MATH - Mathematics

MATH 104 - A World of Mathematics

A non-calculus based course that highlights the nature and significance of mathematics and its widespread applicability across a variety of disciplines. Applications of mathematics and mathematical modeling may come from areas such as financial management, economics, political science, government, medicine, the natural sciences, and the arts. An emphasis will be placed upon developing the student's skills in critical thinking and in applying analytical skills to interpret quantitative information.[Q]

Prerequisite
(Not open to students who have credit for any mathematics course numbered above 120, except by permission of instructor.)

MATH 110 - Statistical Concepts

An introduction to the concepts and reasoning underlying the interpretation of data and chance. Emphasis is on understanding how statistical analysis is used to gain insight into a wide variety of areas of human interest. Topics include elements of descriptive statistics, design of experiments, laws of probability, and inference from a sample to a population (including confidence intervals and hypothesis testing). Not open to students who have credit for any mathematics course numbered above 120, except by permission of instructor. [Q]

MATH 125 - Modeling and Differential Calculus

An introduction to mathematical modeling and the use of differential calculus. Topics include: analysis and manipulation of elementary functions, including trigonometric, exponential, and logarithmic functions; the differential calculus of such functions; and optimization. An ongoing emphasis will be the use of elementary functions as well as the differential calculus to model phenomena in the natural, social and life sciences. Not open to students who have credit for MATH 161 or MATH 165. [Q]

Prerequisite
Two years of high school algebra

MATH 141 - Differential Calculus and Economic Modeling

This course in the differential calculus of one and several variables is intended for students who plan to major in Economics or Policy Studies. Mathematical concepts include exponentials and logarithms, limits, ordinary and partial derivatives, techniques of differentiation, contours, and optimization in both one and several variables. Economic concepts and models include supply and demand curves, market equilibrium, present and future value, marginal analysis, total and average cost, elasticity of demand, and optimization subject to a budget constraint. Not open to students who have credit for MATH 161 or MATH 165. [Q]

Prerequisite
Three years of High School mathematics

MATH 161 - Calculus I

The sequence MATH 161, MATH 162, MATH 263 provides an introduction to calculus for students of mathematics, engineering, and the sciences. Topics include limits, derivatives, techniques of differentiation, definite integrals, the fundamental theorem of calculus, and applications of derivatives and integrals. [Q]

Prerequisite
High school trigonometry

MATH 162 - Calculus II

A continuation of MATH 161. Topics include techniques and applications of integration, introduction to differential equations, parametric curves and polar coordinates, infinite series and Taylor approximation.

Prerequisite
A grade of C- or better in MATH 161 or MATH 165

MATH 165 - Calculus I+

A course which covers the same topics as MATH 161 while using a workshop experience and collaborative learning to give special emphasis to the development of problem-solving skills. Enrollment is by invitation of the Department of Mathematics. [Q]

Prerequisite
High school trigonometry

MATH 166 - Calculus II+

A course which covers the same topics as MATH 162 while using a workshop experience and collaborative learning to give special emphasis to the development of problem-solving skills. Enrollment is by invitation of the Department of Mathematics.

Prerequisite
A grade of C- or better in MATH 161 or MATH 165

MATH 182 - Discrete Structures

An introduction to discrete structures and algorithms and some mathematical tools and methods of reasoning that aid in their development and analysis. Topics include: sets, counting, probability, algorithms, mathematical induction, relations, graphs, and trees.

Prerequisite
CS 104, CS 105, or CS 106, MATH 161 or MATH 165.

MATH 186 - Applied Statistics

An introductory course emphasizing standard methods and reasoning used in analyzing data. Topics include exploratory data analysis, design of experiments, least squares analysis, probability, sampling distributions and methods of inferential statistics. Includes an introduction to a statistical computing package. Not open to students who have credit for PSYC 120. [Q]

Prerequisite
MATH 125, MATH 141, MATH 161 or MATH 165, or permission of instructor

MATH 256 - Evolutionary Game Theory

An introduction to the concepts, techniques, and application of evolutionary game theory. The mathematics of game theory and natural selection offer insights valuable to the study of economics, biology, psychology, anthropology, sociology, philosophy, and political science. This course is intended to serve students with interests in any of these fields learn the approach, requiring minimal mathematical background, with special attention to apparent paradoxes, such as the evolution of altruism.

Prerequisite
MATH 141,MATH 161, or MATH 165; and one of the following: ECON 101, BIOL 102, A&S 102, A&S 103, PSYC 110, GOVT 101, GOVT 102, GOVT 103, GOVT 104, PHIL 200, PHIL 245, PHIL 250, PHIL 260, or NEUR 201

MATH 263 - Calculus III

A continuation of MATH 162. Topics include vector algebra, vector calculus, partial derivatives, gradients and directional derivatives, tangent planes, the chain rule, multiple integrals and line integrals.

