The course listing represents a sampling of courses taught by the faculty in this department in the 2009-10 academic year. To select courses for Fall 2009, see the catalog listing; similarly, for Spring 2010 refer to the relevant catalog.
MATH-35 - Exploring the integers
Offered: First and Second SemesterCredit Hours: 3 Hours
This course is an introduction to number theory, the area of mathematics concerned with the integers. The study of the integers is filled with problems that are simple to state and easy to begin work on. The course focuses on a variety of such problems related to divisibility, the prime numbers, modular arithmetic, sums of squares, elliptic curves, cryptography, and other topics. An emphasis will be placed on exploration and discovery.
The only mathematical prerequisite is high school algebra.
MATH-30 - Topics in Contemporary Mathematics
Offered: First Semester, Second SemesterCredit Hours: 3 hours
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. Prerequisites and notes: 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.
MATH-113 - Stat Methods for the Social and Behavioral Sciences
Offered: First Semester, Second SemesterCredit Hours: 4 hours
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.
Prerequisites and Notes: 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.
MATH-131 - Calculus Ia: Limits, Continuity and Differentiation
Offered: First SemesterCredit Hours: 3 hours
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.
MATH-132 - Calculus Ib: Integration and Applications
Offered: Second SemesterCredit Hours: 3 hours
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.
Prerequisites and Notes: MATH 131 or an appropriate score on the Calculus Readiness Exam.
MATH-133 - Calculus I: Limits, Continuity, Differentiation, Integration and Applications
Offered: First Semester, Second SemesterCredit Hours: 4 hours
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.
MATH-134 - Calculus II: Special Functions, Integration Techniques and Power Series
Offered: First Semester, Second SemesterCredit Hours: 4 hours
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. The course sequences MATH 133, 134 and MATH 131, 132, 134 both provide a standard introduction to single-variable calculus.
MATH-220 - Discrete Mathematics
Offered: First Semester, Second SemesterCredit Hours: 3 hours
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.
MATH-231 - Multivariable Calculus
Offered: First Semester, Second SemesterCredit Hours: 3 hours
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.
MATH-232 - Linear Algebra
Offered: First Semester, Second SemesterCredit Hours: 3 hours
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.
MATH-234 - Differential Equations
Offered: First SemesterCredit Hours: 3 hours
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.
MATH-301 - Advanced Calculus
Offered: First SemesterCredit Hours: 3 hours
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. Note: MATH 220 is also highly recommended.
MATH-302 - Dynamical Systems
Offered: Second SemesterCredit Hours: 3 hours
A first course in discrete dynamical systems in dimensions one and higher. Topics include hyperbolicity, bifurcations, symbolic dynamics, chaos and fractals. Student projects, consisting of a presentation and an expository paper, will be based on independent reading.
Prerequisites: Math 231 and 232. Note: Taught in alternate years only.
MATH-317 - Number Theory
Offered: Second Semester, 2010-2011Credit Hours: 3 hours
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 and 232, or consent of instructor. Note: Taught in alternate years only.
MATH-327 - Group Theory
Offered: Second SemesterCredit Hours: 3 hours
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.
MATH-328 - Computational Algebra and Algebraic Geometry
Offered: First Semester, 2010-2011Credit Hours: 3 hours
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, Grobner bases, resultants and elimination 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.
Prerequisites: MATH 231 and MATH 232. MATH 220 is also highly recommended. Note: Given in alternate years only.
MATH-329 - Rings & Fields
Offered: First SemesterCredit Hours: 3 hours
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. Note: Given in alternate years only.
MATH-331 - Optimization
Offered: First SemesterCredit Hours: 3 hours
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.
MATH-335 - Probability
Offered: First SemesterCredit Hours: 3 hours
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.
MATH-336 - Mathematical Statistics
Offered: Second SemesterCredit Hours: 3 hours
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: Given in alternate years only.
MATH-338 - Probability Models and Random Processes
Offered: Second SemesterCredit Hours: 3 hours
An introduction to operations research models which incorporate methods of probability theory. Topics will be chosen from inventory theory, queuing 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.
MATH-340 - Mathematical Logic
Offered: Second SemesterCredit Hours: 3 hours
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: One 300-level Mathematics course
MATH-343 - Combinatorics
Offered: Second Semester, 2010-2011Credit Hours: 3 hours
An advanced course in discrete mathematics. Topics covered include enumeration, combinatorial identities, generating functions, partitions and set systems.
Prerequisite: Any one of MATH 317, 327, 328, 329, or 335.
MATH-345 - Information Theory
Offered: Second Semester, 2010-2011Credit Hours: 3 hours
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 or consent of instructor.
MATH-350 - Geometry
Offered: First SemesterCredit Hours: 3 hours
This 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 century caused a scientific and philosophical revolution second only to the Copernican revolution.
Prerequisite: MATH 220 or consent of instructor.
MATH-353 - Topology
Offered: Second SemesterCredit Hours: 3 hours
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.
MATH-356 - Complex Analysis
Offered: Second Semester, 2010-2011Credit Hours: 3 hours
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.
MATH-401 - Honors
Offered: First Semester, Second SemesterCredit Hours: 2-4 hours
Consent of instructor required.
MATH-550 - Research
Offered: First SemesterCredit Hours: 1-3 hours
Projects for original investigation. Interested students are encouraged to talk to individual faculty members about possible projects. Consent of the department chair required.
MATH-551 - Research
Offered: Second SemesterCredit Hours: 1-3 hours
Projects for original investigation. Interested students are encouraged to talk to individual faculty members about possible projects. Consent of the department chair required.
MATH-900 - OCEAN: Statistics
Offered: First Semester, Second SemesterCredit Hours: 1-3 hours
Projects for original investigation. Interested students are encouraged to talk to individual faculty members about possible projects. Consent of the department chair required.
MATH-995 - Private Reading
Offered: First Semester, Second SemesterCredit Hours: 0.5-3 hours
Signed permission of the instructor is required.
To register for a private reading, the student must obtain the signatures of the instructor and department chair on a private reading card and turn the card in to the Office of the Registrar.
