Mathematics Course Descriptions

Prerequisites: MT202 Multivariable Calculus, MT210 Linear Algebra, and familiarity with using a computer.

Topics include the solution of linear and nonlinear algebraic equations, interpolation, numerical differentiation and integration, numerical solution of ordinary differential equations, approximation theory.

Prerequisites: MT202 Multivariable Calculus and familiarity with using a computer.

This course provides a general introduction to modern probability theory.

Topics include probability spaces, discrete and continuous random variables, joint and conditional distributions, mathematical expectation, the central limit theorem, and the weak law of large numbers. Applications to real data will be stressed, and we will use the computer to explore many concepts.

Prerequisites: MT426 Probability and familiarity with using a computer.

Topics studied include the following: sampling distributions, parametric point and interval estimation, hypothesis testing, goodness-of-fit, parametric and nonparametric two-sample analysis. Applications to real data will be stressed, and the computer will be used to explore concepts and analyze data.

Prerequisite: MT216 Introduction to Abstract Mathematics.

Topics covered include divisibility, unique factorization, congruences, number-theoretic functions, primitive roots, diophantine equations, continued fractions, quadratic residues, and the distribution of primes. An attempt will be made to provide historical background for various problems and to provide examples useful in the secondary school curriculum.

Prerequisite: MT210 Linear Algebra.

The MT 435-436 sequence demonstrates how mathematical theory can be developed and applied to solve problems from management, economics, and the social sciences.

Topics studied from linear programming include a general discussion of linear optimization models, the theory and development of the simplex algorithm, degeneracy, duality, sensitivity analysis, and the dual simplex algorithm. Integer programming problems, and the transportation and assignment problems are considered,and algorithms are developed for their resolution. Other topics are drawn from game theory, dynamic programming, Markov decision processes (with finite and infinite horizons), network analysis, and nonlinear programming.

Prerequisites: MT202 Multivariable Calculus and MT410 Differential Equations or permission of the instructor.

This course is an introduction to nonlinear dynamics and their applications, emphasizing qualitative methods for differential equations.

Topics include fixed and periodic points, stability, linearization, parameterized families and bifurcations, and existence and nonexistence theorems for closed orbits in the plane. The final part of the course is an introduction to chaotic systems and fractals, including the Lorenz system and the quadratic map.

Prerequisites: MT202 Multivariable Calculus and at least one of MT210 Linear Algebra or MT216 Introduction to Abstract Mathematics. Not open to students who have completed MT245 or MC248 or CS245.

This is a course in enumeration and graph theory. The object of the course is to develop proficiency in solving discrete mathematics problems.

Among the topics covered are the following: counting methods for arrangements and selections, the pigeonhole principle, the inclusion-exclusion principle, generating functions, recurrence relations, graph theory, trees and searching, and network algorithms. The problem-solving techniques developed apply to the analysis of computer systems, but most of the problems in the course are from recreational mathematics.

Prerequisite: MT216 Introduction to Abstract Mathematics.

This course surveys the history and foundations of geometry from ancient to modern times.

Topics will be selected from among the following: Mesopotamian and Egyptian mathematics, Greek geometry, the axiomatic method, history of the parallel postulate, the Lobachevskian plane, Hilbert's axioms for Euclidean geometry, elliptic and projective geometry, the trigonometric formulas, models, geometry and the study of physical space.

Prerequisites: MT202 Multivariable Calculus and MT210 Linear Algebra.

This is a course primarily for mathematics majors with the purpose of introducing the student to the creation, use and analysis of a variety of mathematical models and to reinforce and deepen the mathematical and logical skills required of modelers.

A secondary purpose is to develop a sense of the existing and potential roles of both small and large scale models in our scientific civilization. It proceeds through the study of the model-building process, examination of exemplary models, and individual and group efforts to build or refine models through a succession of problem sets, laboratory exercises, and field work.

In Spring, 2008, the course will be offered by Professor Bond, and the topic will be Introduction to Cryptography. Prerequisites: MT310 Introduction to Abstract Algebra (or MT816 Introduction to Modern Algebra).

This course is an introduction to Cryptography with a particular emphasis on public key cryptography. Among the topics covered are: affine ciphers, the RSA algorithm, discrete logarithms, digital signatures, primality testing, and methods of factoring large integers. The necessary topics from number theory, especially the theory of congruences, will be discussed as the need arises.