Academic Bulletin Mathematics - Course Descriptions - 2010-11

This course is intended solely for those students who wish to take calculus, but whose preparation makes a slower-paced course in calculus advisable. Topics covered include a review of algebra (solving equations and inequalities, simplification of algebraic expressions), properties of polynomials and rational functions, limits, continuity, an introduction to derivatives via polynomials and rational functions, and applications of the derivative. Mathematics 010 can not be used for any distribution credit. (For students who desire a distribution credit in mathematics but do not wish to take calculus, Mathematics 103, 104, 106 and 108 are recommended.) This course is offered fall semester.

Prerequisite: Admission by department placement only.

Topics include a brief introduction to probability, conditional probability, and expected values as well as the application of probabilistic reasoning to interesting problems in the areas of medical testing, investing, insurance, retirement annuities, and the analysis of rare events. Mathematics 103 does not count toward the mathematics major or minor. This course is offered every semester.

In this course, we present the classical approach to statistical reasoning, both the p-value argument to testing claims and the confidence interval approach to estimation. Other topics include correlation, prediction, and paradoxes involving averages. Mathematics 104 does not count toward the mathematics major or minor. This course is offered every semester.

INTRODUCTORY

A reflective examination of basic mathematical ideas. Through participation and discovery, students will consider an articulation of mathematics that focuses on patterns, abstraction, and inquiry. Topics will vary, but could include logic, Euclidean geometry, algorithms, etc. This course does not count towards the major or minor in mathematics. This course is offered in the spring semester.

Introductory—An introduction to discrete mathematics for students not planning to major in mathematics. Topics include sets and logic, proof methods, counting arguments, recurrence relations, graphs, and trees. This course may be used to meet the mathematics requirement for the computer science minor. However, it does not count toward the mathematics major or minor. Students may not present both mathematics 108 and 219 for credit toward graduation. This course is offered in the fall semester. This course does not count toward the major or minor in mathematics.

Introductory–This course is intended solely for those students who took and passed Mathematics 010 and desire to complete a course in calculus. Successful completion of this course is equivalent to completion of Mathematics 111. Topics covered include an introduction to integration via polynomials and rational functions, applications of the integral, Fundamental Theorem of Calculus, and introduction to exponential, logarithmic and trigonometric functions, and the application of the derivative and integral to these families of functions. The focus is on understanding basic concepts and gaining basic computational skills. This course counts as a distribution credit in mathematics. Credit cannot be given for both Mathematics 110 and Mathematics 111. This course is offered in the spring semester.

Prerequisite: Mathematics 010

Introductory—Basic calculus of one variable from an intuitive point of view. Topics include limits, continuity, derivatives and integrals of the elementary functions, Fundamental Theorem of Calculus, and applications. The focus is on understanding basic concepts and gaining basic computational skills.

Prerequisite: Departmental placement examination.

Introductory—A continuation of Mathematics 111. Numerical and symbolic techniques of integration, applications of integration, an introduction to partial derivatives and multiple integrals, sequences and series, and Taylor’s Theorem.

Prerequisite: Mathematics 110 or 111, departmental placement examination, AP examination, or permission of the department.

Intermediate—This course is an introduction to combinatorial reasoning. Topics include graphs, circuits in graphs, graph coloring, trees, counting principles, generating functions, and recurrence relations. This course is offered alternate years. Next anticipated offerings will be spring semesters of 2011 and 2013.

Prerequisite: Mathematics 223 or consent of instructor. Students may not present both Mathematics 108 and Mathematics 219 for credit towards graduation.

Intermediate—A development of Euclidean and non-Euclidean geometries from a modern viewpoint. This course is offered in the spring semester.

Prerequisite: Mathematics 112 or permission of the instructor.

Intermediate—A study of elementary number theory. Topics include divisibility, congruences, properties of prime numbers, number theoretic functions, diophantine equations, and additional selected topics. This course is offered alternate years. Next anticipated offerings will be spring semesters of 2011 and 2013.

Prerequisite: Mathematics 112 or consent of the instructor.

