## Mathematics (MAT)

Course meets General Education Aims Curriculum Requirement(s) in specified area(s).

## MAT 111 – Mathematics for Liberal Arts 4cr

This course is a survey of mathematics that may be from a historical, philosophical, computational, and/or aesthetic point of view. The faculty member teaching this course chooses topics from his or her fields of expertise and interests. Students may study topics including: history and philosophy of mathematics, systems of numeration, logic, mathematical modeling, space-time and the Theory of Relativity, probability, problem solving, logarithms and musical scales, mathematics in art, non-Euclidean geometry, fractals, cryptography, and mathematical puzzles.

Aim 8 Mathematical Reasoning

Prerequisites: Sufficient score on the math placement exam.

## MAT 141 – Statistics 4cr

This course is an introductory course in descriptive and inferential statistics. Students explore methods of collecting and displaying data, perform statistical inference, carry out statistical studies, and use graphing calculators and statistical software. Examples will cross disciplines and focus on normal distributions, Chi Square procedures, and Analysis of Variance (ANOVA).

Aim 8 Mathematical Reasoning

Prerequisites: Sufficient score on the math placement exam.

## MAT 150 – Precalculus 4cr

This course is a continuation of the standard High School Algebra sequence. It provides the background in basic functions necessary for MAT 241 Calculus I and for applications in the sciences, environmental studies, and finance. Students will master linear and quadratic functions and investigate general polynomial, rational, inverse, exponential, logarithmic, and trigonometric functions. Graphing calculators, DERIVE, and MAPLE, are employed to explore functions and complete computations.

Aim 8 Mathematical Reasoning

Prerequisites: Sufficient score on the math placement exam.

## MAT 151 – Precalculus I: Algebraic Functions 2cr

This course is a continuation of the standard high school algebra sequence. It provides background in some of the basic functions necessary to study MAT 241 Calculus I and for applications in the sciences, environmental studies, and finance. Students will investigate linear, quadratic, general polynomial, and rational functions.

Partially satisfies Aim 8 Mathematical Reasoning

Prerequisite: Sufficient score on the math placement exam.

## MAT 152 – Precalculus II: Transcendental Functions 2cr

This course is a continuation of MAT 151 Precalculus I. It provides background in more of the basic functions necessary to study MAT 241 Calculus I and for applications in the sciences, environmental studies, and finance. Students will investigate exponential, logarithmic, and trigonometric functions.

Partially satisfies Aim 8 Mathematical Reasoning

Prerequisites: MAT 151 Precalculus I: Algebraic Functions or sufficient score on the math placement exam.

## MAT 201 – Computer Science I 4cr

This is an introductory course emphasizing the fundamental concepts of modern programming from an object-oriented perspective. The object-oriented paradigm will be explored using the Java programming language (standard edition). Topics will include programming basics, data types, control structures, methods, classes and objects, arrays, and an introduction to graphical user interfaces. There will be significant emphasis on the methodical development of proper (Java) syntax as well as discussions on abstract computer programming concepts.

Prerequisites: Sufficient score on the mathematics placement exam.

## MAT 202 – Computer Science II 4cr

This course is a continuation of MAT 201; this is a second course in object-oriented programming using the Java programming language (standard edition). Topics will include a further study of classes and objects, inheritance, polymorphism, exceptions, file I/O, threads, and a continuation of the implementation of graphical user interfaces. This course will also provide an introduction to the Java Micro Edition through the use of Sun SPOTS (Small Programmable Object Technology) and the interaction between programs and other languages/applications such as (X)HTML, PHP and MySQL.

Prerequisite: MAT 201 Computer Science I or equivalent.

## MAT 241 – Calculus I 4cr

This course is an introduction to the mathematics of rates of change. Students explore limits, investigate the concept of the derivative, master differentiation techniques, apply the first and second derivatives to the graphing of functions, related rates problems, and maxima and minima problems, and glimpse an introduction to integration. Graphing calculators, DERIVE, and MAPLE may be used extensively to explore and reinforce the material.

Aim 8 Mathematical Reasoning

Prerequisite: MAT 150 Precalculus; or both MAT 151 Precalculus I: Algebraic Functions and MAT 152 Precalculus II: Transcendental Functions; or sufficient score on the math placement exam.

