Course Descriptions
MAT 010 Precalculus with an Introduction to Calculus I
This course is intended solely for those students who wish to take calculus, but whose preparation makes a slowerpaced 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. MAT 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, MAT 103, 104, 106 and 108 are recommended.) Offered fall semester.
Prerequisite: Instructor permission.
Credits: 1

MAT 103 Probability
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. MAT 103 does not count toward the mathematics major or minor.
Prerequisite: None
Credits: 1/2

MAT 104 Statistics
In this course, we present the classical approach to statistical reasoning, both the pvalue argument to testing claims and the confidence interval approach to estimation. Other topics include correlation, prediction, and paradoxes involving averages. MAT 104 does not count toward the mathematics major or minor.
Prerequisite: None. (MAT 103 is not a prerequisite for MAT 104).
Credits: 1/2

MAT 106 Topics in Contemporary Mathematics
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 toward the major or minor in mathematics.
Prerequisite: None.
Credits: 1

MAT 108 Introduction to Discrete Structures
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. Offered fall semesters.
Prerequisite: None.
Credits: 1

MAT 110 Calculus I with Precalculus Review
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 MAT 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 MAT 110 and MAT 111. Offered spring semesters.
Prerequisite: MAT 010
Credits: 1

MAT 111 Calculus I
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.
Credits: 1

MAT 112 Calculus II
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: MAT 110 or 111, departmental placement examination, or AP examination.
Credits: 1

MAT 219 Combinatorics
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 2012 and 2014. Students may not present both MAT 108 and MAT 219 for credit towards graduation.
Prerequisite: MAT 223.
Credits: 1

MAT 221 Foundations of Geometry
A development of Euclidean and nonEuclidean geometries from a modern viewpoint. Offered spring semesters.
Prerequisite: MAT 112.
Credits: 1

MAT 222 Theory of Numbers
A study of elementary number theory. Topics include divisibility, congruences, properties of prime numbers, number theoretic functions, diophantine equations, and additional selected topics. Offered spring semesters of oddnumbered years.
Prerequisite: MAT 112.
Credits: 1

MAT 223 Elementary Linear Algebra
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.
Prerequisites: MAT 112, departmental placement examination, or AP examination.
Credits: 1

MAT 224 Elementary Differential Equations
Introduction to ordinary differential equations. Special solution techniques and some theory for firstorder and linear equations including integrating factors, constant coefficients, undetermined coefficients, variation of parameters, power series solutions, Laplace transforms, and systems of differential equations applications. Offered spring semesters.
Prerequisites: MAT 112 and 223.
Credits: 1

MAT 225 Multivariable Calculus
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. Offered fall semesters.
Prerequisites: MAT 112 and 223.
Credits: 1

MAT 226 Operations Research
Linear and nonlinear optimization, linear programming, integer programming, duality, combinatorics, the simplex method and related algorithms, game theory, Markov chains, queuing theory. Offered irregularly.
Prerequisite: MAT 223.
Credits: 1

MAT 251 Mathematical Finance
The course gives an overview of the mathematical reasoning behind the pricing of options. Topics include binomial models, putcall parity, a probabilistic derivation of the BlackScholes pricing formula for call options, and delta hedging. We will also look at Asian, gap, and barrier options. Offered fall semesters.
Prerequisite: MAT 112
Credits: 1/2

MAT 252 Mathematical Interest Theory
This course will involve a thorough treatment of the mathematical theory of interest, with special attention paid to calculating present and accumulation values for annuities (series of payments made at regular time intervals). Some topics include nominal and effective rates of interest and discount, force of interest, amortization schedules, sinking funds, and bonds. This course is offered in the fall semester.
Prerequisite: MAT 112.
Credits: 1/2

MAT 253 Probability Models
This course is an introduction to discrete and continuous random variables. Distributions considered include the hypergeometric, binomial, geometric, Poisson, uniform, normal, gamma, chisquare, t and F. We will cover the Central Limit Theorem, multivariate distributions, and transformations of random variables. Offered fall semesters.
Prerequisite: MAT 112.
Credits: 1/2

