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
Math 110: Diving into Mathematics Research
An opportunity for first-year student to develop an understanding and appreciation for the work of mathematicians by actively participating in new and on-going cutting-edge research. This year, the research theme is Mathematical Psychology -- Emotion Space. Students will investigate new mathematical approaches to describe the psychology of emotion, discuss their underlying mathematical and psychological issues, and work on developing mathematical models for better understanding emotional phenomena. Mr. Rudolph
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