 or 21, but who require preparation in precalculus. In particular, students who fail the Math 51 Readiness Exam must pass Math 0 before being admitted to Math 51. The credits for this course do not count toward graduation, but do count on the GPA and current credit count. Prerequisite: department permission.
5. Introduction to Mathematical Thought (3) spring
Meaning, content, and methods of mathematical thought illustrated by topics that may be chosen from number theory, abstract algebra, combinatorics, finite or non-Euclidean geometries, gam e theory, mathematicallogic, set theory, topology. (MA)
9. Introduction to Finite Mathematics (4) fall
Systems of linear equations, matrices, introduction to linear programming. Sets, counting methods, probability, random variables, introduction to Markov chains. (MA)
12. Basic Statistics (4) fall-spring
A first course in the basic concepts and methods of statistics with illustrations from the social, behavioral, and biological sciences. Descriptive statistics; frequency distributions, mean and standard deviation, two-way tables, correlation and regression; random sampling, rules of probability, probability distributions and parameters, parameter estimation, confidence intervals, hypothesis testing, statistical significance. (MA)
21. Calculus I (4) fall-spring
Functions and graphs; limits and continuity; derivative, differential, and applications; Taylor's Theorem and other approximations; indefinite and definite integrals; trigonometric, logarithmic, exponential, and hyperbolic functions. (MA)
22. Calculus II (4) fall-spring
Applications of integration; techniques of integration; separable differential equations; infinite sequences and series; curves and vectors in the plane. Prerequisite: Math 21 or Math 31. (MA)
23. Calculus III (4) fall-spring
Vectors in space; partial derivatives; Lagrange multipliers; multiple integrals; vector analysis; exact differential equations and second-order differential equations with constant coefficients. Prerequisite: Math 22 or Math 32. (MA)
31. Honors Calculus I (4) fall
Same topics as in Math 21, but taught from a more thorough and rigorous point of view. (MA)
32. Honors Calculus II (4) spring
Same topics as in Math 22, but taught from a more thorough and rigorous point of view. Prerequisite: Math 31. (MA)
33. Honors Calculus III (4) fall
Same topics as in Math 23, but taught from a more thorough and rigorous point of view. Prerequisite: Math 32. (MA)
43. Survey of Linear Algebra (3) fall
Matrices, vectors, vector spaces and mathematical systems, special kinds of matrices, elementary matrix transformations, systems of linear equations, convex sets, introduction to linear programming. (MA)
51. Survey of Calculus I (4) fall-spring
Limits. The derivative and applications to extrema, approximation, and related rates. Exponential and logarithm functions, growth and decay. Integration. Partial derivatives and extrema. (MA)
52. Survey of Calculus II (3) fall-spring
Trigonometric functions and related derivatives and integrals. Techniques of integration. Differential equations. Probability and calculus. Prerequisite: Math 21 or 31 or 51. (MA)
61. Linear Algebra for Business and Economics (2) fall-spring
Matrices, solutions of linear systems, linear programming, examples from business and economics, computer solutions. (MA) Students may not receive credit for both Math 61 and 43.
75. Calculus I, Part A (2) fall
Covers the same material as the first half of Math 21 with some precalculus review. Meets three hours per week, allowing more class time for each topic than does Math 21. (MA)
76. Calculus I, Part B (2) spring
Continuation of Math 75, covering the second half of Math 21 with some precalculus review. Meets three hours per week. Final exam for this course is identical to the Math 21 final. Prerequisite: Math 75. (MA)
171. Readings (1-3) fall-spring
Study of a topic in mathematics under individual supervision. Intended for students with specific interests in areas not covered in the listed courses. Prerequisite: consent of the department chairperson. (MA)
202. Problem Solving (1)
Practice in solving problems using calculus, linear algebra, probability, and statistics. Problems taken from actuarial examinations and mathematics contests. Prerequisites: Math 205 and Math 231 or consent of the department.
