# Mathematics Course Descriptions

**MAT 003 Pre-calculus**

This course is intended solely for those students who wish to take calculus, but whose preparation makes a refresher course in pre-calculus advisable. Topics covered include a review of algebra (solving equations and inequalities, simplification of algebraic expressions) and properties of elementary functions (polynomial, rational, exponential, logarithmic, and trigonometric functions) with special emphasis on graphing these functions. MAT 003 cannot be used for any distribution credit or any area of concentration. (For students who desire a distribution credit in mathematics but do not wish to take calculus, MAT 103, 104, 106, and 108 are recommended.) This course is offered in the fall semester.

*Prerequisite: Permission of the instructor.*

Credits: 0.5

**MAT 010 Pre-calculus with an Introduction to Calculus I**

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. MAT 010 cannot be used for any distribution credit or any area of concentration. (For students who desire a distribution credit in mathematics but do not wish to take calculus, MAT 103, 104, 106, and 108 are recommended.) This course is offered in the fall semester.

*Prerequisite: Permission of the instructor.*

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.

*Prerequisites: None.*

Credits: 1/2

Distribution: III. D. (Natural Science/Mathematics) and III.E. (Quantitative Skills)

**MAT 104 Statistics**

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. MAT 104 does not count toward the mathematics major or minor.

*Prerequisites: None. (MAT 103 is not a prerequisite for MAT 104)*

Credits: 1/2

Distribution: III. D. (Natural Science/Mathematics) and III.E. (Quantitative Skills)

**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.

*Prerequisites: None.*

Credits: 1

Distribution: III. D. (Natural Science/Mathematics) and III.E. (Quantitative Skills)

**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 MAT 108 and 219 for credit toward graduation. This course is offered in the fall semester.

*Prerequisites: None.*

Credits: 1

Distribution: III. D. (Natural Science/Mathematics) and III.E. (Quantitative Skills)

**MAT 110 Calculus I with Pre-calculus Review**

This course is intended solely for those students who took and passed MAT 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. This course is offered in the spring semester.

*Prerequisite: MAT 010** with a grade of C- or better**.*

Credits: 1

Distribution: III. D. (Natural Science/Mathematics) and III.E. (Quantitative Skills)

**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. It is recommended that students who take MAT 003 earn a grade of C- or better before taking MAT 111.

*Prerequisite: None. *

Credits: 1

Distribution: III. D. (Natural Science/Mathematics) and III.E. (Quantitative Skills)

**MAT 112 Calculus II **

A continuation of MAT 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.

*Prerequisites: MAT 110 or 111** with a grade of C- or better**, departmental placement examination, or AP examination. *

Credits: 1

Distribution: III. D. (Natural Science/Mathematics) and III.E. (Quantitative Skills)

**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 in the spring semester of even-numbered years.

Students may not present both MAT 108 and 219 for credit towards graduation.

*Prerequisite: MAT 223. *

Credits: 1

Distribution: III. D. (Natural Science/Mathematics) and III.E. (Quantitative Skills)

**MAT 221 Foundations of Geometry **

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

*Prerequisite: MAT 112. *

Credits: 1

Distribution: III. D. (Natural Science/Mathematics) and III.E. (Quantitative Skills)

**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. This course is offered in the spring semester of odd-numbered years.

*Prerequisite: MAT 112.*

Credits: 1

Distribution: III. D. (Natural Science/Mathematics) and III.E. (Quantitative Skills)

**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

Distribution: III. D. (Natural Science/Mathematics) and III.E. (Quantitative Skills)

**MAT 224 Elementary Differential Equations **

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: MAT 112 **with a grade of C- or better** and 223. *

Credits: 1

Distribution: III. D. (Natural Science/Mathematics) and III.E. (Quantitative Skills)

**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. This course is offered in the fall semester.

*Prerequisites: MAT 112** with a grade of C- or better** and 223. *

Credits: 1

Distribution: III. D. (Natural Science/Mathematics)

**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. This course is offered irregularly.

*Prerequisite: MAT 223. *

Credits: 1

Distribution: III. D. (Natural Science/Mathematics)

**MAT 251 Mathematical Finance**

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: MAT 112. *

Credits: 1/2

Distribution: III. D. (Natural Science/Mathematics) and III.E. (Quantitative Skills)

**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

Distribution: III. D. (Natural Science/Mathematics) and III.E. (Quantitative Skills)

**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, 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: MAT 112. *

Credits: 1/2

Distribution: III. D. (Natural Science/Mathematics) and III.E. (Quantitative Skills)

**MAT 254 Statistical Models**

This course gives an overview of confidence intervals, classical hypothesis testing procedures: z-tests, t-tests, F-tests, Chi-square tests, 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: MAT 112.*

Credits: 1/2

Distribution: III. D. (Natural Science/Mathematics) and III.E. (Quantitative Skills)

**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 in the fall semester of even-numbered years.

*Prerequisite: MAT 224. *

Credits: 1

Distribution: III. D. (Natural Science/Mathematics)

**MAT 323 Topics in Linear Algebra **

An in-depth study of some of the topics covered in MAT 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: MAT 223. *

Credits: 1

Distribution: III. D. (Natural Science/Mathematics)

**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. This course is offered in the fall semester of odd-numbered years.