Prerequisite
A grade of C- or better in MATH 162 or MATH 166

MATH 264 - Differential Equations with Linear Algebra

An introductory course in ordinary differential equations including techniques of elementary linear algebra. Emphasis is on first-order equations, and higher-order linear equations and systems of equations. Topics include qualitative analysis of differential equations, analytical and numerical solutions, Laplace transforms, existence and uniqueness of solutions, and elemental models in science and engineering.

Prerequisite
MATH 263

MATH 272 - Linear Algebra with Applications

An introductory course in linear algebra emphasizing applications to fields such as economics, natural sciences, computer science, statistics, and engineering. The course covers solutions of systems of equations, matrix algebra, vector spaces, linear transformations, determinants, eigenvalues and eigenvectors. Not open to students who have credit for MATH 300.

MATH 282 - Techniques of Mathematical Modeling

A course that introduces students to the fundamentals of mathematical modeling through the formulation, analysis, and testing of mathematical models in a variety of areas. Modeling techniques covered include proportionality, curve fitting, elementary linear programming, and simulation.

Prerequisite
MATH 162 or MATH 166

MATH 290 - Transition to Theoretical Mathematics

An introduction to the concepts and techniques that permeate advanced mathematics. Topics include set theory, propositional logic, proof techniques, relations, and functions. Special emphasis on developing students' facility for reading and writing mathematical proofs. Examples and additional topics are included from various branches of mathematics, at the discretion of the instructor.

MATH 300 - Vector Spaces

A first course in theoretical linear algebra, emphasizing the reading and writing of proofs. Topics include systems of linear equations, matrix algebra, vector spaces and linear transformations, eigenvectors and diagonalization, inner product spaces, and the Spectral Theorem. Not open to students with credit for MATH 272.

Prerequisite
MATH 290 or permission of instructor

MATH 301 - Case Studies in Mathematical Modeling

A course which engages students in the creation of mathematical models to answer questions about a variety of phenomena. Students work in small teams on a sequence of projects which require the formulation, analysis, and critical evaluation of a mathematical model and conclude with the submission of a written report by each student. [W]

Prerequisite
MATH 272 or MATH 300

MATH 306 - Operations Research

A study of some mathematical methods of decision making. Topics include: linear programming (maximizing linear functions subject to linear constraints), the simplex algorithm for solving linear programming problems, sensitivity analysis, networks and inventory problems and applications.

Prerequisite
MATH 272 or MATH 300 or permission of instructor

MATH 310 - Ordinary Differential Equations

A course in the theory and applications of ordinary differential equations which emphasizes qualitative aspects of the subject. Topics include analytic and numerical solution techniques for systems of equations, graphical analysis, stability, existence-uniqueness theorems, and applications.

Prerequisite
MATH 263, and MATH 272 or MATH 300

MATH 312 - Partial Differential Equations

An introduction to partial differential equations and their applications. Formulation of initial and boundary value problems for these equations and methods for their solution are emphasized. Separation of variables and Fourier analysis are developed. The course includes interpretation of classical equations and their solutions in terms of applications.

Prerequisite
MATH 263

MATH 323 - Geometry

Various geometries are considered including absolute, Euclidean, and the classical non-Euclidean geometries. General properties of axiomatic systems, models, and the role of Euclidean geometry in the development of other branches of mathematics are discussed.

Prerequisite
MATH 162 or permission of instructor

MATH 325 - Combinatorics

An introduction to the techniques and theory of enumeration of finite sets. Topics include combinations, permutations, generating functions, recurrence relations, the inclusion-exclusion principle, block designs, and graph theory.

Prerequisite
MATH 263, or permission of instructor; reading and writing proofs will be a significant part of the course, so MATH 290 could be useful, though it is not a prerequisite

MATH 328 - Number Theory

An introduction to the theory of the integers and techniques for their study and application. Topics include primality, modular arithmetic, arithmetic functions, quadratic residues, and diophantine equations.

Prerequisite
MATH 263 or permission of instructor; reading and writing proofs will be a significant part of the course, so MATH 290 could be useful, though it is not a prerequisite.

MATH 335 - Probability

A development of basic probability theory including the axioms, random variables, expected value, the law of large numbers and the central limit theorem. Additional topics include distribution functions and generating functions.

Prerequisite
MATH 263

MATH 336 - Mathematical Statistics

A mathematical development of fundamental results and techniques in statistics. Topics include estimation, sampling distributions, hypothesis testing, correlation and regression.

Prerequisite
MATH 335

MATH 343 - Advanced Multivariable Calculus

A continuation of multivariable calculus from MATH 263 , using concepts from linear algebra. Topics include the derivative as a linear transformation, the Chain Rule, the Inverse and Implicit Function Theorems, the Change of Variables Theorem, and the integral theorems of Green, Gauss and Stokes; additional topics may include differential forms and series of functions.

