Most courses are marked with the symbols F (Fall) or S (Spring) to indicate the semester when they are most likely to be offered. Courses marked FS are normally offered twice a year. "AF" and "AS" denote alternate F or S semesters. Courses not marked in this way are offered only irregularly.Math 309 is usually offered during the Summer Sessions but other upper level courses usually are not.
A tentative schedule of courses for each semester should be available on the Undergraduate Web Page early in the preceding semester.
AF Math 302 Elementary Geometry from an Advanced Point of View A rigorous development of Euclidean geometry along with an introduction to non-Euclidean geometry. Provides background useful for future high school mathematics teachers. Prerequisite: 310 or permission of instructor. Math 302 is offered in even-numbered fall semesters.
S Math 308 Mathematics for the Physical Sciences Continuation of Math 233 (Calculus III) with topics that are particularly useful to the physical sciences, Topics in multivariable and vector calculus may include: vector fields, div, grad, curl; line and surface integrals and connections to electromagnetism; Fourier series and integrals; boundary value problems (diffusion and wave equations); topics from calculus of variations. Prerequisite: Math 233. (Students cannot receive credit toward the math major/minor for BOTH 308 and 318).
FS Math 309 Matrix Algebra (Identical with ESE 309) Theory of matrices and vector spaces from a concrete, computational point of view. Topics include systems of linear equations, row reduction, rank and dimension, determinants, eigenvalues and eigenvectors, diagonalization of symmetric matrices. Some related computational computer software might be used. Prerequisite: 132FS Math 310 An introduction to the rigorous techniques used in advanced mathematics. Topics include set theory, methods of proof, counterexamples, basic logic, foundations of mathematics, construction of number systems, and elementary analysis. Some counting methods, combinatorial arguments and a little number theory may be included. The purpose of the course is to help bridge the gap between the more computationally oriented introductory courses and more theoretical advanced courses and that students learn to read and write simple proofs. Therefore it is a good idea for a major to complete 310 as early as possible. Math 310 is the recommended prerequisite for many other upper level courses that involve proof-writing, e.g., Math 302, 331, 4111, 429. Prerequisite: 233 (or 233 concurrently, with the instructor's permission).
F Math 310W Foundations for Higher Mathematics with Writing is a 4-credit version of Math 310 which has an extra meeting each week devoted to writing. It satisfies the College's requirement for a "writing intensive" (WI) course. College policy is that WI credit must be earned in the junior or senior year, so students should not take 310W as freshmen or sophomores to fulfill the WI (unless you have a written OK from the College Office). Because it is to each major's advantage to complete 310 as early as possible, we do NOT recommend postponing 310/310W to the junior year simply to be eligible for the WI. It is not required that the WI requirement be fulfilled within the major department, so earn it on some other course in another department!. Math 310W is only offered in the fall semester.
Math 312 Differential Equations and Dynamical Systems The qualitative theory of ordinary differential equations. Picard's existence and uniqueness theorem, the phase plane, Poincare-Bendixson theory, stationary points, attractors and repellors, graphical methods. Physical applications, including chaos, will be indicated. Prerequisite: 217, 309 and 318, or permission of instructor.
FS Math 318 Introduction to Calculus of Several Variables Continuation of Math 233, Calculus III, dealing with the calculus of functions of several variables. There is an attempt to introduce a little more rigor and, in addition to some new material, some topics from 233 are covered again from this point of view. This course is less rigorous than Math 4111-4121 sequence, but begins to introduce some work with proofs in analysis. Prerequisite: 233 and 309 (Students cannot receive credit toward the math major/minor for BOTH 308 and 318).
FS Math 3200 Elementary to Intermediate Statistics with Data Analysis An introduction to probability and statistics. Discrete and continuous random variables, mean and variance, hypothesis testing and confidence limits, Bayesian inference, nonparametric methods, Student's t, contingency tables, multifactor analysis of variance, fixed effects, random effects, mixed models, multiple regression, maximum likelihood, and logistic regression. Prerequisite: 233, or permission of instructor.
S Math 322 Biostatistics A followup course to Math 3200 (or 2200, with permission of instructor). Reviews basic statistics with biological/medical examples and introduces such topics as incidence and prevalence, medical diagnosis, sensitivity and specificity, Bayes' rule, decision making, maximum likelihood, logistic regression, ROC curves and survival analysis. SAS is used throughout the course. Prerequisite: Math 3200, or 2200 with permission of instructor.)
AF Math 331 Algebraic Systems Elementary theory of numbers including primes, congruences, quadratic residues and a few applications. Basics of abstract algebra including groups, rings, fields, field extensions and constructions with straight-edge and compass. Historical highlights where appropriate. Provides background useful for future high school mathematics teachers. Prerequisite: Math 310 or permission of instructor. Math 331 is offered in odd-numbered fall semesters.
AS Math 3351 Elementary Theory of Numbers Number theory does not require a lot of mathematical background beyond the level to read and be comfortable with doing proofs. Divisibility properties of integers, congruences, quadratic reciprocity, Diophantine equations. Introduction to continued fractions, and a brief discussion of public key cryptography. Useful for prospective high school teachers. Prerequisite: Math 310 or permission of instructor.
