Mathematics Department

Undergraduate Course Descriptions

103. Pre-calculus Mathematics
Fall (3)
A study of the real number system, sets, functions, graphs, equations, inequalities and systems of equations, followed by a study of the trigonometric functions and their properties. This course is designed only for students intending to take Math 108 or Math 111, and whose background is deficient in algebra and trigonometry. Juniors and seniors must obtain permission from the instructor to enroll. This course may not be applied toward either the minor or major in mathematics or the satisfaction of GER requirements. A student may not receive credit for this course after successfully completing a Mathematics course numbered above 107, with the exception of Math 150.

104. The Mathematics of Powered Flight
(GER 1) Fall and Spring (3,3)
Applications of elementary mathematics to airplane flight. Wind and its effect on airport design and aircraft operation. Maps and map projections. Magnetic variation and compass navigation. Static air pressure: buoyancy and the altimeter. Use of a flight simulator will illustrate the mathematical analysis of certain aircraft instruments. Not open to students who have successfully completed a Mathematics course numbered higher than 210. Click here for more information.

106. Elementary Probability and Statistics
(GER 1) Fall and Spring (3,3)
Introduction to basic concepts and procedures of probability and statistics including descriptive statistics, probability, classical distributions, estimation, hypothesis testing, correlation and regression, in the context of practical applications to data analysis from other disciplines. Not open to students who have successfully completed a mathematics course numbered above 210. Click here for more information.

108. Brief Calculus with Applications
(GER 1) Fall and Spring (4,4)
An introduction to the calculus of polynomial, rational, exponential and logarithmic functions, including some multivariable calculus, with applications in business, social and life sciences. Algebra proficiency required. MAPLE will be used in the course. Students may not receive credit for more than one of Math 108, 111, and 131, and may not receive credit for Math 108 after receiving credit for any Mathematics course numbered higher than 108, with the exception of Math 150. To use Math 108 as a prerequisite for Math 112 or 132, students need approval of the department chair. Concurrent enrollment in Math 108 calculus lab required. Click here for more information [PDF].

110. Topics in Mathematics
Fall and Spring (3,3)
An introduction to mathematical thought with topics not routinely covered in existing courses. Material may be chosen from calculus, probability, statistics and various other areas of pure and applied mathematics.

111. Calculus I
(GER 1) Fall and Spring (4,4)
Standard functions and their graphs: Linear, polynomial, trigonometric, exponential, logarithmic. Tangents, derivatives, the definite integral and the fundamental theorem. Formulas for differentiation. Applications to physics, geometry and economics. Requires graphing calculator. Concurrent enrollment in Math 111 calculus lab required. Students may not receive credit for more than one of Math 108, 111, and 131. Click here for more information.

112. Calculus II
(GER 1) Fall and Spring (4,4) Prerequisite: MATH 111 or MATH 131.
Methods of integration. Applications of the integral to geometry, physics and economics. Slope fields and the qualitative behavior of solutions to differential equations. Approximations: sequences, series, and Taylor series. Concurrent enrollment in Math 112 Maple calculus lab required. Students may not receive credits for more than one of Math 112 and 132. Click here for more information.

131. Calculus I for Life Sciences
(GER 1) Fall (4)
Mathematical topics parallel to those in Math 111. Applications in Math 131 focus on issues of importance in the Life Sciences, e.g., mathematical models of population dynamics, ecology, physiology, genetics, neurology. Students may not receive credit for more than one of Math 108, 111, and 131. Concurrent enrollment in Math 131 calculus lab required.

132. Calculus II for Life Sciences
(GER 1) Spring (4) Prerequisite: MATH 111 or MATH 131. Corequisite: Any 100 or 200 level Biology course.
Mathematical topics parallel those in Math112. Applications in this course focus on issues of importance in the Life Sciences, e.g., mathematical models of population dynamics, ecology, physiology, and epidemiology. Students may not receive credit for both Math 112 and Math 132. Concurrent enrollment in Math 132 Maple calculus lab required.

150W. Freshman Seminar: Topics in Mathematics
Fall and Spring (4,4)
Each seminar is devoted to a specific mathematical topic. Writing of mathematics is emphasized. Normally only available to first-year students.

211. Linear Algebra
Fall and Spring (3,3) Prerequisite: MATH 112 or MATH 132.
Linear equations, matrices, determinants, vector spaces, linear transformations, eigenvalues, orthogonality. Optional topics include least squares problems, matrix factorization, applications. A computer lab using the software package Matlab may accompany the class.

212. Introduction to Multivariable Calculus
Fall and Spring (3,3) Prerequisite: MATH 112 or MATH 132.
Functions of several variables, surfaces in three-space, vectors, techniques of partial differentiation and multiple integration with applications. MAPLE will be used in this course. Students may not receive credit for both Math 212 and 213.

213. Multivariable Calculus for Science and Mathematics
Fall and Spring (4,4) Prerequisite: MATH 112 or MATH 132.
Covers all MATH 212 material plus other vector calculus topics (including Gauss' and Stokes' theorems). Students may not receive credit for both MATH 212 and MATH 213. MATH 213 may replace MATH 212 as a prerequisite and is particularly recommended for science and mathematics students.