## MAT 242 – Calculus II 4cr

This course builds on the concepts and skills developed in Mat 241 Calculus I. Students master integration techniques, apply integration to area and volume problems, explore numerical integration, manipulate sequences and series, and employ Taylor’s Theorem to approximate transcendental functions. Graphing calculators, DERIVE, and MAPLE may be used extensively to explore and reinforce the material.

Aim 8 Mathematical Reasoning

Prerequisite: MAT 241 Calculus I or equivalent.

## MAT 243 – Multivariable Calculus 4cr

This course is an introduction to the calculus of functions in more than one variable. Students explore topics including vector algebra, lines and planes, partial derivatives, the gradient, graphing in three dimensions, multiple integrals, vector integral calculus, and Stokes’ and Divergence Theorems. Graphing calculators, DERIVE, and MAPLE may be used extensively to explore and reinforce the material.

Prerequisite: MAT 242 Calculus II or equivalent.

## MAT 250 – Linear Algebra 4cr

This course is an introduction to solving linear systems of equations, matrix algebra, and abstract vector spaces. Students explore methods of solving linear systems of equations including Gaussian elimination, matrix algebra, geometry in three-dimensional Euclidean space, and general vector spaces and master the concepts of linear independence, eigenvalues, and eigenvectors and their applications. Graphing calculators, DERIVE, and MAPLE may be used extensively to explore and reinforce the material.

Prerequisite: MAT 242 Calculus II or equivalent.

## MAT 251 – Differential Equations 4cr

This course is an introduction to the theory of differential equations–the methods and theory of solving them. Students will learn to classify differential equations by type, to consider uniqueness and existence properties, and to employ analytic methods for solving first-order and second-order differential equations. Students explore series solutions, matrix methods, Laplace transforms, and numerical methods on computer and calculator to solve differential equations and applications. Graphing calculators, DERIVE, and MAPLE may be used extensively to explore and reinforce the material.

Prerequisite: MAT 242 Calculus II or equivalent.

## MAT 253 – Statistics for Natural Sciences 4cr

This course is designed to introduce students in the natural sciences to descriptive and inferential statistics. Students investigate and produce data, design experiments, summarize data graphically and numerically, and analyze data using confidence intervals and testing hypotheses. They master reading and comprehending statistics, distinguishing and evaluating the validity of different statistical testing techniques, and using appropriate statistical technology. Students may not receive credit for both this course and MAT 141 Statistics.

Aim 8 Mathematical Reasoning

Prerequisites: Sufficient score on the math placement exam. Sophomore standing and a major/minor in Biology, Chemistry, Environmental Studies, or Math (or consent of instructor).

## MAT 288 – Mathematical Rigor 4cr

This course is designed for students desiring to pursue mathematical knowledge beyond Calculus. Students learn the language of mathematics through a study of logic and proof techniques. Students learn the culture of mathematics by reading and critiquing published, peer-reviewed, undergraduate, research papers. Students learn how to use various mathematical software packages such as Maple, Geogebra, and SAS. They also learn how to create mathematical documents using a mark-up language such as Latex.

Prerequisite: MAT 242 Calculus II or equivalent (may be taken concurrently).

## MAT 303 – Data Structures 4cr

In this course, object-oriented programming in Java is used to develop, understand, and program more complex algorithms and data structures: lists, sorting and searching, linked lists, recursion, stacks, queues, trees, hash tables, heaps, graphs, memory management, and accessing files.

Prerequisite: MAT 202 Computer Science II or permission of instructor.

## MAT 304 – Computer Organization 4cr

This course introduces principles of computer organization: levels of computer organization, digital logic, microprocessing, machine language, assembly language, operating system processes, memory, interrupts, addressing, controls, paging, tasking, and linkage.

Prerequisite: MAT 202 Computer Science II or permission of instructor.

## MAT 310 – Abstract Algebra 4cr

This course is an introduction to abstract mathematical structures, principally groups, and rings. Students investigate axiomatic and abstract structures by exploring elementary group, ring, and field theory. They examine the properties of Symmetry Groups, Permutation Groups, and subgroups of the Real Numbers, homomorphisms, and isomorphisms and refine proof-writing and proof reading skills.

Prerequisites: MAT 242 Calculus II and MAT 288 Mathematical Rigor.

