**First
Year Seminars**

177. What is Mathematics and Why Won't It Go Away? 3 hours

3NS, QPf

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 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.

179. From Logic to Persuasion to Propaganda 3 hours

3NS, QPf

Argumentation and persuasion, more formally, the fields of logic and rhetoric will be used as a lens to examine contemporary culture. Students will learn how to construct arguments using tools from deductive and inductive logic, including the propositional calculus, the predicate calculus and elementary statistics. These tools plus others from classical rhetoric and the 'new rhetoric', will be used to analyze and synthesize arguments in areas of current political and social controversy. A final theme is the development of persuasion into a science and an industry, in the form of advertising and propaganda.

**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, voting systems, discrete models, 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. (Not open to any student who has received credit for a mathematics course numbered 131 or higher). It is intended for students who have not satisfied the quantitative proficiency requirement. *Enrollment limit:* 30.

050. Dots, Lines, and Coin Flips 3 hours

3NS, QPf

An introduction
to two important ways of describing the world mathematically. Graphs model
maps and networks—-road, telephone, computer, social. Probability theory
describes the order that can lurk in random phenomena. Using both these tools,
we will examine questions like: How random is the stock market? How tightly
is the World Wide Web connected? Are there just six degrees of separation?
Note: This course does not count toward a major in Mathematics.
It is intended for students who have not satisfied the quantitative proficiency
requirement. 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 and is not
open to any student who has received credit for a course in mathematics course
numbered 131 or higher. Enrollment
Limit: 30.

095. Discrete Mathematical Models 3 hours

3NS, QPf

An introduction to discrete mathematical models. Mathematical techniques to be discussed include difference equations, iteration, convergence, elementary probability and optimization. Basic financial, population, economic, and physical models will be explored with applications to personal financial decision-making, ecology, population management, and drug selection, as well as other areas. The course will make extensive use of spreadsheet software. *Note*: This course does not count towards a major in mathematics. It is intended for students who have not satisfied the quantitative proficiency requirement and is not open to any student who has received credit for a mathematics course numbered 113 or higher. Enrollment Limit: 30

100. Elementary Statistics 3 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. 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. It is intended for
students in the social sciences and humanities with minimal mathematical experience
who have not satisfied the quantitative proficiency requirement. Enrollment Limit: 30

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. * Consent of instructor required. Prerequisite*: An appropriate score on the Statistics Readiness Exam.

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: *32.

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. *Prerequisite*: An appropriate score on the Calculus Readiness Exam. The two-course sequence
MATH 131, MATH 132 is equivalent to the more intensive MATH 133. 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. *Prerequisite*: An appropriate score on the Calculus Readiness Exam. This
course is equivalent to the two-course sequence MATH 131, MATH 132. 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. *Prerequisite:* MATH 132 or MATH 133. *Note: *The course sequences MATH 133, 134 and MATH 131, 132, 134 both provide a standard introduction to single-variaable calculus. 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.

236. Partial Differential Equationsand Applied Complex Analysis 3 hours

3NS, QPf

An introduction to complex analysis in the context of applications to partial differential equations. Topics to include: analytic functions, complex integration and residue calculus techniques, Fourier series, partial differential equations in rectangular, cylindrical and spherical coordinates, and associated special functions, Fourier and Laplace transfoms. Depending on student interest, numerical methods including finite difference and finite element techniques may be covered. *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.

302. Dynamical Systems 3 hours

**3NS,
QPf**

A first course in discrete and continuous dynamical systems in dimensions one and higher. Topics include phase portraits, periodic orbits, hyperbolicity, bifurcations, symbolic dynamics, chaos and fractals. Prerequisite: MATH 231 and 232. Note: MATH 234 is recommended. Taught in alternate
years only.

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. *Prerequisites *: MATH 220 & 232 or consent of the instructor. *Note *: Taught in alternate years only.

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. *Note: *MATH 220 is also highly recommended.

328. Computational Algebra and Algebraic Geometry 3 hours

3NS, QPf

*Prerequisites*: MATH 231 and MATH 232. MATH 220 is also highly recommended. *Note*: Given in alternate years only.

329. Abstract Algebra: Rings and Fields 3 hours

3NS, QPf

This is one of two courses introducing algebraic
structures and techniques fundamental to mathematics and useful in many areas
of science and engineering. Topics
include: rings, subrings, ideals, fields, integral domains, polynomial rings,
extension fields, finite fields, famous impossible constructions, and Galois
theory. *Prerequisite*: MATH
327 or consent by instructor. *Note*: Taught in alternate years only.

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. Prerequisites : MATH 232, MATH 335. Note : Taught in alternate years only.

337. Data Analysis 3 hours

3NS, QPf

In this course students will be given an introduction to the theory and use of regression graphics. Special regression and graphics software will be used to study relationships among several variables. Topics will include regression smoothing, residual plots, scatterplot matrices, three-dimensional plots, transformations of predictors and of response variables, and added-variable plots. *Note*: Taught in alternate years only. Prerequisites: MATH 113 or 114 and MATH 232 or consent of the instructor.

