# Course Descriptions

105. Fundamentals of Algebra and Trigonometry. (1h, 2h, or 3h) Review of the essentials of algebra and trigonometry. Admission by permission only (generally, a student must have taken fewer than three years of high school mathematics to be eligible for admission). Not to be counted towards any major or minor offered by the department.

105L. Fundamentals of Algebra and Trigonometry Lab. (1h or 2h) A review of the essentials of algebra and trigonometry in a guided laboratory setting. Admission by permission only. Not to be counted towards any major or minor offered by the department. Pass/Fail only.

107. Explorations in Mathematics. (4h) Introduction to mathematical reasoning and problem solving. Topics vary by instructor and may include one or more of the following: knot theory, Euclidean and non-Euclidean geometry, set theory, cryptography, discrete models, number theory, discrete mathematics, chaos theory, probability, and MAPLE programming. Lab. (D, QR)

109. Elementary Probability and Statistics. (4h) Probability and distribution functions, means and variances, and sampling distributions. Lab. (D, QR)

111. Calculus with Analytic Geometry I. (4h) Functions, trigonometric functions, limits, continuity, differentiation, applications of derivatives, introduction to integration, and the fundamental theorem of calculus. Lab. (D, QR)

112. Calculus with Analytic Geometry II. (4h) Techniques of integration, indeterminate forms, improper integrals, transcendental functions, sequences, Taylor’s formula, and infinite series, including power series. Lab. (D, QR)

113. Multivariable Calculus. (4h) The calculus of vector functions, including geometry of Euclidean space, differentiation, extrema, line integrals, multiple integrals, and Green’s, Stokes’, and divergence theorems. Credit not allowed for both 113 and 205. Lab. (D, QR)

117. Discrete Mathematics. (4h) Introduction to various topics in discrete mathematics applicable to computer science including sets, relations, Boolean algebra, propositional logic, functions, computability, proof techniques, graph theory, and elementary combinatorics. Lab. (D, QR)

121. Linear Algebra I. (4h) Vectors and vector spaces, linear transformations and matrices, determinants, eigenvalues, and eigenvectors. Credit not allowed for both 121 and 205. Lab. (D, QR)

165. Problem-Solving Seminar. (1h) Weekly seminar designed for students who wish to participate in mathematical competition such as the annual Putnam examination. Not to be counted toward any major or minor offered by the department. May be repeated for credit. Pass/Fail only.

205. Applied Multivariable Mathematics. (4h) Introduction to several topics in applied mathematics including complex numbers, probability, matrix algebra, multivariable calculus, and ordinary differential equations. Warning: not to be counted toward any major or minor offered by the department except for the major in mathematical business. Credit not allowed for both 205 and 121, or for both 205 and 113. Lab. P—MTH 112 or POI.

206. Applied Matrix Algebra and Topics. (2h) Matrices, determinants, solutions of linear equations, special matrices, eigenvalues and eigenvectors of matrices. Additional topics will be covered as time permits. Not to be counted toward any major offered by the department except for the major in mathematical business. Credit not allowed for both MTH 206 and 121. Credit not allowed for both MTH 206 and 205. P—MTH 111 or POI.

211. Advanced Calculus. (3h) Rigorous proof-oriented development of important ideas in calculus. Limits and continuity, sequences and series, pointwise and uniform convergence, derivatives and integrals. Credit not allowed for both 211 and 311. P—MTH 117 or POI. (D)

214. Multivariable Analysis. (3h) Functions between Euclidean spaces, multivariable limits, differentiation, change of variables, line and surface integrals, vector fields, integration theorems for vector fields, Implicit & Inverse Function Theorems, Contraction Mapping Theorem, applications, other selected topics from analysis in multiple dimensions. P—MTH 113 and MTH 121, or Math 205.

243. Codes and Cryptography. (3h) Essential concepts in coding theory and cryptography. Congruences, cryptosystems, public key, Huffman codes, information theory, and other coding methods. P—MTH 117 or POI. (D)

251. Ordinary Differential Equations. (3h) Linear equations with constant coefficients, linear equations with variable coefficients, and existence and uniqueness theorems for first order equations. P—MTH 112 or POI. (D, QR)

253. Operations Research. (3h) Mathematical models and optimization techniques. Studies in allocation, simulation, queuing, scheduling, and network analysis. P—MTH 111 and MTH 121, 205 or 206 or POI. (D, QR)

254. Optimization Theory. (1.5h) Unconstrained and constrained optimization problems; Lagrange multiplier methods; sufficient conditions involving bordered Hessians; inequality constraints; Kuhn-Tucker conditions; applications primarily to problems in economics. P—MTH 113 and 121 or POI.

255. Dynamical Systems. (1.5h) Introduction to optimal control, including the Pontryagin maximum principle, and systems of nonlinear differential equations, particularly phase space methods. Applications to problems in economics, including optimal management of renewable resources. P—MTH 113 and 121 or POI.

256. Statistical Methods. (3h) A project-oriented course emphasizing data analysis, with introductions to nonparametric methods, multiple and logistic regresssion, model selection, design, categorical data or Bayesian methods. P—MTH 109, ANT 380, BIO 380, BEM 201 or 202, HES 262 or 369, PSY 311 or 312, SOC 271, or POI. (D, QR)

257. Design and Sampling. (3h) Experimental designs, sample size and power determination, survey design, and estimation with stratified, cluster, and other sampling schemes. P—MTH 109 or 256 or POI. (D)

306. Advanced Mathematics for the Physical Sciences. (3h) Advanced topics in linear algebra, special functions, integral transforms, and partial differential equations. Not to be counted toward any major offered by the department except for the major in mathematical business. P—MTH 205 or POI.