Intermediate—An introduction to linear mathematics. Linear systems of equations, matrices, determinants, vector spaces, bases and dimension, function spaces, linear transformations, eigenvalues and eigenvectors, inner products, and applications. An important aspect of the course is to introduce the student to abstract thinking and proofs. This course is offered every semester.

Prerequisites: Mathematics 112, departmental placement examination, AP examination, or permission of the department.

Intermediate—Introduction to ordinary differential equations. Special solution techniques and some theory for first-order and linear equations including integrating factors, constant coefficients, undetermined coefficients, variation of parameters, power series solutions, Laplace transforms, and systems of differential equations, applications. This course is offered in the spring semester.

Prerequisites: Mathematics 112 and 223.

Intermediate—Calculus in higher dimensions. Limits, continuity, differentiability, directional derivatives, constrained and unconstrained optimization, geometry of curves, multiple integrals, general coordinate systems, path and surface integrals, vector calculus, theorems of Green and Stokes, applications. This course is offered in the fall semester.

Prerequisites: Mathematics 112 and 223.

Intermediate—Linear and nonlinear optimization, linear programming, integer programming, duality, combinatorics, the simplex method and related algorithms, game theory, Markov chains, queuing theory. This course is offered irregularly.

Prerequisite: Mathematics 223 or consent of the instructor.

The course gives an overview of the mathematical reasoning behind the pricing of options. Topics include binomial models, put-call parity, a probabilistic derivation of the Black-Scholes pricing formula for call options, and delta hedging. We will also look at Asian, gap, and barrier options. This course is offered in the fall semester.

Prerequisite: Mathematics 112 (Calculus II)

The course gives an overview of the mathematical reasoning behind the pricing of options. Topics include binomial models, put-call parity, a probabilistic derivation of the Black-Scholes pricing formula for call options, and delta hedging. We will also look at Asian, gap, and barrier options. This course is offered in the fall semester.

Prerequisite: Mathematics 112 (Calculus II)

This course is an introduction to discrete and continuous random variables. Distributions considered include the hypergeometric, binomial, geometric, Poisson, uniform, normal, gamma, chi-square, t and F. We will cover the Central Limit Theorem, multivariate distributions, and transformations of random variables. This course is offered in the fall semester.

Prerequisite: Mathematics 112 (Calculus II)

This course gives an overview of confidence intervals, classical hypothesis testing procedures: z-tests, t-tests, F-tests, Chi-square tests, basic factorial, complete block, and Latin square designs, and regression. An intuitive but mathematical treatment is given for all the distributions and procedures involved. This course is offered in the spring semester.

Prerequisite: Mathematics 112 (Calculus II)

Advanced—A course to develop the basic skills of formulation, simplification, and analysis of mathematical models for describing and predicting phenomena in the natural and social sciences, with special emphasis in modeling with differential equations. Topics may be taken from fields such as physics, chemistry, biology, psychology, economics, and political science. This course is offered alternate years. Next anticipated offerings will be fall semesters of 2010 and 2012.

Prerequisite: Mathematics 224.

An in-depth study of some of the topics covered in Mathematics 223, including the theory of vector spaces, linear transformations, and Euclidean spaces, together with some additional topics, which may include isomorphisms, duality, canonical forms, and applications of linear algebra. This course is offered irregularly.

Prerequisite: Mathematics 223 or consent of the instructor.

Advanced—A second course in differential equations, offering study of special topics in more depth or beyond those covered in Mathematics 224. Topics may include existence and uniqueness theory, stability theory, Green’s functions, dynamical systems, partial differential equations, and applications of differential equations. This course is offered alternate years. Next anticipated offerings will be fall semesters of 2011 and 2013.

Prerequisite: Mathematics 224 or consent of the instructor.

Advanced—A first course in higher abstract mathematics. Emphasis is placed on writing proofs. Topics include groups and rings. This course is offered in the spring semester.

Prerequisite: Mathematics 223 or consent of the instructor.

Advanced—A continuation of Mathematics 331. Topics will depend on the instructor, but may include fields, modules, Galois theory, or advanced topics in groups and rings. This course is offered irregularly.

