First Year Seminars
177. What is Mathematics and Why Won't It Go Away? 3 hours
3NS, QPf, WR
This seminar will provide opportunities to engage in various activities (problem-solving, conjecture, and proof) and to explore the nature of mathematical thinking and discourse. Works of both non-fiction and fiction will be discussed and issues such as problem-solving vs.theory-building, the nature of mathematical truth and proof, aesthetic qualities in mathematics, mathematics and madness, cognition and mathematics will be considered. Intended for students without extensive background beyond high school mathematics. Enrollment Limit: 14
Introductory
Courses
030. Topics in Contemporary Mathematics 3 hours
3NS, QPf
The interaction
of mathematics with the social sciences is the central theme. Topics are drawn
from: graph theory, game theory, linear programming, coding theory, exploratory
data analysis, and combinatorics. Applications
are given to social choice, decision-making, management and ecological modeling.
Prerequisite: A working knowledge of
elementary algebra and geometry. Note: This course does not count toward a major in Mathematics.
It is intended for students who have not satisfied the quantitative proficiency
requirement. (Not
open to any student who has received credit for a course in mathematics course
numbered 131 or higher).Enrollment
Limit: 30.
090. Environmental Mathematics 3 hours
3NS, QPf
This course focuses
on the application of mathematics to problems concerning the environment. Topics include simulation (models of population
growth, predator-prey relationships, and epidemics); optimization (applications
to groundwater hydrology, herbivore foraging, and transportation of hazardous
wastes); and decision analysis (applications to management of endangered species
and resolution of environmental disputes).
Note: This course
does not count toward a major in mathematics.
It is intended for students who have not satisfied the quantitative
proficiency requirement. (Not
open to any student who has received credit for a course in mathematics course
numbered 131 or higher). Enrollment
Limit: 20.
100. Elementary Statistics 4 hours
4NS, QPf
An introduction
to the statistical analysis of data. Topics include exploratory data analysis,
probability, sampling, estimation, and hypothesis testing. Statistical software
is introduced, but no prior computer experience is assumed. This course focuses
on statistical ideas and downplays mathematical formulas. It is intended for
students in the social sciences and humanities with minimal mathematical experience
who have not satisfied the quantitative proficiency requirement. Note: MATH 100 does not count toward a mathematics or economics
major and is not open to students who have completed a semester of calculus.
Students may not receive credit for more than one of MATH 100, MATH 113, and
MATH 114. Enrollment Limit: 36
113. Statistical Methods for the Social and Behavioral Sciences 4 hours
4NS, QPf
A
standard introduction to statistics for students with a good background in
mathematics. Topics covered include exploratory data analysis, descriptive
statistics, probability, sampling, estimation, and statistical inference.
A broad spectrum of examples is employed. Statistical software is introduced,
but no prior computer experience is assumed. Prerequisite: An appropriate score on the Statistics Readiness Exam.
Note: The statistical content
of this course is largely the same as MATH 114; the applications are different.
Students may not receive credit for more than one of MATH 100, MATH 113, and
MATH 114. Consent of instructor required. Enrollment Limit: 36.
114. Statistical Methods for the Biological Sciences 4 hours
4NS, QPf
A
standard introduction to statistics for students with a good background in
mathematics. Topics covered include exploratory data analysis, descriptive
statistics, probability, sampling, estimation, and statistical inference.
Biological and medical examples are emphasized. Statistical software is introduced,
but no prior computer experience is assumed. Prerequisite: An appropriate score on the Statistics Readiness Exam.
Note: The statistical content
of this course is largely the same as MATH 113; the applications are different.
Students may not receive credit for more than one of MATH 100, MATH 113, and
MATH 114. Consent of instructor required. Enrollment Limit: 36.
131. Calculus Ia: Limits, Continuity and Differentiation 3 hours
4NS, QPh
A first course
in the calculus of functions of one variable including supporting material
from algebra and trigonometry. Topics include limits, continuous functions,
solution of equations and inequalities, differentiation of real-valued functions
of one variable, and the graphical analysis of functions. The two-course sequence
MATH 131, MATH 132 is equivalent to the more intensive MATH 133. Prerequisite: An appropriate score on the Calculus Readiness Exam.
Consent of instructor required. Enrollment Limit: 32
132. Calculus Ib: Integration and Applications 3 hours
4NS, QPf
Continuation of MATH 131. Topics include integration of real-valued functions of one variable, basic properties of the trigonometric and exponential functions, the fundamental theorems of the calculus, and applications. Prerequisite: MATH 131 or an appropriate score on the Calculus Readiness Exam. Consent of instructor required. Enrollment Limit: 32
133. Calculus
I: Limits, Continuity, Differentiation,
4 hours
Integration, and Applications
4NS, QPf
A standard first
course in the calculus of functions of one variable. Topics include limits,
continuous functions, differentiation and integration of real-valued functions
of one variable, the fundamental theorems of calculus, and applications. This
course is equivalent to the two-course sequence MATH 131, MATH 132. Prerequisite: An appropriate score on the Calculus Readiness Exam.
Consent of instructor required. Enrollment Limit: 32.