311, 312. Introductory Real Analysis I, II. (3h, 3h) Limits and continuity in metric spaces, sequences and series, differentiation and Riemann-Stieltjes integration, uniform convergence, power series and Fourier series, differentiation of vector functions, implicit and inverse function theorems. Credit not allowed for both 211 and 311. P—MTH 117 or POI. (D)

317. Complex Analysis I. (3h) Analytic functions, Cauchy’s theorem and its consequences, power series, and residue calculus. Credit not allowed for both 303 and 317. P—MTH 113 or POI. (D)

321. Modern Algebra I. (3h) Introduction to modern abstract algebra through the study of groups, rings, integral domains, and fields. P—MTH 121 or POI. (D)

322. Modern Algebra II. (3h) Continuation of modern abstract algebra through the study of additional properties of groups, rings, and fields. P—MTH 117 and 321, or POI. (D)

324. Linear Algebra II. (3h) Thorough treatment of vector spaces and linear transformations over an arbitrary field, canonical forms, inner product spaces, and linear groups. P—MTH 121 and 321 or POI. (D)

326. Numerical Linear Algebra. (3h) Numerical methods for solving matrix and related problems in science and engineering using a high-level matrix-oriented language such as MATLAB. Topics include systems of linear equations, least squares methods, and eigenvalue computations. Special emphasis given to applications. Also listed as CSC 352. P—MTH 112 and MTH 121, 205 or 206 or POI. (D)

331. Geometry. (3h) Introduction to axiomatic geometry including a comparison of Euclidean and non-Euclidean geometries. P—MTH 117 or POI. (D)

334. Differential Geometry. (3h) Introduction to the theory of curves and surfaces in two and three dimensional space, including such topics as curvature, geodesics, and minimal surfaces.

P—MTH 113 or POI. (D)

345, 346. Elementary Theory of Numbers I, II. (3h, 3h) Properties of integers, including congruences, primitive roots, quadratic residues, perfect numbers, Pythagorean triples, sums of squares, continued fractions, Fermat’s Last Theorem, and the Prime Number Theorem. P—MTH 117 or POI. (D)

347. Graph Theory. (3h) Paths, circuits, trees, planar graphs, spanning trees, graph coloring, perfect graphs, Ramsey theory, directed graphs, enumeration of graphs, and graph theoretic algorithms. P—MTH 117 or POI. (D)

348, 349. Combinatorial Analysis I, II. (3h, 3h) Enumeration techniques, generating functions, recurrence formulas, the principle of inclusion and exclusion, Polya theory, graph theory, combinatorial algorithms, partially ordered sets, designs, Ramsey theory, symmetric functions, and Schur functions. P—MTH 117 or POI. (D)

352. Partial Differential Equations. (3h) Detailed study of partial differential equations, including the heat, wave, and Laplace equations, using methods such as separation of variables, characteristics, Green’s functions, and the maximum principle. P—MTH 113 and 251 or POI. (D)

353. Mathematical Models. (3h) Development and application of probabilistic and deterministic models. Emphasis given to constructing models which represent systems in the social, behavioral, and management sciences. (D)

354. Discrete Dynamical Systems. (3h) Introduction to the theory of discrete dynamical systems as applied to disciplines such as biology and economics. Includes methods for finding explicit solutions, equilibrium and stability analysis, phase plane analysis, analysis of Markov chains, and bifurcation theory. P—MTH 112 and 121 or POI. (D)

355. Introduction to Numerical Methods. (3h) Numerical computations on modern computer architectures; floating point arithmetic and round-off error. Programming in a scientific/engineering language such as MATLAB, C, or FORTRAN. Algorithms and computer techniques for the solution of problems such as roots of functions, approximation, integration, systems of linear equations and least squares methods. Also listed as CSC 355. P—MTH 112 and MTH 121, 205 or 206 or POI. (D)

357. Probability. (3h) Probability distributions, mathematical expectation, and sampling distributions. MTH 357 prepares students for Actuarial Exam #1. P—MTH 112 or POI. (D)

358. Mathematical Statistics. (3h) Derivation of point estimators, hypothesis testing, and confidence intervals, using both maximum likelihood and Bayesian approaches. P—MTH 357 or POI. (D)

362. Multivariate Statistics. (3h) Multivariate and generalized linear methods for classification, modeling, discrimination, and analysis. P—MTH 112, MTH 121 or 205, and MTH 256 or POI. (D)

364. Computational and Nonparametric Statistics. (3h) Computationally intensive methods to fit statistical models to data. Topics include simulation, Monte Carlo integration and Markov Chain Monte Carlo, sub-sampling, and non-parametric estimation and regression. Students will make extensive use of statistical software throughout the course. P—MTH 109 or 256, and MTH 357, or POI. (D)

367. Linear Models. (3h) Theory of estimation and testing in linear models. Topics include least squares and the normal equations, the Gauss-Markov Theorem, testing general linear hypotheses, and generalized linear models. P—MTH 121 or 205 or 206, and MTH 256 or 357. (D)

381. Individual Study. (1h, 2h, or 3h) Independent study directed by a faculty adviser. By prearrangement.

383. Selected Topics. (1h, 2h, or 3h) Topics in mathematics not considered in regular courses or which continue study begun in regular courses. Content varies.

391. Senior Seminar Preparation. (1h) Independent study or research directed by a faculty adviser by prearrangement with the adviser.

392. Senior Seminar Presentation. (1h) Preparation of a paper, followed by a one-hour oral presentation based upon work in MTH 391.