*Prerequisite: MAT 224. *

Credits: 1

Distribution: III. D. (Natural Science/Mathematics)

**MAT 331 Abstract Algebra I **

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: MAT 223. *

Credits: 1

Distribution: III. D. (Natural Science/Mathematics)

**MAT 332 Abstract Algebra II **

A continuation of MAT 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: MAT 331. *

Credits: 1

Distribution: III. D. (Natural Science/Mathematics)

**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 single-variable calculus. This course is offered in the fall semester.

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

Credits: 1

Distribution: III. D. (Natural Science/Mathematics)

**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. This course is offered irregularly.

*Prerequisite: MAT 333. *

Credits: 1

Distribution: III. D. (Natural Science/Mathematics)

**MAT 337 Introduction to Numerical Analysis (CSC 337)**

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 in the fall semester of even-numbered years.

*Prerequisites: CSC 111 and MAT 223.*

Credits: 1

Distribution: III. D. (Natural Science/Mathematics)

**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. This course is offered in the fall semester of odd-numbered years.

*Prerequisite: CSC 111 and MAT 112. Some topics may have additional prerequisites.*

Credits: 1

Distribution: III. D. (Natural Science/Mathematics)

**MAT 341 Topology **

A study of elementary topology. Topics discussed will include topologies, separation axioms, connectedness, compactness, continuity, and metric spaces. This course is offered in the spring semester of even-numbered years.

*Prerequisite: MAT 223. *

Credits: 1

Distribution: III. D. (Natural Science/Mathematics)

**MAT 344 Complex Analysis **

Analytic functions, mapping of elementary functions, integrals, residue theory, conformal mapping. This course is offered in the spring semester of odd-numbered years.

*Prerequisite: MAT 223. *

Credits: 1

Distribution: III. D. (Natural Science/Mathematics)

**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, mixed random variables, Brownian motion and stochastic calculus. We will look at a wide variety of probability problems associated with insurance. This course is offered in the fall semester.

*Prerequisite*: MAT 253.

Credits: 1/2

Distribution: III. D. (Natural Science/Mathematics)

**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, likelihood ratio tests, most powerful tests, uniformly most powerful tests, and Bayesian statistics. This course is offered in the spring semester, irregularly.

*Prerequisites: MAT 253 and 254.*

Credits: 1/2 Distribution: III. D. (Natural Science/Mathematics)

**MAT 355 Regression Models**

This course takes a matrix-based look at regression (introduced in MAT 254, Statistical Models). We focus on the probabilistic reasoning behind regression, in particular the 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.

*Prerequisites: MAT 223, 253 and 254.*

Credits: 1/2

Distribution: III. D. (Natural Science/Mathematics)

**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. This course is offered irregularly.

*Prerequisites: Specific to topic, if any.*

Credits: 1 or 1/2

Distribution: III. D. (Natural Science/Mathematics)

**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

Distribution: III. D. (Natural Science/Mathematics)

**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

Distribution: III. D. (Natural Science/Mathematics)

**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. This course is offered irregularly.

*Prerequisites: None.*

Credits: 1/2

Distribution: III. D. (Natural Science/Mathematics)

**Computer Science Courses**

**CSC 101 Introduction to Computer Science **

An introduction to the field of computer science as the study of algorithmic process. Students will study the history of the field as well as issues currently confronting the computer science community including ethical issues raised by a rapidly changing technology. Students will learn fundamental concepts of computer science such as computer architecture, data representation, and the issues of computability. Students will engage in hands-on algorithm-building activities and some basic programming exercises. This course is offered in the spring semester. *Distribution in Natural Science and Mathematics or Quantitative Skills.*

*Prerequisites: None.*

Credits: 1

Distribution: III. D. (Natural Science/Mathematics) and III.E. (Quantitative Skills)

**CSC 111 Introduction to Programming**

An introduction to programming in a higher-level, general-purpose language (currently Java). Programming topics include primitive data types, simple data types such as arrays, program constructs such as conditionals, loops and procedures, in an object-oriented context. Applications are chosen from areas such as graphics, simulation, and file processing. This course is offered in the fall semester. *Distribution in Natural Science and Mathematics or Quantitative skills.* [WT1]

*Prerequisite: CSC 101 (With appropriate background and instructor permission, a student may possibly take CSC 111 without having taken CSC 101 first).*

Credits: 1

Distribution: III. D. (Natural Science/Mathematics) and III.E. (Quantitative Skills)

**CSC 112 Advanced Programming**

A variety of topics that are important in developing large-scale software. Object oriented programming in a language such as C++. Dynamic data structures such as lists, queues, and stacks. An introduction to a rigorous analysis of the efficiency of an algorithm. Advanced algorithms such as Quicksort, mergesort, and the use of hash tables. An introduction to using the Unix operating system and Unix tools for software development such as Make. This course is offered in the semester.