205. Linear Methods (3) fall-spring
Linear differential equations and applications; matrices and systems of linear equations; vector spaces; eigenvalues and application to linear systems of differential equations. Prerequisite: Math 23 or Math 33 or Math 52. (MA)
207. (ChE 207) Introduction to Biomedical Engineering and Mathematical Physiology (3) fall
Topics in human physiology and mathematical analysis of physiological phenomena, including the cardiovascular and respiratory systems, biomechanics, and renal physiology; broad survey of bioengineering. Independent study projects. Prerequisite: Math 205. (MA)
208. Complex Variables (3) fall-spring
Functions of a complex variable; calculus of residues; contour integration; applications to conformal mapping and Laplace transforms. Prerequisite: Math 23 or Math 33. (MA)
219. Principles of Analysis I (4) fall
Existence of limits, continuity and uniform continuity; Heine-Borel Theorem; existence of extreme values; mean value theorem and applications; conditions for existence of the Riemann integral; absolute and uniform convergence; emphasis on theoretical material from the calculus of one variable. Prerequisite: Math 23 or Math 33. (MA)
220. Principles of Analysis II (4) spring
Continuation of Math 219. Functions of several variables; line and surface integrals; implicit functions. Prerequisite: Math 219. (MA)
230. Numerical Methods (3) fall
Representation of numbers and rounding error; numerical solution of equations; quadrature; polynomial and spline interpolation; numerical solution of initial and boundary value problems. Prerequisites: Math 205 (previously or concurrently) and knowledge of either FORTRAN or PASCAL. (MA)
231. Probability and Statistics (3) fall-spring
Probability and distribution of random variables; populations and random sampling; chi-square, t, and F distributions; estimation and tests of hypotheses; correlation and regression theory of two variables. Prerequisite: Math 23 or Math 33 or Math 52. (MA)
234. Fractal geometry (3-4)
Metric spaces and iterated function systems; various types of fractal dimension; Julia and Mandelbrot sets. Other topics such as chaos may be included. Small amount of computer use. Prerequisite: Math 23 or Math 33. (MA)
243. Algebra (3-4) spring
Introduction to basic concepts of modern algebra: groups, rings, and fields. (MA)
244. Linear Algebra (3-4) fall
Thorough treatment of the solution of m simultaneous linear equations in n unknowns, including a discussion of the computational complexity of the calculation. Vector spaces, linear dependence, bases, orthogonality, eigenvalues. Application as time permits. Prerequisite: Math 43 or Math 205 or Math 243. (MA)
251. Combinatorics (3-4)
Topics selected from enumeration, graphs and networks, Ramsey theory, ordered sets, min-max duality, and designs. Theory will be motivated by applications from operations research and computer science. Prerequisite: Math 22 or consent of instructor. (MA)
261. (CSc 261) Discrete Structures (3)
Topics in discrete mathematical structures chosen for their applicability to computer science and engineering. Sets, propositions, induction, recursion; combinatorics; binary relations and functions; ordering, lattices and Boolean algebra; graphs and trees; groups and homomorphisms. Prerequisites: Math 21, and either CSc 11 or Engr 1. (MA)
303. Mathematical Logic (3-4) fall
A course, on a mathematically mature level, designed not only to acquaint the student with logical techniques used in mathematics but also to present symbolic logic as an important adjunct to the study of the foundations of mathematics. (MA)
304. Axiomatic Set Theory (3-4) spring
A development of set theory from axioms; relations and functions; ordinal and cardinal arithmetic; recursion theorem; axiom of choice; independence questions. Prerequisite: Math 219 or consent of the department chairman. (MA)
307. General Topology I (3-4) fall
An introductory study of topological spaces, including metric spaces, separation and countability axioms, connectedness, compactness, product spaces, quotient spaces, function spaces. Prerequisite: Math 219. (MA)
309. Theory of Probability (3) fall
Probabilities of events on discrete and continuous sample spaces; random variables and probability distributions; expectations; transformations; simplest kind of law of large numbers and central limit theorem. The theory is applied to problems in physical and biological sciences. Prerequisite: Math 23 or Math 33 or Math 52. (MA)
310. Probability and Its Applications (3) spring
Continuation of Math 309. Random variables, characteristic functions, limit theorems; stochastic processes, Kolmogorov equations; Markov chains, random walks. Prerequisite: Math 309 or consent of the department chairperson. (MA)
312. Applied Statistics (3)