214. Foundations of Mathematics
Fall and Spring (3,3) Prerequisite: MATH 112 or MATH 132.
Fundamentals of advanced mathematics: Propositional logic, quantifiers and methods of proof; naive set theory including mathematical induction, relations, orders, functions, and countability.

302. Ordinary Differential Equations
Fall and Spring (3,3) Prerequisite: MATH 212 or MATH 213.
First-order separable, linear, and nonlinear differential equations. First-order systems and forced second order linear equations. Systems of linear equations and linearization. Numerical methods, bifurcations, and qualitative analysis. Applications to biology, chemistry, economics, physics, and social sciences.

307. Abstract Algebra
Fall and Spring (3,3) Prerequisites: MATH 211, MATH 214 or consent of instructor.
Groups, rings, fields, isomorphisms; polynomials. Additional topics chosen from group theory and ring theory, as time permits.

311. Elementary Analysis
Fall and Spring (3,3) Prerequisites: MATH 212 or MATH 213, MATH 214 or consent of instructor.
An introduction to the theory of real variables. The topology of the real line, convergence and uniform convergence, limits and continuity, differentiation, Riemann integration and the Fundamental Theorem of Calculus.

323. Operations Research - Deterministic Models
Fall (3) Prerequisite: MATH 211.
An introduction to deterministic Operations Research techniques and applications. Topics include search algorithms, simplex search for linear programs, duality and sensitivity analysis for linear programs, shortest path problems, network models and discrete optimization.

345. Introduction to Mathematical Biology
Fall (3) Prerequisite: MATH 112 or 132 or consent of instructor.
An introduction to developing, simulating, and analyzing models to answer biological questions. Mathematical topics may include matrix models, non-linear difference and differential equations, and stochastic models. Biological topics may include ecology, epidemiology, evolution, molecular biology, and physiology.

351. Applied Statistics
Spring and Fall (3,3) Prerequisite: MATH 112 or MATH 132 or consent of instructor.
Basic concepts of statistical inference. Topics include: 1- sample and 2-sample location problems, analysis of variance, linear regression, applications of probability models and statistical methods to practical situations and/or actual data sets. No previous knowledge of probability is assumed. This course is recommended for students who wish to take a single, self-contained statistics course that emphasizes analysis of experimental data. Mathematics concentrators with an interest in applications are also encouraged to take this course followed by the more theoretical Math 401 and Math 452.

352. Data Analysis
Fall and Spring (3,3) Prerequisite: MATH 351 or consent of instructor.
Case studies are used to provide in-depth exposure to the practice of statistics. Topics include: experimental design, data collection, data management, statistical analysis (beyond Math 351), statistical software, interpreting and reporting results.

380. Topics in Mathematics
Fall and Spring (1-3) Prerequisites: MATH 211, MATH 212 or MATH 213, or consent of instructor.
A study of 300-level mathematical topics not covered by existing courses. Topics may be pure or applied. Course may be repeated for credit with permission of instructor.

401. Probability
Fall and Spring (3,3) Prerequisites: MATH 211, MATH 212 or MATH 213, MATH 214 or consent of instructor.
Topics include: combinatorial analysis, discrete and continuous probability distributions and characteristics of distributions, sampling distributions.

403. Intermediate Analysis
Spring (3) Prerequisite: MATH 311.
Sequences and series of functions; analysis in metric spaces and normed linear spaces; general integration and differentiation theory.

405. Complex Analysis
Fall (3) Prerequisite: MATH 311 or consent of instructor.
The complex plane, analytic functions, Cauchy Integral Theorem and the calculus of residues. Taylor and Laurent series, analytic continuation.

408. Advanced Linear Algebra
Fall (3) Prerequisites: MATH 211, MATH 214 or consent of instructor.
Eigenvalues, singular values, matrix factorizations, canonical forms, vector and matrix norms; positive definite, hermitian, unitary and nonnegative matrices.

410. Special Topics in Mathematics
Fall and Spring (1-3,1-3)
A treatment of topics of interest not routinely covered by existing courses. Material may be chosen from topology, algebra, differential equations and various other areas of pure and applied mathematics. This course may be repeated for credit with permission of the instructor.

412. Introduction to Number Theory
Fall (3) Prerequisite: MATH 214 or consent of instructor.
An elementary course in the theory of integers, divisibility and prime numbers, a study of Diophantine equations, congruences, number-theoretic functions, decimal expansion of rational numbers and quadratic residues.

413. Introduction to Numerical Analysis I
Fall (3) Prerequisites: MATH 212 or MATH 213, CSCI 141, MATH 214 or consent of instructor.
A discussion of the mathematical theory underlying selected numerical methods and the application of those methods to solving problems of practical importance. Computer programs are used to facilitate calculations. The topics covered are: roots of equations, systems of linear equations, interpolation and approximation, and numerical integration. Students planning to take 414 are strongly encouraged to take 413 first.