MAT 254 Statistical Models
This course gives an overview of confidence intervals, classical hypothesis testing procedures: ztests, ttests, Ftests, Chisquare tests, basic factorial, complete block, Latin square designs, and regression. An intuitive but mathematical treatment is given for all the distributions and procedures involved. Offered spring semesters.
Prerequisite: MAT 112.
Credits: 1/2

MAT 314 Modeling with Differential Equations
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 2012 and 2014.
Prerequisite: MAT 224.
Credits: 1

MAT 323 Topics in Linear Algebra
An indepth 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. Offered irregularly.
Prerequisite: MAT 223.
Credits: 1

MAT 324 Topics in Differential Equations
A second course in differential equations, offering study of special topics in more depth or beyond those covered in MAT 224. Topics may include existence and uniqueness theory, stability theory, Green’s functions, dynamical systems, partial differential equations, and applications of differential equations. Offered fall semester of oddnumbered years.
Prerequisite: MAT 224.
Credits: 1

MAT 331 Abstract Algebra I
A first course in higher abstract mathematics. Emphasis is placed on writing proofs. Topics include groups and rings. Offered spring semesters.
Prerequisite: MAT 223.
Credits: 1

MAT 332 Abstract Algebra II
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. Offered irregularly.
Prerequisite: MAT 331.
Credits: 1

MAT 333 Introduction to Functions of a Real Variable I
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 singlevariable calculus. Offered fall semester.
Prerequisite: MAT 223. It is recommended that students take MAT 331 before MAT 333.
Credits: 1

MAT 334 Introduction to Functions of a Real Variable II
A continuation of MAT 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. Offered irregularly.
Prerequisite: MAT 333.
Credits: 1

MAT 337 Introduction to Numerical Analysis
(CSC 337)
This course will address topics such as numerical solution of nonlinear equations in one variable, interpolation, approximation, differentiation, integration, difference equations, differential equations and their applications, boundary value problems, linear systems, matrices, and optimization. Offered fall semesters of evennumbered years.
Prerequisites: CSC 111 and MAT 223.
Credits: 1

MAT 338 Topics in Computational Mathematics
(CSC 338)
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. Offered fall semesters of oddnumbered years.
Prerequisite: CSC 111. Some topics may have additional prerequisites.
Credits: 1

MAT 341 Topology
A study of elementary topology. Topics discussed will include topologies, separation axioms, connectedness, compactness, continuity, and metric spaces. Offered spring semesters of evennumbered years.
Prerequisite: MAT 223.
Credits: 1

MAT 344 Complex Analysis
Analytic functions, mapping of elementary functions, integrals, residue theory, conformal mapping. Offered spring semesters of oddnumbered years.
Prerequisite: MAT 223.
Credits: 1

MAT 353 Probability Models II
This course is a continuation of MAT 253 (Probability Models). Topics include survival functions, hazard functions, order statistics, continuous and discrete distributions not considered in MAT 253 and mixed random variables. We will look at a wide variety of probability problems associated with insurance. Offered fall semesters.
Prerequisite: MAT 253.
Credits: 1/2

MAT 354 Mathematical Statistics
This course takes a more theoretical look at estimation and hypothesis testing than MAT 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. Offered spring semesters irregularly.
Prerequisites: MAT 253 and MAT 254.
Credits: 1/2

MAT 355 Regression Models
This course takes a matrixbased 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. Offered spring semesters.
Prerequisites: MAT 223, MAT 253, and MAT 254.
Credits: 1/2

MAT 377 Special Topics in Mathematics
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. Offered irregularly.
Prerequisite: Specific to topic, if any.
Credits: 1 or 1/2

MAT 387 Independent Study
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.
Prerequisites: Permission of the instructor and department chair.
Credits: 1 or 1/2

MAT 388 Independent Study
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.
Prerequisites: Permission of the instructor and department chair.
Credits: 1 or 1/2

MAT 400 Seminar
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. Offered irregularly.
Prerequisite: None.
Credits: 1/2
