105 History of Mathematics / Lecture, Discussion

Explores major themes--calculation, number, geometry, algebra, infinity--and their historical development in civilizations ranging from the antiquity of Babylonia and Egypt through classical Greece, the Middle and Far East, and then modern Europe. Analyzes the tension between applications of mathematics and the tendency toward formalism. Emphasizes presentations and discussions. Satisfies the historical perspective. Mr. Joyce / Offered periodically


113 Mathematical Problem Solving / Lecture, Workshop

Intended for students who will use mathematics in such subjects as management and the social sciences, but who are not necessarily planning to go on to calculus. Math 113 cannot be used as a prerequisite for; either calculus sequence, and does not satisfy any requirement of either the major or the minor in mathematics or computer science. Covers some "pre-calculus" topics (algebraic manipulations, functions and graphs, exponentials and logarithms), but major emphasis is on mathematical analysis of concrete situations (word problems, mathematical modeling, exponential growth, applications of linear systems, elementary probability).  Prerequisites: A suitable score on the mathematics placement test. Staff / Offered every semester.


114 Discrete Mathematics/Lecture

Covers mathematical structures that naturally arise in computer science. Includes elementary logic and set theory, equivalence relations, functions, counting arguments, asymptotic complexity, inductively defined sets, recursion, graphs and trees, Boolean algebra and combinatorial circuits, finite state automata, and diagonalization and countability arguments. Emphasizes proofs and problem solving. Prerequisite: One semester of calculus (Math 120 or 124) or CSci 101. Mr. Chou, Mr. Green, Mr. Joyce/Offered every semester


119 Precalculus Mathematics / Lecture, Discussion

Intended for students who plan to go on to calculus. Math 119 is to be used, when necessary, as preparation for Math 120 or Math 124 and does not satisfy any requirement of either the major or the minor in mathematics or computer science. Students should have a solid grasp of elementary algebra. Covers more advanced algebraic techniques (linear and nonlinear inequalities, quadratic equations, linear systems) and gives a rigorous look at elementary functions (polynomial, exponential, logarithmic, trigonometric). Prerequisites: A suitable score on the mathematics placement test. Staff/Offered every Spring. 120, 121 and 122 (Calculus I, II, and III) / Lecture

Calculus is essential for majors in biology, chemistry, computer science, mathematics, physics, and environmental science and policy.  Part I includes functions, limits, continuity, differentiation of algebraic and trigonometric functions, mean value theorem, and various applications. Part II includes; Riemann sums and integrals, techniques and applications of integration, improper integrals, transcendental functions; (logarithms, exponential functions, and inverse trigonometric functions). Part III includes further topics from calculus proper (sequences, series, polar coordinates) and introduces linear algebra (vectors, matrices, and linear systems). Though not all results are derived rigorously, care is taken to distinguish intuitive arguments from rigorous proofs. Math 120, 121, and 122 fulfill the Formal Analysis requirement. Math 122 is a prerequisite for Math 131 for students who have taken Math 120-121.  Prerequisite for Math 120: appropriate score on the mathematics placement test, or appropriate grade in Math 119.; Ms. Bernhofen, staff / Offered every fall (120, 122) and spring (121).


124 and 125 Honors Calculus I and II / Lecture

Two-course sequence for; strong students with interest in mathematics, computer science, physics, and other; natural sciences. Physics majors usually take Math 124 simultaneously with Physics 120 and Math 125 simultaneously with Physics 121. Previous experience with Calculus is; recommended but not required. The Honors Calculus sequence covers much the same topics from calculus as the regular sequence (Math 120- 121-122), but takes two semesters instead of three, and emphasizes both mathematical rigor and physical intuition. Math 124 and Math 125 fulfill the Formal Analysis requirement.  Prerequisite: appropriate score on the; mathematics placement test.  Mr. Morris,; Ms. Sternberg / Offered every; fall (124) and spring (125).


126 Elementary Number Theory / Lecture

Introduces number theory and trains students to understand mathematical reasoning and to write proofs. Includes the unique factorization of integers as products of primes, the Euclidean algorithm, Diophantine equations, congruences, Fermat's theorem, and Euler's theorem (and some applications: calendar problems, magic squares, cryptology). Prerequisite: Math 114, or one semester of Calculus (Math 120 or 124), or permission. Mr. Morris / Offered periodically


128 Modern Geometry / Lecture

Recalls Euclidean geometry and then proceeds to modern related topics: Hilbert's axioms; hyperbolic (Lobachevskian), elliptic, and projective geometries, and philosophical implications of geometries without the Parallel Postulate; finite geometries; automorphism groups (Klein's Erlanger Programme). One aim is to show the beauty of deduction in mathematics.  Prerequisites: high school geometry, and either a semester of college mathematics or permission.  Mr. Joyce, Mr. Rudolph / Offered periodically


130 Linear Algebra / Lecture

A; requirement for all mathematics majors; highly recommended for all computer science majors. Topics include vector spaces, systems of linear equations, linear transformations, dual spaces, eigenvectors and eigenvalues, determinants, and bilinear forms. Possible additional topics include applications to computer graphics, linear regression (least squares), Fourier series, and differential equations. Prerequisite: Math 121 or 125. Mr.  Rudolph, Ms. Sternberg / Offered every fall


131 Multivariate Calculus / Lecture

A continuation of Calculus (Math 120-121-122 or 124-125) . Topics include partial differentiation, multiple integration,; integration over parametrized curves and surfaces, culminating in Stokes's Theorem.; Prerequisites: Math 122 or Math 130. Mr. Chou, Ms. Sternberg / Offered every spring.