## MAT 320 – Geometry 4cr

This course is an introduction to modern geometries, specifically Euclidean geometry, Riemannian geometry, and hyperbolic geometry. Students investigate the geometric properties of the plane, sphere, cylinder, cone, and hyperbolic plane and write mathematical arguments and proofs based on these investigations. Additionally, students complete a research paper and a written and oral presentation of a proof from Euclid’s The Elements. The software package Geometer’s Sketchpad and other appropriate technologies may be used to explore and reinforce the material.

Prerequisites: MAT 242 Calculus II and MAT 288 Mathematical Rigor.

## MAT 330 – Mathematical Modeling 4cr

This course is designed to focus on the application of mathematical techniques to real world problems. The course content varies depending on instructor and student interest. Students may explore difference equations, Markov Processes and basic probability theory, probability and modeling random phenomena, dynamical systems, fractals, game theory, or mathematical methods in the physical sciences.

Prerequisites: MAT 242 Calculus II and MAT 288 Mathematical Rigor.

## MAT 331 – Complex Analysis 4cr

This course is an introduction to both the rigor and the applications of the complex numbers. Students explore the topology and the algebraic structure of the complex number system, differentiation and integration of complex-valued functions, power series and Laurent series, Cauchy’s theorem, and the residue calculus.

Prerequisites: MAT 242 Calculus II and MAT 288 Mathematical Rigor.

## MAT 341 – History and Philosophy of Mathematics 4cr

This course is a seminar designed to survey the central ideas in the history and philosophy of mathematics. Students consider mathematics as a human intellectual endeavor inspired by and impacting our culture, history, and philosophy. They explore the history and philosophy of mathematics by studying original proofs of great mathematical theorems, reading and discussing advanced mathematical results in their historical contexts, analyzing mathematical creative thought, rigor, and abstraction by studying mathematical thought from the Greek civilization through the twentieth century, and writing a research paper on a philosophical school and preparing a presentation on a recognized great theorem.

Prerequisites: MAT 242 Calculus II and MAT 288 Mathematical Rigor.

## MAT 366 – Number Theory 4cr

This course is an introduction to both the classical and modern questions about numbers. Students explore the integers, examining issues such as primes, divisibility, congruences, primitive roots, quadratic residues, and quadratic reciprocity. They master a variety of number theoretic techniques and computations and apply these in applications such as cryptography and coding theory.

Prerequisites: MAT 242 Calculus II and MAT 288 Mathematical Rigor.

## MAT 380 – Discrete Mathematics 4cr

In this course, topics include sets, propositional and predicate calculus, recursive definitions, and recurrence relations, combinatorial techniques, partially ordered sets, graphs, trees, Boolean algebra, and algebraic systems.

Prerequisites: MAT 242 Calculus II and MAT 288 Mathematical Rigor.

## MAT 388 – Pre-Thesis Research Seminar 2cr

This course is designed for students preparing to embark upon study for a senior thesis in mathematics (see MAT 489 Senior Thesis). Students read mathematical journal articles and present the material to the class. Students investigate several topics and, in conference with the professor, choose a particular topic for advanced study. Students complete sufficient background study to develop a cohesive plan for future research. A synopsis of this study together with a written research proposal is submitted to the mathematics faculty for approval.

Prerequisites: MAT 242 Calculus II and MAT 288 Mathematical Rigor. Junior standing is recommended.

## MAT 400 – Real Analysis 4cr

This course is a theoretical exploration of the topology and calculus of the real number system. Students examine the real numbers as a linear vector space equipped with a norm; specifically the concepts of open and closed sets, limits, compactness, connectedness, continuity, metric spaces, and continuity of functions on metric spaces.

Prerequisites: MAT 242 Calculus II, MAT 288 Mathematical Rigor, and permission of the instructor.

## MAT 489 – Senior Thesis 2cr

This course is designed as the culminating course for students completing a major in mathematics. Students complete the research approved in MAT 388 Pre-Thesis Research Seminar, submit written reports in the form of a thesis to the mathematics faculty for approval, and present their work in a public on-campus seminar.

Prerequisite: MAT 388 Pre-Thesis Research Seminar.

Course meets General Education Aims Curriculum Requirement(s) in specified area(s).