Prerequisite: Mathematics 331.

Advanced—A first course in the foundations of modern analysis. Topics include set theory, topology of the real numbers, sequences, series, differentiation, integration, and rigorous proofs of the major theorems of single-variable calculus. This course is offered in the fall semester.

Prerequisite: Mathematics 223.  It is recommended that students take Mathematics 331 before Mathematics 333.

Advanced—A continuation of Mathematics 333. Topics will depend on the instructor, but may include sequences and series of functions, Fourier analysis, elementary functional analysis, advanced multivariable calculus or metric spaces. This course is offered irregularly.

Prerequisite: Mathematics 333.

Advanced—This course will address topics such as numerical solution of non-linear equations in one variable, interpolation, approximation, differentiation, integration, difference equations, differential equations and their applications, boundary value problems, linear systems, matrices, and optimization. This course is offered alternate years. Next anticipated offerings will be fall semesters of 2010 and 2012.

Prerequisite: Computer Science 111 (or permission of the instructor) and Mathematics 223.

Advanced—A course to develop mathematical and computational techniques in areas of mathematics or interdisciplinary study in which computation plays a central and essential role. Topics vary by semester but may include computational geometry, computer algebra, scientific computing, and symbolic computation. This course is offered alternate years. Next anticipated offerings will be fall semesters of 2011 and 2013.

Prerequisite: Computer Science 111.  Some topics may have additional prerequisites.

Advanced—A study of elementary topology. Topics discussed will include topologies, separation axioms, connectedness, compactness, continuity, and metric spaces. This course is offered alternate years. Next anticipated offerings will be spring semesters of 2012 and 2014.

Prerequisite: Mathematics 223 or consent of the instructor.

Advanced—Analytic functions, mapping of elementary functions, integrals, residue theory, conformal mapping. This course is offered alternate years. Next anticipated offerings will be spring semesters of 2011 and 2013.

Prerequisite: Mathematics 223 or consent of the instructor.

This course is a continuation of Mathematics 253 (Probability Models). Topics include survival functions, hazard functions, order statistics, continuous and discrete distributions not considered in Mathematics 253 and mixed random variables. We will look at a wide variety of probability problems associated with insurance. This course is offered in the fall semester.

Prerequisite: Mathematics 253 (Probability Models)

This course takes a more theoretical look at estimation and hypothesis testing than Mathematics 254 (Statistical Models). Topics include maximum likelihood estimators (MLE’s), the information inequality, asymptotic theory of MLE’s, complete sufficient statistics, uniformly minimum variance unbiased estimators, likelihood ratio tests, most powerful tests, uniformly most powerful tests, and Bayesian statistics. This course is offered in the spring semester on an irregular basis.

Prerequisite: Mathematics 253 (Probability Models) and Mathematics 254 (Statistical Models)

This course takes a matrix-based look at regression (introduced in Mathematics 254, Statistical Models). We focus on the probabilistic reasoning behind regression, in particular inferences we can make using linear combinations of normal random variables. We also look briefly at some time series models. This course is offered in the spring semester on an irregular basis.

Prerequisite: Mathematics 223 (Linear Algebra), Mathematics 253 (Probability Models) and Mathematics 254 (Statistical Models)

This course is designed for the treatment of material outside the regular offerings of the department. For a given semester the course content and other particulars will be announced before advance registration for that semester. This course is offered irregularly. Level varies, will be announced with course description the semester it is offered.

Directed reading and research on special topics for qualified students. May be repeated for credit. Level varies (intermediate or advanced), determined in consultation with instructor.

Prerequisite: Permission of the department.

Directed reading and research on special topics for qualified students. May be repeated for credit. Level varies (intermediate or advanced), determined in consultation with instructor.

Prerequisite: Permission of the department.

Advanced — Topics in the history and foundations of mathematics, the special emphasis varying from year to year. Every student will be expected to write a term paper.

Prerequisites: Usually taken by mathematics major. Admission in other cases is by permission of the department chair.