AS Math 370 Introduction to Combinatorics The basics of enumeration (combinations, permutations and enumeration of functions between finite sets), generating functions; the inclusion-exclusion principle, partition theory and introductory graph theory. If time permits, other topics may include: Ramsey's Theorem, probabilistic methods in combinatorics and algebraic methods in combinatorics. Prerequisites: Math 131-132, 309 and 310 (or equivalent), or permission of the instructor.
Math 407 Introduction to Differential Geometry Properties of curves and surfaces in 3 dimensional Euclidean space. The course is essentially a modern recount of a seminal paper of Gauss. Prerequisites: Math 233 and 309.
AS Math 408 Nonparametric Statistics Statistical methods that make no or almost no assumptions about the data distribution. Permutation tests of different types; nonparametric confidence intervals and correlation coefficients; jackknife and bootstrap resampling; nonparametric regressions. If there is time, topics chosen from density estimation and kernel regression. Short computer programs will be written in a language like R or C. Prerequisite: Math 420 or 493.
Math 410 Introduction to Fourier Series and Integrals The basic theory of Fourier series and Fourier integrals including their different types of convergence. Having developed these ideas which lie at the core of harmonic analysis, the course will proceed with applications to certain differential equations. This leads to the theory of harmonic functions both on the disc and the half-plane. If time permits, the course may discuss generalizations of these topics to higher dimensions. Prerequisites, Math 233 and 309. Background including some of 4111, 4121 and 429 might be helpful but are not required.
F Math 4111 Introduction to Analysis The real number system and the least upper bound property; metric spaces (completeness, compactness, and connectedness); continuous functions (in R^n; on compact spaces; on connected spaces); C(X) (pointwise and uniform convergence; Weierstrass approximation theorem); differentiation (mean value theorem; Taylor's theorem); the contraction mapping theorem; the inverse and implicit function theorems. Math 4111 replaces the former course Math 411. STUDENTS WITH CREDIT FOR MATH 411 CANNOT ALSO RECEIVE CREDIT FOR MATH 4111. Prerequisite: Math 310 or permission of instructor.
S Math 4121 Introduction to Lebesgue Integration Riemann integration; measurable functions; measures; the Lebesgue integral; integrable functions; L^p spaces; modes of convergence; decomposition of measures; product measures; Lebesgue measure. Math 4121 replaces the former Course Math 412. STUDENTS WITH CREDIT FOR MATH 412 CANNOT ALSO RECEIVE CREDIT FOR MATH 4121. Prerequisite: 4111 or permission of instructor.Math 415 Partial Differential Equations An introduction to PDE's with applications to selected classical problems in physics and engineering. Linear and quasi-linear first order equations, derivation of some of the classical PDE's of physics, and standard solution techniques for boundary and initial value problems. Preliminary topics such as orthogonal functions, Fourier series and variational methods are introduced as needed. Prerequisite: 217 and 309, or permission of instructor.
AF Math 416 Complex Variables Introduction to the theory of analytic functions. Contains the classic results on line integrals, power series, residues, conformal mapping, etc. The material is very pretty mathematically and also applicable to physics and engineering. Prerequisite: 318, SSM 317, or 411
F Math 417 Introduction to Topology and Modern Analysis I This is an introductory course in topology covering some set theory, the theory of metric spaces, and some material about general topological spaces. Connections to analysis may be made as appropriate but topology is the main theme. An excellent preparatory course for graduate study. Prerequisite: 4111
S Math 418 Introduction to Topology and Modern Analysis II Continuation of Math 417, covering additional material from general topology and perhaps some algebraic topology. The precise content of 418 will vary with the instructor. Prerequisite: 417
AS Math 420 Experimental Design This a good successor course to Math 3200 for those wishing a solid introduction to statistics. It is a first course in the design and analysis of experiments, from the point of view of regression. Factorial, randomized block, split-plot, Latin square, and similar design. Prerequisite: 3200or equivalent, or permission of instructor.
F Math 429 Linear Algebra A rigorous proof-oriented course in linear algebra, taught from the point of view of abstract vector spaces rather than the more computational "matrix" approach. Prerequisite: 309, 310
S Math 430 Modern Algebra Introduction to groups, rings, and fields. Includes permutation groups, group and ring homomorphisms, field extensions, connections with linear algebra which may use material from Math 429. Prerequisite: 429
AF Math 434 Survival Analysis Life table analysis and testing, mortality and failure rates, Kaplan-Meier or product-limit estimators, hypothesis testing and estimation in the presence of random arrivals and departures, and the Cox proportional hazards model. Used in medical research, industrial planning and the insurance industry. Prerequisite: Math 309 and 3200, or permission of instructor.
AF Math 439 Linear Statistical Models Introduction to statistical methods based in linear algebra. Topics: multivariate normal distribution; quadratic forms; linear models and their classification; general linear hypothesis; regression models, analysis of variance; factorial, block, and variance components models; canonical correlation; factor analysis. Prerequisites: a course in linear algebra, such as Math 309 or 429, and a course in statistics that includes regression (Math 3200, Math 493-494, or a strong performance in Math 2200 and permission of instructor.)