Exploratory data analysis; Monte Carlo methods; radomization and resampling. Computational aspects based on software tools and statistical packages. Prerequisite: Math 12 or Math 231. (MA)
316. Complex Analysis (3-4) spring
Concept of analytic function from the points of view of the Cauchy-Riemann equations, power series, complex integration, and conformal mapping. Prerequisite: Math 219. (MA)
320. Ordinary Differential Equations (3-4) spring
The analytical and geometric theory of ordinary differential equations, including such topics as linear systems, systems in the complex plane, oscillation theory, stability theory, geometric theory of nonlinear systems, finite difference methods, general dynamical systems. Prerequisite: Math 205, or both Math 23 and Math 244. (MA)
322. Methods of Applied Analysis I (3) fall
Fourier series, eigenfunction expansions, Sturm-Liouville problems, Fourier integrals and their application to partial differential equations; special functions. Emphasis is on a wide variety of formal applications rather than logical development. Prerequisite: Math 205 or consent of the department chairperson. (MA)
323. Methods of Applied Analysis II (3) spring
Green's functions; integral equations; variational methods; asymptotic expansions, method of saddle points; calculus of vector fields, exterior differential calculus. Prerequisite: Math 322. (MA)
327. Groups and Rings (3-4) fall
An intensive study of the concepts of group theory including the Sylow theorems, and of ring theory including unique factorization domains and polynomial rings. Prerequisite: Math 243 or consent of the department chairperson. (MA)
329. Recursive Functions and the Theory of Computation (3-4)
Core development of classical recursion theory, enumeration, index and recursion theorems, using a simple programming language as a model of computation. Other models of computation and Church's Thesis. Recursive operators and their fixed points. (MA)
334. Mathematical Statistics (3-4) spring
Populations and random sampling; sampling distributions; theory of statistical estimation; criteria and methods of point and interval estimation; theory of testing statistical hypotheses. Prerequisite: Math 231 or Math 309. (MA)
338. Regression Analysis (3-4) spring
Least square principles in multiple regression and their interpretations; estimation, hypothesis testing, confidence and prediction intervals; residual analysis, multicollinearity, selection of regression models; comparison of data sets, analysis of variance and covariance, simultaneous inference procedures. Use of computer packages for statistical analysis. Prerequisite: Math 12 or 231. (MA)
340. (CSc 340) Design and Analysis of Algorithms (3) spring
Algorithms for searching, sorting, counting, graph and tree manipulation, matrix multiplication, scheduling, pattern matching and fast Fourier transforms. Abstract complexity measures and the intrinsic complexity of algorithms and problems in terms of asymptotic behavior; correctness of algorithms. Prerequisites: Math 23 and CSc 15, or consent of the department chairperson. (MA)
341. Mathematical Models and Their Formulation (3) spring
Mathematical modeling of engineering and physical systems with examples drawn from diverse disciplines such as traffic flow, laser drilling, mold solidification, rocket design and business planning. Prerequisite: Math 205. (MA)
342. Number Theory (3-4)
A survey of elementary and nonelementary algebraic and analytic methods in the theory of numbers. Includes the Euclidean algorithm, Diophantine equations congruences, quadratic residues, primitive roots, number-theoretic functions as well as one or more of the following topics: distribution of primes, Pell's equation, Fermat's conjecture, partitions. Prerequisite: Math 219 or consent of the department chairperson. (MA)
347. Problem Solving (1) fall-spring
Emphasis on problems in analysis, linear algebra, and applications. May be repeated for credit with consent of the department chairperson. Prerequisites: Math 219 and Math 244. (MA)
350. Special Topics (3) fall-spring
A course covering special topics not sufficiently covered in listed courses. Prerequisite: consent of the department chairman. May be repeated for credit. (MA)
371. Readings (1-3) fall-spring
The study of a topic in mathematics under appropriate supervision, designed for the individual student who has studied extensively and whose interests lie in areas not covered in the listed courses. Prerequisite: consent of the department chairman. May be repeated for credit. (MA)
374. Statistical Project (3)
Supervised field project or independent reading in statistics or probability. Prerequisite: consent of the department chairperson. (MA)
To begin graduate work in mathematics a student must present evidence of adequate undergraduate preparation. The undergraduate program should have included a year of advanced calculus, a semester of linear algebra, and a semester of abstract algebra.