Prerequisite
MATH 263, and MATH 272 or MATH 300

MATH 345 - Complex Analysis

An introductory course in the calculus of complex functions including the algebra and geometry of complex numbers, elementary mappings, complex derivatives and integrals,Cauchy-Riemann equations, harmonic functions, Cauchy's Integral Theory, Taylor and Laurent series, residues.

Prerequisite
MATH 263

MATH 347 - Financial Mathematics

A wide range of topics in mathematical finance are covered, including: continuous time models such as the Brownian motion model for stock prices, the Black-Scholes model for options prices, the Ho-Lee, Vasicek and other models for interest rates, also different hedging strategies and numerical approaches for derivative pricing such as binomial trees, Monte-Carlo simulation and finite difference methods, and price models for credit derivatives such as asset swaps, credit default swaps and collateralized debt obligations.

Prerequisite
ECON 101, MATH 335

MATH 351 - Abstract Algebra I

An introduction to some of the fundamental ideas and structures of abstract algebra. Homomorphisms and isomorphisms, substructures and quotient structures are discussed for algebraic objects such as fields, vector spaces, rings, and groups. Other topics may include factorization in rings, and finite group theory. [W]

Prerequisite
MATH 290

MATH 352 - Abstract Algebra II

The course covers field extensions and Galois Theory. Additional topics are included at the discretion of the instructor.

Prerequisite
MATH 351

MATH 356 - Introduction to Real Analysis

A rigorous development of the calculus of functions of one real variable including the topology of the real line, limits, continuity, differentiation and integration. [W]

Prerequisite
MATH 290

MATH 357 - Real Analysis II

An introduction to metric spaces and measure theory. Topics covered include metric space topology, compactness and completeness, uniform convergence of functions; basic measure theory, construction of Lebesgue measure on the real line, and the definition and basic convergence properties of the Lebesgue integral.

Prerequisite
MATH 356

MATH 358 - Topology

The main topics are set theory, the separation axioms, connectedness, compactness, and the continuity of functions. Classical general topological spaces are studied including regular spaces, normal spaces, first or second countable spaces, and metrizable spaces.

Prerequisite
MATH 356 or permission of instructor

MATH 360 - History of Mathematics

Mathematics is a living, changing subject whose truths, once identified, have remarkable staying power. In this course students analyze various episodes in the history of mathematics that illustrate how mathematical knowledge has developed over the years. Topics include: Egyptian and Babylonian mathematics, indigenous mathematics from outside of the Western tradition, the contributions of Euclid and Ancient Greek mathematics, the birth of calculus, and selected topics from the 19th and 20th centuries. [W]

Prerequisite
MATH 263 or permission of instructor

MATH 372 - Mathematics Seminar

This course offers a major branch of mathematics not covered by the regular offerings of the department. Course descriptions are available in the department office.

Prerequisite
Depend on subject matter. Usually, completion of the calculus sequence constitutes a minimal prerequisite.

MATH 373-389 - Advanced Special Topics

Chosen from among a wide range of mathematical topics accessible to junior and senior mathematics majors. When offered, the special topic to be studied will be listed in the Semester Course and Hour Schedule, and course descriptions will be available in the department office.

MATH 391-394 - Independent Study

Study by an individual student, under the supervision of a mathematics faculty member, of a mathematical subject not covered by courses offered by the department. The program of study must be drawn up by the student and the faculty supervisor and approved by an ad hoc committee of the department.

MATH 400 - Senior Seminar

A course in which each student undertakes a thorough and independent study of one or more topics in mathematics. Students are required to make oral presentations on their work and to prepare written reports on their topics. [W]

Prerequisite
Senior standing and satisfactory completion of at least two 300-level courses in mathematics

MATH 495-496 - Thesis

Students desiring to take Honors in Mathematics should inform their department advisers early in the second semester of the junior year. Honors work involves a guided program of independent study culminating in a thesis on a topic to be selected by the student in consultation with his or her adviser and approved by the department. [One W credit only upon completion of both 495 and 496]

MATH 246 - Evolutionary Game Theory

An introduction to the concepts, techniques, and application of evolutionary game theory. The mathematics of game theory and natural selection offer insights valuable to the study of economics, biology, psychology, anthropology, sociology, philosophy, and political science. This course is intended to serve students with interests in any of these fields learn the approach, requiring minimal mathematical background, with special attention to apparent paradoxes, such as the evolution of altruism. [V]

Prerequisite
MATH 141, MATH 161, or MATH 165 and one of the following: ECON 101, BIOL 102, A&S 102, A&S 103, PSYC 110, GOVT 101, GOVT 102, GOVT 103, GOVT 104, PHIL 145, PHIL 200, PHIL 250, PHIL 260, or NEUR 201