The mathematics necessary for calculus: algebraic manipulations; radicals and exponents; logarithmic, exponential and trigonometric functions; graphing and analytical geometry; theory of polynomials; complex numbers, and how such mathematics is developed. This course is designed for students who wish to take calculus but are not adequately prepared by their high school background. Prerequisite: First- or second-year standing. Not open to juniors and seniors without departmental permission. Not open to students who have received credit for calculus.

An introduction to differential and integral calculus. Limits and continuity, derivatives and integrals of polynomial, trigonometric, exponential, and logarithmic functions, applications of derivatives to optimization and approximation, the Mean Value Theorem, and the Fundamental Theorem of Calculus. (1S) Offered each semester. Prerequisite: four years of high school mathematics, including trigonometry and either college algebra or precalculus.

Techniques of integration, L’Hôpital’s Rule, infinite sequences and series, Taylor series and applications, first-order differential equations, and introduction to the calculus of multivariable functions, including partial derivatives and multiple integrals. (1S) Offered each semester. Prerequisite: Mathematics 110.

This is a transition course that develops the reasoning skills necessary for later mathematics courses with an emphasis on improving writing and presentation skills. Students engage with mathematical language and methods of conjecture, proof and counterexample, with emphasis on proofs. To motivate this content, students engage with the culture and history of the epistemology of mathematics. (1S) Prerequisite: Mathematics 110.

Introduction to the mathematical basis for computer science, including logic, counting, graphs and trees, and discrete probability. Offered even years, fall semester. Prerequisite: Computer Science 111. Prerequisite or co-requisite: Mathematics 110.

Differentiation and integration of functions of several variables; integration on surfaces; vector analysis; theorems of Green, Stokes, and Gauss; applications to ordinary and partial differential equations and to geometry. Offered even years, spring semester. Prerequisite: Mathematics 115.

Probability calculus for discrete and continuous probability distributions of one and several variables, including order statistics, combining and transforming random variables, and the use of moment-generating functions. Introduction to hypothesis testing. Offered even years, fall semester. Prerequisite: Mathematics 115.

Selected aspects of mathematics reflecting the interests and experience of the instructor. May be repeated for credit if topic is different. Offered occasionally. Prerequisite: varies with topic.

Linear equations and matrices, abstract vector spaces and linear transformations, orthogonality, eigenvalues and eigenvectors. Emphasizes development of abstract thinking and a variety of applications of linear algebra in science and social science. (1S) Offered each semester. Prerequisite: Mathematics 115. Prerequisite or co-requisite: Mathematics 150.

Solution methods for first-order differential equations, linear differential equations, power-series solutions, the Laplace transform, numerical methods, stability, applications. Offered odd years, spring semester. Prerequisite: Mathematics 115.

Construction and investigation of mathematical models of real-world phenomena, including team projects and use of computer packages as needed. Offered odd years, fall semester. Prerequisite: 1 unit of computer science and 2 mathematics courses numbered 275 or higher.

Properties of point estimators, development of hypothesis tests by means of the generalized likelihood ratio, and inference using the normal and related distributions. One- and two-sample, goodness of fit, and distribution-free hypothesis tests. Inference for regression and analysis of variance. Offered odd years, spring semester. Prerequisite: Mathematics 205.

Axiomatic treatment of selected algebraic structures including groups, rings, integral domains, and fields, with illustrative examples. Also includes elementary factorization theory. Offered each spring. Prerequisite: Mathematics 275.

Topological invariants of knots, classification of compact surfaces, structure of three-dimensional manifolds. Introduction to homotopy groups and abstract topological spaces. Offered odd years, spring semester. Prerequisite: Mathematics 275 or 208.

The real numbers, metric concepts and continuity, differentiation and integration of real functions, infinite sequences and series of functions. Offered each fall. Prerequisite: Mathematics 208 or 275.

The complex plane, analytic functions, complex integration, Taylor and Laurent series, residues and poles, conformal mapping, applications. Offered even years, spring semester. Prerequisite: Mathematics 275.

Selected topics in mathematics, reflecting the interests and experience of the instructor. May be repeated for credit if topic is different. Offered occasionally. Prerequisite: varies with topic.

Presentations by participants and faculty on selected topics. with occasional guest speakers. This version of the colloquium is geared towards mathematics minors. May be taken two times for credit if topic is different. Graded credit/no credit. Prerequisite: Mathematics 275.

Attendance required. Students select a faculty guide to assist them in learning to research a mathematical topic, prepare preliminary drafts of a paper, finalize the paper using Latex typesetting software, and then present the results of the paper to the class in a 50-minute talk. Class includes talks by students, some faculty, and often guest speakers. The course may be taken more than once. (CP) Offered each semester. Prerequisite: Mathematics 275, junior standing.

Individual guided investigations of topics or problems in mathematics. Since such investigation is important to the development of mathematical maturity, the department encourages each major to do at least one such project. Prerequisite: approval of the project by the department chair; sophomore standing.

Work with faculty in classroom instruction. Graded credit/no credit.

Course and curriculum development projects with faculty.