*Prerequisites: CSC 111 or equivalent programming background. *

Credits: 1

Distribution: III. D. (Natural Science/Mathematics)

**CSC 121 Introduction to Additional Programming Languages**

An introduction to one or more additional programming languages. Students will build on their previous knowledge of a programming language to learn one or more additional languages. Languages vary by semester but may include any programming paradigm. For a given semester the course content and other particulars will be announced before registration for that semester. This course may be taken multiple times, for credit for each different language.

*Prerequisite: CSC 111*

Credits: 1/2

Distribution: III. D. (Natural Science/Mathematics)

**CSC 211 Introduction to Data Structure**

An introduction to more advanced abstract data types such as lists; sets; trees, including balanced trees; and graphs. Algorithms for traversing, searching, determining connectivity, and so forth. An in-depth study of, and analysis of, the algorithms used to implement these structures. This course is offered in the spring semester.

*Prerequisite: CSC 111. *

Credits: 1

Distribution: III. D. (Natural Science/Mathematics)

**CSC 271 Special Topics in Computer Science**

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 registration for that semester. This course is offered irregularly.

*Prerequisites: CSC 111. Some topics may have additional prerequisites.*

Credits: 1/2 or 1

Distribution: III. D. (Natural Science/Mathematics)

**CSC 311 Introduction to Machine Organization**

A study of the various layers at which a machine can be studied, including higher-level languages, assembly language, machine language, and digital circuits. Data representation. A comparison of RISC and CISC architectures. Some programming in a representative assembly language. Issues of cross-language programming. This course is offered irregularly.

*Prerequisite: CSC 211 or concurrent enrollment. *

Credits: 1

Distribution: III. D. (Natural Science/Mathematics)

**CSC 321 Programming Languages**

A study of the paradigms of programming languages, including procedural languages such as Pascal or ‘C’, object-oriented languages such as C++ or Smalltalk, functional languages such as ML or Scheme, logic-oriented languages such as Prolog, and concurrency such as in Ada. Consideration of how concepts are implemented, such as modules, parameter passing, function evaluation, data types and type checking, memory management, exception handling, and threads. This course is offered irregularly.

*Prerequisite: CSC 121.*

Credits: 1

Distribution: III. D. (Natural Science/Mathematics)

**CSC 331 Analysis of Algorithms**

Advanced topics and problems in analyzing algorithms. Algorithms involving structures such as sequences, sets, and graphs, and topics such as geometric and numeric algorithms. An introduction to the question of P=NP and NP-Complete problems. Parallel algorithms. This course is offered irregularly.

*Prerequisites: CSC 211 and MAT 108 or 219. *

Credits: 1

Distribution: III. D. (Natural Science/Mathematics)

**CSC 337 Introduction to Numerical Analysis (MAT 337) **

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 in the fall semester of even-numbered years.

*Prerequisites: CSC 111 and MAT 223.*

Credits: 1

Distribution: III. D. (Natural Science/Mathematics)

**CSC 338 Topics in Computational Mathematics (MAT 338) **

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 in the fall semesters of odd-numbered years.

*Prerequisites: CSC 111 and MAT 112. Some topics may have additional prerequisites.*

Credits: 1

Distribution: III. D. (Natural Science/Mathematics)

**CSC 341 Introduction to Automata, Computability, and Formal Languages**

An introduction to theoretical computer science. Finite state machines and regular expressions. Context-free languages and push-down automata. Turing machines, effective computability, and the Halting Problem. This course is offered irregularly.

*Prerequisites: CSC 111 and MAT 108 or 219.*

Credits: 1

Distribution: III. D. (Natural Science/Mathematics)

**CSC 387 Independent Study**

Directed study on special topics for qualified students. May be repeated for credit.

*Prerequisites: Permission of the instructor and department chair.*

Credits: 1/2

Distribution: III. D. (Natural Science/Mathematics)

**CSC 388 Independent Study**

Directed study on special topics for qualified students. May be repeated for credit.

*Prerequisites: Permission of the instructor and department chair.*

Credits: 1/2

Distribution: III. D. (Natural Science/Mathematics)

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