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This course aims to give non-mathematics majors a sense of the importance of mathematics in human thought and an appreciation of the beauty and vitality of present-day mathematics. Material varies. Sample topics include combinatorial puzzles, number theory, tilings, networks, symmetries, map coloring, knots and surfaces, alternative number systems, and infinite sets. (1S) Offered occasionally. Prerequisite: Not open to students who have taken a mathematics course numbered 110 or higher or who have Advanced Placement credit for calculus.
What we think of as “mathematical” ideas may be viewed by other cultures within the contexts of art, navigation, religion, record-keeping, games, or kin relationships. This course treats mathematical ideas investigated by cultures such as North and South American Indians, Africans, and various peoples of the Pacific Islands, and analyzes them through Western mathematics (developed in Europe, the Middle East, and India). The course helps the student understand what mathematics is, both to Western culture and to other cultures, and how cultural factors influenced the development of modern mathematics. (Also listed as Interdisciplinary Studies 103.) (2A) Offered once per year.
An introduction to finite methods in mathematics: probability, graphs, linear programming, game theory, and patterns. The course emphasizes ways in which these methods can be used to build mathematical models applicable to the social and biological sciences. Offered occasionally. Prerequisite: three years of high school mathematics.
Introductory probability and statistics with illustrations from the behavioral, social, and natural sciences. Descriptive statistics, elementary probability, hypothesis testing, analysis of variance, contingency tables, linear regression and correlation, nonparametric tests. Offered each semester. Prerequisite: facility in high school algebra. Not open to students who have completed or are taking Mathematics 205, Anthropology 240, or Psychology 161.
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.
Limits and continuity. Derivatives and integrals of the elementary functions and the basic theorems of calculus; concepts, methods, and theorems illustrated by examples from biology, chemistry, geology, physics, and economics. Some use of Mathematica or Matlab in numerical and symbolic calculations. At least one project dealing with modeling. (1S) Offered once a year. Prerequisite: precalculus or four years of high school mathematics, including trigonometry and algebra. Open to students who have not taken Mathematics 110.
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 or 113.
Presentations by faculty, participants, and occasional guest speakers on a variety of topics related to calculus and its applications to other disciplines. Graded credit/no credit. Offered each fall. Prerequisite: concurrent enrollment in a mathematics course numbered 110 or higher or Advanced Placement credit for calculus.
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 and Mathematics 110 or 115.
Combinatorial counting principles, generating functions and recurrence relations, introduction to graph theory, graph-theoretic algorithms, and their implementation. Applications to operations research, computer science, and social science. Offered odd years. Prerequisite: Mathematics 115.
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.
An introduction to the mathematical theory of dynamical systems, with special attention to systems exhibiting chaotic behavior. One-dimensional dynamics: fixed points, periodic orbits, chaotic orbits, and the transition to chaos. Two-dimensional dynamics: fractal images, Julia sets, and the Mandelbrot set. Includes computer experiments with chaotic systems; applications. Offered odd years, spring semester. Prerequisite: Mathematics 115.
Topics chosen to illustrate modern approaches to geometry. May be repeated for credit if topic is different, with the approval of the department. Offered occasionally. Prerequisite: Mathematics 175, or other courses depending on the topic.
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; some computer programming experience is desirable.
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 175 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 175 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 175.
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 175, 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.