With a judicious choice of courses a student in the master's program can specialize in pure mathematics, applied mathematics, or statistics. The M.S. degree can serve both as a final degree in mathematics or as an appropriate background for the Ph.D. degree.
The department accepts candidates for the Ph.D. who desire to specialize in any of the areas listed above. Each candidate's plan of work must be approved by a special committee of the department. Although there are no specific course requirements, the Ph.D. candidates normally take several courses related to their area of specialization.
Set theory, real numbers; introduction to measures, Lebesgue measure; integration, general convergence theorems; differentiation, functions of bounded variation, absolute continuity; Lp spaces. Prerequisites: Math 220 or consent of department chairperson.
402. Real Analysis II (3) spring
Metric spaces; Introduction to Banach and Hilbert space theory; Fourier series and Fejer operators; general measure and integration theory, Radon-Nikodym and Riesz representation and theorems; Lebesgue-Stieltes integral. Prerequisites: Math 307 and Math 401.
404. Mathematical Logic (3)
Topics in quantification theory relevant to formalized theories, recursive functions, Godel's incompleteness theorem; algorithms and computability.
405. Partial Differential Equations I (3) fall
Classification of partial differential equations; methods of characteristics for first order equations; methods for representing solutions of the potential, heat, and wave equations, and properties of the solutions of these equations; maximum principles. Prerequisite: Math 220 or its equivalent.
406. Partial Differential Equations II (3) spring
Continuation of Math 405. Emphasis on second order equations with variable coefficients and systems of first order partial differential equations. Prerequisite: Math 405.
407. Theory and Technique of Optimization (3)
Linear programming: simplex and revised simplex methods, duality theory; unconstrained optimization by one dimensional search methods; convexity and Kuhn-Tucker conditions, applications to methods for constrained optimization.
408. Algebraic Topology I (3)
Polyhedra; fundamental groups; simplicial and singular homology.
409. Mathematics Seminar (1-6) fall
An intensive study of some field of mathematics not offered in another course. Prerequisite: consent of the department chairperson.
410. Mathematics Seminar (1-6) spring
Continuation of the field of study in Math 409 or the intensive study of a different field. Prerequisite: consent of the department chairperson.
414. Topics in Ordinary Differential Equations (3)
Topics from the analytical and qualitative theory of differential equations and dynamical systems such as: structural stability, ordered chaos and strange attractors, bifurcation theory, normal forms, asymptotic methods, spectral theory of differential operators, boundary value problems. Prerequisite: consent of the department chairperson.
416. Complex Function Theory (3) fall
Continuation of Math 316. Prerequisite: Math 316 or consent of the department chairperson.
419. Linear Operators on Hilbert Space (3)
Algebra and calculus of bounded and unbounded operators on Hilbert space; spectral analysis of self-adjoint, normal, and unitary operators. Interplay between operator theory and classical function theory is emphasized. Prerequisites: Math 220, and Math 208 or Math 316.
421. Introduction to Wavelets (3)
Continuous and discrete signals; review of Fourier analysis; discrete wavelets; time-frequency spaces; Haar and Walsh systems; multiresolution analysis; Hilbert spaces; quadratic mirror filters; fast wavelet transforms; computer code; applications to filtering, compression, and imaging. Prerequisite: ECE 108, Math 205, or consent of instructor.
423. Differential Geometry I (3)
Differential manifolds, tangent vectors and differentials, submanifolds and the implicit function theorem. Lie groups and Lie algebras, homogeneous spaces. Tensor and exterior algebras, tensor fields and differential forms, de Rham cohomology, Stoke's theorem, the Hodge theorem. Prerequisite: Math 219, 220, or Math 243 or Math 244 or Math 205 with consent of instructor.