F Math 449 Numerical Applied Mathematics Computer arithmetic, error propagation, condition number and stability; mathematical modeling, approximation and convergence; roots of functions; calculus of finite differences; implicit and explicit methods for initial and boundary value problems; numerical integration; numerical solution of linear systems, matrix equations, and eigensystems; Fourier transforms; optimization. Various software packages are introduced and used. STUDENTS WITH CREDIT FOR MATH 404 or 405 CANNOT ALSO RECEIVE CREDIT FOR 449. Prerequisites: Math 1201 or equivalent programming experience, 217, and 309.
S Math 450 Topics in Applied Mathematics The topic will vary and this may affect the prerequisite. Usually, however, the prerequisite will be Math 449. The sequence 449-450 is new (beginning Fall 2005). Offering 450 every spring is the current goal.
Math 459 Bayesian Statistics This course introduces the Bayesian approach to statistical inference for data analysis in a variety of applications. The topics include: comparison of Bayesian and frequentist methods, Bayesian model specification, choice of priors, computational methods, empirical Bayes method, hands-on Bayesian data analysis using appropriate software. Prerequisite: Math 493 or permission of the instructor.
F Math 475 Statistical Computation: Applied Statistics using SAS. An introduction to SAS and SAS programming; contingency tables and Mantel-Haenszel tests; general linear models and matrix operations; simple, multilinear, and stepwise regressions; ANOVAs with nested and crossed interactions; ANOVAs and regressions with vector-valued data (MANOVAs). Topics chosen from discriminant analysis, principal components analysis, logistic regression, survival analysis, and generalized linear models. This course is highly recommended for students who plan to use statistics "on the job" or seeking statistics-related summer internships. Prerequisite: 3200 and 493 (or 493 concurrently)
F Math 493 Probability Theory and application of mathematical probability. Some prior knowledge of statistics (e.g., Math 3200) and linear algebra (e.g., Math 309) is recommended. Prerequisite: Math 318 or 308, or permission of instructor. This course provides useful information for the first exam of the Society of Actuaries.S Math 494 Mathematical Statistics A course in statistics based on the material covered in Math 493. Parametric and nonparametric significance and hypothesis testing; order statistics; theory of estimation; theory of runs, sampling schemes, analysis of variance, sequential analysis. The presentation is primarily mathematical, but with emphasis on concepts and methods of application, making the course suitable for nonmathematicians. Prerequisite: Math 493, or permission of the department.
AS Math 495 Stochastic Processes Topics include random walks, Markov chains, Gaussian processes, and empirical processes. Prerequisite: 318 and 493
FS Math 501C-502C (=Physics 501-502 Methods of Theoretical Physics I-II) Math 501includes theory of functions of a complex variable, residue theory; review of ordinary differential equations; introduction to partial differential equations; integral transforms. Prerequisite, Math 217. Math 502 includes introduction to function spaces; self-adjoint and unitary operators; eigenvalue problems, partial differential equations, special functions; integral equations; introduction to group theory. The prerequisite in Math 501. Taught by the Department of Physics.
FS Math 5021-5022 Complex Analysis I, II Intensive, rigorous courses in analytic function theory. These are introductory graduate level courses, formerly numbered 421-422. Prerequisite: 418 or permission of instructor.
FS Math 5031-5032 Algebra I-II Intensive, rigorous courses in modern algebra. These are introductory graduate level courses, formerly numbered 431-431. Prerequisite: 430 or permission of instructor.
F/AS Math 5041-5042 Geometry I, II Intensive, rigorous courses in differential geometry. These are introductory graduate level courses, formerly numbered 441-442. Math 5041 is offered every fall. Math 5042 and Math 5043 are follow-up offerings in alternate spring semesters. Prerequisite: 4121, 418 and 429, or permission of instructor.
AS Math 5043 Algebraic Topology Offered in alternate spring semesters as a followup to Math 5041.
FS Math 5051-5052 Measure Theory and Functional Analysis I-II Intensive, rigorous course in measure theory, integration and functional analysis. These are introductory graduate level courses, formerly number 451-452. Prerequisite: 418 or permission of instructor.
AF Math 5061 Theory of Statistics I An introductory graduate level course. Probability spaces; derivation and transformation of probability distributions; generating functions and characteristic functions; conditional expectation, sufficiency, uniformly minimum variance unbiased estimators, Rao-Blackwell theorem, information inequality; order statistics. Prerequisite: Math 4111-4121 or the equivalent.
AS Math 5062 Theory of Statistics II Continuation of Math 5061. Bayes estimates, minimaxity, admissibility; maximum likelihood estimation, consistency, asymptotic efficiency; confidence regions; Neyman-Pearson theory of hypothesis testing, uniformly most powerful tests; likelihood ratio tests and large-sample approximation; decision theory. Prerequisite, Math 5061 or permission of instructor.