338. Probability Models and Random Processes 3 hours

3NS, QPf

An introduction
to operations research models which incorporate methods of probability theory. Topics will be chosen from inventory theory,
queueing theory, decision analysis, game theory, simulation, Markov chains,
and project management. Computer
software for selected topics will also be discussed and utilized. Prerequisite: MATH 335. Note:
Taught in alternate years only.

343. Combinatorics 3 hours

3NS, QP

An advanced course in discrete mathematics. Topics covered include enumeration, combinatorial identities, generating functions, partitions, and set systems. Prerequisites : any one of MATH 317, 327, 328, 329, or 335.

345. Information Theory 3 hours

3NS, QP

An introduction to Information Theory and Coding Theory. Topics include information and entropy, data compression, Shannon theory and noisy channels, error-correcting codes, and applications to statistics, computer science, economics, and the natural sciences. *Prerequisites* : MATH 220, 232, or MATH 335, or consent of instructor.

348. Graphical Models 3 hours

3NS, QP

An introduction to graphical models and Bayesian networks. This course will emphasize both the theory and the applications of these probabilistic models. Topics may include: background in probability and graph theory, building models, tuning and updating models, decision making, algorithms to accomplish all of these tasks, and applications to machine learning, biology and medicine, statistics and other fields. *Prerequisites: *MATH 220.

350. Geometry 3 hours

3NS, QPf

The course takes a modern approach to geometry based on group theory and the Erlangen Programm making possible the survey of a wide spectrum of geometries, Euclidean and non-Euclidean. Geometries treated include Moebius geometry, hyperbolic geometry, elliptic geometry, and absolute geometry. The discovery of these geometries in the 19th centry caused a scientific and philosophical revolution second only to the Copernican revolution. Prerequisites: MATH 220 or consent of instructor.

353. Topology 3 hours

3NS, QPf

An introduction to point-set and algebraic topology. The fundamental notion of a topological space is introduced and properties of separation, compactness and connectedness. Topological spaces are also studied by means of algebraic invariants including homotopy and homology. Some of the famous theorems to be proved using these tools include the Brouwer Fixed Point Theorem, Poincare Index Theorem, Classification of Surfaces and the Ham Sandwich Theorem. *Prerequisite: *Math 301 or 327 or consent of instructor. *Note: *Taught in alternate years only.

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 mappings. *Prerequisite* : MATH 301. Note : Taught in alternate years only.

358. Real Analysis 3 hours

3NS, QPf

This course presents important generalizations of integration and differentiation developed in the twentieth century. An introduction to metric spaces, Lebesgue's theory of the integral, and general measure and integration theory. *Prerequisite *: MATH 301.

360. Mathematical Methods for Computational Neuroscience 3 hours

3NS, QPf

An introduction to analytical and numerical mathematical methods with application to computational neuroscience. Methods include numerical solution of nonlinear ordinary differential equations, Markov chains, bifurcation theory, partial differential equations, and information theory. Neuroscience applications include dynamics of ion channels and nerve membranes, reliability and precision of patterns of action potentials, synaptic transmission and plasticity, and information processing in neural networks. Students will use the NEURON programming language to develop simulations at various levels of biophysical complexity. Prerequisites: MATH 232 and MATH 234, or consent of instructor.

362. Mathematical Biology 3 hours

3NS, QPf

A research-oriented seminar course on the mathematical modeling of biological systems. Topics include applications of ODEs and PDEs, Monte Carlo methods, stochastic differential equations and bifurcation theory. Biological topics include synchronization, population dynamics, patterning in growth & development, reaction-diffusion systems, coordination of movement and chemotaxis. Student research projects will comprise a significant part of the course. Prerequisites: MATH 231 and consent of instructor.

383. Theory of Computer Science 3 hours

3NS, QP

397. Seminar in Mathematical Modeling 3 hours

3NS, QPf

Teams of students will work on projects involving optimization or probability theory. Possible projects include realignment of teams in the National Football League, simulation of the spread of HIV in prostitutes in Central Africa, selection of portfolios of stocks and bonds, analysis of the behavior of cellular automata, graph drawing and image compression. *Prerequisites: *MATH 331 or MATH 335.

398. Seminar in Mathematical Logic 3 hours

3NS, QPf

An introduction to set theory and computability. This seminar will examine both the foundations of mathematics and the limitations of formal reasoning. Student projects, consisting of a presentation and an expository paper, will be based on independent reading. *Prerequisite: *Two 300-level mathematics course.

399. Seminar in Number Systems 3 hours

3NS, QPf

*Prerequisite*: One 300-level mathematics course.

401. Honors 2-4 hours

2-4NS

Consent of instructor required550, 551. Research 1-2 hours

3NS, QPf

*Prerequisite*: Consent of the chair of the department.