424. Differential Geometry II (3)
Curves and surfaces in Euclidean space; mean and Gaussian curvatures, covariant differentiation, parallelism, geodesics, Gauss-Bonnet formula. Riemannian metrics, connections, sectional curvature, generalized Gauss-Bonnet theorem. Further topics. Prerequisite: Math 423.
428. Fields and Modules (3) spring
Field theory, including an introduction to Galois theory; the theory of modules, including tensor products and classical algebras. Prerequisite: Math 327.
430. Numerical Analysis (3) spring
Multistep methods for ordinary differential equations; finite difference methods for partial differential equations; numerical approximation of functions. Use of computer required. Prerequisite: Math 230 or consent of the department chairperson.
431. Calculus of Variations (3)
Existence of a relative minimum for single and multiple integral problems; variational inequalities of elliptic and parabolic types and methods of approximating a solution. Prerequisite: Math 220 or its equivalent.
435. Functional Analysis I (3) fall
Banach spaces and linear operators; separation and extension theorems; open mapping and uniform boundedness principles; weak topologies; local convexity and duality; Banach algebras; spectral theory of operators; and compact operators. Prerequisites: Math 307 and Math 401.
436. Functional Analysis II (3) spring
Continuation of Math 435. Topics such as distribution theory, nonlinear operators, fixed point theory and applications to classical analysis. Prerequisite: Math 435.
443. General Topology II (3)
Continuation of Math 307, with such topics as filters and nets, topological products, local compactness, paracompactness, metrizability, uniformity, function spaces, dimension theory. Prerequisite: Math 307.
444. Algebraic Topology II (3)
Continuation of Math 408. Cohomology theory, products, duality. Prerequisite: Math 408.
445. Topics in Algebraic Topology (3)
Selected topics reflecting the interests of the professor and the students. Prerequisite: Math 444.
449. Topics in Algebra (3)
Intensive study of topics in algebra with emphasis on recent developments. Prerequisite: consent of the department chairman. May be repeated for credit with the consent of the department chairperson.
450. Special Topics (3) fall-spring
Intensive study of some field of the mathematical sciences not covered in listed courses. Prerequisite: consent of the department chairman. May be repeated for credit with the consent of the department chairperson.
453. Function Theory (3)
The development of one or more topics in function theory, such as analytic continuation, maximum modulus principle, conformal representation, Taylor series analysis, integral functions, Dirichlet series, functions of several complex variables. Prerequisite: Math 416.
455. Topics in Number Theory (3)
Selected topics in algebraic and analytic number theory. Prerequisites: Math 316 and Math 327. May be repeated for credit with consent of the department chairperson.
461. Topics in Mathematical Statistics (3)
An intensive study of one or more topics such as theory of statistical tests, statistical estimation, regression, analysis of variance, nonparametric methods, stochastic approximation, and decision theory. Prerequisites: Math 334 and Math 401. May be repeated for credit with consent of the department chairperson.
462. Nonparametric Statistics (3) fall
Order and rank statistics; tests based on runs, signs, ranks, and order statistics; chi-square and Kolmogorov-Simirnov tests for goodness of fit; the two-sample problem; confidence and tolerance intervals. Prerequisite: Math 231 or 309.
463. Advanced Probability (3)
Measure theoretic foundations; random variables, integration in a measure space, expectations; convergence of random variables and probability measures; conditional expectations; characteristic functions; sums of random variables, limit theorems. Prerequisites: Math 309 and Math 401.
464. Advanced Stochastic Processes (3)
Theory of stochastic processes; stopping times; martingales; Markov processes; Brownian motion; Skorohod imbedding; Brownian bridge, laws of suprema; Gaussian processes. Prerequisites: Math 309 and Math 401.
471. Homological Algebra (3)
Modules, tensor products, categories and functions, homology functors, projective and injective modules. Prerequisite: Math 428.
472. Group Representations (3)
Linear representations and character theory with emphasis on the finite and compact cases. Prerequisite: Math 428 or consent of the department chairperson.
490. Thesis
499. Dissertation