134. Calculus
II: Special Functions, Integration Techniques,
4 hours
and Power Series
4NS, QPf
Continuation of
the study of the calculus of functions of one variable. Topics include logarithmic,
exponential and the inverse trigonometric functions, techniques of integration,
polar coordinates, parametric equations, infinite series, and applications.
The course sequences MATH 133, 134 and MATH 131, 132, 134 both provide a standard
introduction to single-variable calculus. Prerequisite: MATH 132 or MATH 133. Enrollment Limit: 32.
Intermediate
Courses
220. Discrete Mathematics 3 hours
3NS, QPf
An introduction
to a wide variety of mathematical ideas and techniques that do not involve
calculus. Topics such as graph theory, combinatorics, difference equations,
elementary number theory, recursion, mathematical induction, and logic. Prerequisite: MATH 133. Enrollment Limit: 32.
231. Multivariable Calculus 3 hours
3NS, QPf
An
introduction to the calculus of several variables. Topics considered include
vectors and solid analytic geometry, multidimensional differentiation and
integration, and a selection of applications. Prerequisite: MATH 134. Enrollment Limit: 32.
232. Linear Algebra 3 hours
3NS, QPf
An introduction to linear algebra. Topics considered include the algebra and geometry of Euclidean n-space, matrices, determinants, abstract vector spaces, linear transformations, and diagonalization. Prerequisite: MATH 134 or MATH 220. Enrollment Limit: 32.
234. Differential Equations 3 hours
3NS, QPf
An introduction
to analytic, qualitative and numerical methods for solving ordinary differential
equations. Topics include general first order equations, linear first and
second order equations, numerical methods (Euler, Runge-Kutta), systems of
first order equations, phase plane analysis, and Laplace Transforms. There
is emphasis throughout the course on geometric and qualitative interpretations
of differential equations, as well as applications to the natural sciences.
Prerequisite: MATH 231. Enrollment Limit: 32.
Advanced Courses
301. Advanced Calculus 3 hours
3NS, QPf
A rigorous examination of the basic elements of analysis. The structure of the real number system, continuity, differentiability, uniform continuity, integrability of functions of a single variable, sequences, series, and uniform convergence are typical topics to be explored. Prerequisite: MATH 231. MATH 220 is also highly recommended.
317. Number Theory 3 hours
3NS, QPf
This course is an introduction to number theory. Topics include primality, divisibility, modular arithmetic, finite fields, quadratic reciprocity, and elliptic curves. Emphasis will be placed both on theoretical questions and on algorithms for computation. . Prerequisite: MATH 220 & 232 or consent of the instructor.
327. Group Theory 3 hours
3NS, QPf
A first course in the modern algebraic structures and techniques fundamental to mathematics and useful in many areas of science and engineering. Topics include: groups, subgroups, quotient groups, isomorphism theorems, permutation groups, finite groups, and applications to combinatorics, geometry, symmetry, and crystallography. Prerequisite: MATH 232. MATH 220 is also highly recommended.
328. Computational Algebra and Algebraic Geometry 3 hours
3NS, QPf
This course examines connections between the algebra and geometry of the set of solutions to a system of polynomial equations (called a variety) and the use of algorithms to effect concrete calculations. Topics studied include rings and ideals, , Grober bases, resultants and eliminatin theory, Hilbert's Nullstellensatz, the correspondence between polynomial ideals and algebraic varieties, and applications of the methods to other areas of mathematics. There will be opportunities for computer experimentation and student projects. Prerequisite: MATH 231 and MATH 232. Math 220 is also highly recommended.
331. Optimization 3 hours
3NS, QPf
An introduction to linear, integer, and nonlinear programming. Emphasis is placed on the theory of mathematical programming and the analysis of optimization algorithms. These are applied to significant problems in the fields of medicine, finance, public policy, transportation, and telecommunications. Prerequisites: MATH 231 and MATH 232.
335. Probability 3 hours
3NS, QPf
An
introduction to the mathematical theory of probability and its applications.
Topics include discrete and continuous sample spaces, combinatorial problems,
random variables, probability densities, probability distributions, limit
theorems, and stochastic processes. Prerequisite: MATH 231. MATH 220 is also strongly recommended.
336. Mathematical Statistics 3 hours
3NS, QPf
The
theory of probability is applied to problems of statistics. Topics include
sampling theory, point and interval estimation tests of statistical hypotheses,
regression, and analysis of variance. Prerequisite: MATH 232, MATH 335.
353. Topology 3 hours
3NS, QPf
This
course is an introduction to alebraic topology and is designed to explore
the interplay between algebra and geometry, The focus of study will be the
fundamental group of a topological space. Special attention will be paid to
the case of two-dimensional surfaces. A;;lications to knot theory and the
theory of covering spaces will be included as time allows. Prerequisite: MATH 327 or the consent of the instructor.
356. Complex Analysis 3 hours
3NS, QPf
An
introduction to the theory of differentiable functions of a complex variable,
including the Cauchy theorems, residues, series expansions, and conformal
mapping. Prerequisite: MATH 301.
399. Seminar: Measure and Integration 3 hours
3NS, QPf