414. Introduction to Numerical Analysis II
Spring (3) Prerequisites: MATH 212 or MATH 213, CSCI 141, MATH 214 or consent of instructor.
A discussion of the mathematical theory underlying selected numerical methods and the application of those methods to solving problems of practical importance. Computer programs are used to facilitate calculations. The topics covered are: iterative methods for linear systems, eigenvalue computations and differential equations. Students planning to take 414 are strongly encouraged to take 413 first.

416. Topics in Geometry
Fall of even-numbered years (3) Prerequisites: MATH 211, MATH 212 or MATH 213, MATH 214 or consent of instructor.
A treatment of topics selected from Euclidean geometry, non-Euclidean geometry, projective geometry, finite geometry, differential geometry or algebraic geometry.

417. Vector Calculus for Scientists
Spring. Prerequisites: MATH 211, MATH 212 or MATH 213, and MATH 302 or consent of instructor.
Directional derivatives, differential forms and the PoincarŽ lemma, chain rule: Jacobians, change of variable and application to Lagrangian mechanics; path integrals and the deformation theorem, surface integrals and Stokes' theorem. Additional topics will be covered if time permits.

424. Operations Research - Stochastic Models
Spring (3) Prerequisite: MATH 401.
A survey of probabilistic operations research models and applications. Topics include stochastic processes, Markov chains, queueing theory and applications, Markovian decision processes, inventory theory and decision analysis.

426. Topology
Fall of odd-numbered years (3) Prerequisite: MATH 311 or consent of instructor.
A study of topological spaces, metric spaces, continuity, product spaces, compactness, connectedness and convergence. As time permits, additional topics may be chosen from homotopy theory, covering spaces, manifolds and surfaces, or other topics in algebraic or set theoretic topology.

428. Functional Analysis
Spring of odd-numbered years (3) Prerequisite: MATH 311.
Introduction to the geometry of Hilbert spaces, bounded linear operators, compact operators, spectral theory of compact selfadjoint operators, integral operators and other applications.

430. Abstract Algebra II
Spring of odd-numbered years (3) Prerequisite: MATH 307.
The theory of groups, rings, fields and their applications. Topics may include fundamental theorem of Abelian groups, Sylow theorem, field extensions, Galois theory and coding theory.

432. Combinatorics
Spring of even-numbered years (3) Prerequisites: MATH 211, MATH 214 or consent of instructor.
A study of combinatorial theory and applications to practical problems. Topics include: graph theory, graphical algorithms, enumeration principles, inclusion-exclusion principle, recurrence relations, and generating functions. Optional topics: Polya counting principle, combinatorial designs, coding, Boolean algebra, and switching functions.

441. Introduction to Applied Mathematics I
Fall (3) Prerequisites: MATH 211, MATH 212 or MATH 213. MATH 302 is recommended.
A study of mathematical principles and techniques common to different scientific disciplines. The central topics are differential and matrix equations. Beginning with symmetric linear systems and associated matrix theory, the course continues with equilibrium equations, least squares estimation, vector calculus, calculus of variations, Fourier series and complex variables. Applications to structures, electrical networks, data analysis, etc. are included. Students cannot receive credit for both Applied Science 441 and Mathematics 441. (Cross listed with APSC 441)

442. Introduction to Applied Mathematics II
Spring (3) Prerequisite: MATH/APSC 441.
A continuation of Mathematics/Applied Science 441. Topics are numerical methods for linear and nonlinear equations and eigensystems, finite elements, initial-value problems with introduction to the phase plane and chaos, stability analysis, network flows and optimization. Applications to simple fluid flow, heat transfer, assignment and transportation problems, etc. are included. Students cannot receive credit for both Applied Science 442 and Mathematics 442. (Cross listed with APSC 442)

452. Mathematical Statistics
Spring (3) Prerequisite: MATH 401 or consent of instructor. MATH 351 recommended.
The mathematical theory of statistical inference. Possible topics include: maximum likelihood, least squares, linear models, methods for estimation and hypothesis testing. (Formerly MATH 402)

459. Topics in Statistics
Fall and Spring (1-3, 1-3) Prerequisite: Consent of instructor.
Statistical topics not covered in other courses. Possible topics include: linear models, nonparametrics, multivariable analysis, computationally intensive methods. This course may be repeated for credit as topics change.

490. Seminar
Fall and Spring (3,3) Prerequisite: MATH 214.
Sections of this course will treat a single narrow topic. Possible areas of interest include linear algebra, operator theory, applied analysis, combinatorial theory, operations research, statistics, history of mathematics, mathematical pedagogy and computational mathematics. Students will present written and oral work for discussion in class. May be repeated with permission. Click here for more information.

495-496. Honors
Fall, Spring (3,3)
Students admitted to Honors study in mathematics will be enrolled in this course during both semesters of their senior year. The course comprises: (a) supervised research in the student's special area of interest; (b) presentation by April 15 of an Honors thesis; and (c) satisfactory performance in a comprehensive oral examination in the field of the student's major interest.