172 Introduction to Modern Analysis / Lecture

Modern analysis provides a language and unifying framework for theories encountered throughout mathematics. In this course, students learn to understand, formulate, and prove mathematical statements. Ideas first encountered in calculus-- convergence, completeness, and integration--are studied in depth. Other topics include metric spaces, normed spaces, compactness, and measure theory (Lebesgue integration). Required for mathematics majors by the junior year, and earlier if possible. Prerequisite: Math 122 or Math 125. Mr. Chou, Ms.Sternberg / Offered every year


181 Mathematical Theory of Computation

See Computer Science 270. Mr. Chou, Mr.  Green / Offered every other year


201 Proseminar in Mathematics / Seminar

Senior undergraduates study and speak on topics in mathematics to become acquainted with diverse subjects, learn to research known topics, and get practice in presenting presenting mathematics to peers. Faculty present their research areas. Possible topics include: category theory, knot theory, automorphic forms, topos theory, low-dimensional topology, class field theory, group representation theory, and dynamical systems. This is a capstone course in mathematics. Staff / Offered periodically


212 Numerical Analysis / Lecture, Laboratory

Introduces concepts and techniques of scientific computing to students in mathematics, computer science, and the sciences. Teaches how to set up reasonable computational algorithms and use the algorithms to work on actual projects. Topics include approximation theory, error analysis, numerical differentiation and integration, and solution of ordinary differential equations and linear systems. Prerequisites: Math 130 and Math 172. Mr. Chou, Ms. Sternberg / Offered every other year


214 Modern Analysis / Lecture

Ideas introduced in Math 172 are developed and applied to scientific models. Topics include Hilbert spaces, Lp spaces, Fourier series, Weierstrass approximation theorems, and linear operators. Prerequisites: Math 130 and Math 172.  Mr. Chou, Ms. Sternberg / Offered every other year


216 Functions of a Complex Variable / Lecture

Designed for undergraduate science and mathematics majors. Includes Cauchy's theorem, power series, Laurent series, the residue theorem, harmonic functions, and physical applications, such as problems in two- dimensional flow. An introduction to Riemann surfaces if time permits. Prerequisite: Math 131 and Math 172. Mr. Rudolph / Offered periodically


217 Probability and Statistics / Lecture

An introduction to probability theory and mathematical statistics that emphasizes the probabilistic foundations required to understand probability models and statistical methods.  Topics covered will include the probability axioms, basic combinatorics, random variables and their probability distributions, mathematical expectation and common families of probability distributions. Prerequisite: Math 131. Ms. Bernhofen / Offered every year. 


218 Topics in Statistics / Lecture

The emphasis of this course is to develop the fundamental statistical concepts of inference and hypothesis testing from a classical perspective using the tools of probability theory. Topics investigated include sampling and sample distributions, graphical data analysis, point and interval estimation, hypothesis testing, and an introduction to Bayesian inference. Prerequisite: Math 217 or Econ 260. Ms. Bernhofen / Offered periodically.


219 Linear Models / Lecture
A course in linear regression analysis which explores statistical methods for modeling a linear functional relationship between a response variable and one or more predictor variables. First the underlying theory for simple regression models involving one response and one predictor variable is developed, and then the results are extended to the case of one response variable and multiple predictor variables (multiple regression). Underlying model assumptions are explored and the implications of their violation. Besides the development of the statistical theory, we will emphasize the practical application of the theory to real world examples. The prerequisite for this course is Math 217. Ms. Bernhofen.


225 Modern Algebra I / Lecture

In the 19th century, Kummer introduced "ideal numbers" to salvage unique factorization of integers into primes (which breaks down in some rings of algebraic integers). This course discusses unique factorization and the modern theory of rings and their ideals, emphasizing Euclidean domains. Other algebraic structures (groups, fields) also are introduced. Required for all mathematics majors. Prerequisite: Math 130. Mr. Morris, Mr. Joyce / Offered every year


226 Modern Algebra II / Lecture

In the early 1800s, Abel showed that a general equation of degree at least 5 cannot be solved by extracting roots. Today, group theory, developed by Galois to determine which equations are solvable, is used throughout mathematics, and in much of physics and chemistry. This course focuses on groups and Galois theory.  Other possible topics include canonical forms of matrices and modules. Prerequisite: Math 225.  Mr. Joyce, Mr. Morris / Offered every other year


228 Topology / Lecture

Homology theory is the proper context for Stokes's theorem (Math 131). This course continues the study (begun in Math 131 and Math 172) of the topological properties of subsets of Euclidean space, developing algebraic tools like homology and fundamental groups. Further topics may include fixed-point theory, the Jordan curve theorem, and knot theory. Prerequisites: Math 131 and Math 172. Mr. Rudolph / Offered every other year


244 Differential Equations / Lecture

Most ordinary differential equations occurring in mathematical models of physical, chemical, and biological phenomena cannot be solved analytically. Numerical integrations do not lead to a desired result without qualitative analysis of the behavior of the equation's solutions.  This course studies the flows of scalar and planar ordinary differential equations.  Stability and bifurcation are discussed.  Prerequisite: Math 130 and Math 172. Ms.  Sternberg / Offered every other year