Warren Wilson College Catalog 07-08

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Courses in Mathematics and Computer Science (MAT)

MAT 111 Mathematics for Liberal Arts 4cr

An introductory investigation of mathematics from some of the following- points of view: historical, philosophical, computational, and aesthetic. Theory and applications will be explored as a means for understanding the world. Individual faculty members choose topics from his/her fields of expertise and interests. Such topics may include history and philosophy of mathematics, systems of numeration, logic, mathematical modeling, space-time and the Theory of Relativity, probability, logarithms and musical scales, mathematics in art, non-Euclidean geometry, fractals, cryptography, and mathematical puzzles. (Please consult the department chairperson or course instructor for a specific description of the topics to be presented each semester.) Upon successful completion of this course the student will have an enhanced knowledge of how math is used in society and appears in nature. The student will also gain proficiency in mathematical problem solving through extensive reading and writing of mathematics and mathematical explorations. A working knowledge of algebra and geometry is assumed.
Triad: Mathematics
Prerequisite: Two years of high school algebra and one year of high school geometry.

MAT 141 Statistics 4cr

The course teaches how to analyze data, design and carry out statistical studies, and understand/evaluate statistical studies in students' own fields of interest. Topics include graphical displays of data, probability distributions, correlation/regression, experimental design, and statistical inference. Statistical calculators and computer software are introduced and used extensively.
Triad: Mathematics
Prerequisite: Two years of high school algebra.

MAT 150 Precalculus 4cr

Students will explore functions as formulas, graphs, and lists of ordered pairs within a context. Students will explore linear, quadratic, polynomial, rational, exponential, logarithmic, and trigonometric functions. Graphing calculators are used extensively for exploration. This course can serve as preparation for MAT 241 Calculus I and provides a background in basic functions useful in applications to the sciences, environmental studies, and finance.
Prerequisite: Two years of high school algebra and one year of geometry.

MAT 201 Computer Science I 4cr

This introductory course emphasizes general programming principles. Topics include using Windows and the MS-DOS operating system, writing web pages with HTML, introduction to JavaScript, structured programming using the Java programming language: applets, data types, graphics, graphical user interfaces, decisions, loops, and arrays.
Triad: Mathematics
Prerequisites: Two years of high school algebra and one year of geometry.

MAT 202 Computer Science II 4cr

Continuation of MAT 201. Topics include Object Oriented Programming using the Java programming language: classes, objects, inheritance, string manipulation, exception handing, continuation of graphical user interfaces, layout managers, windows, free standing programs, file IO, threads. Together MAT 201, 202 provide basic competency in writing Java programs and authoring web pages.
Triad: Mathematics
Prerequisite: MAT 201 Computer Science I or equivalent.

MAT 241 Calculus I 4cr

Topics include limits, the concept of the derivative, differentiation techniques, using the first and second derivatives to graph functions, related rates, maxima and minima problems, calculus of exponential and logarithmic functions, and an introduction to integration. Graphing calculators are used extensively to explore and reinforce the mathematical ideas.
Triad: Mathematics
Prerequisite: MAT 150 Precalculus or equivalent.

MAT 242 Calculus II 4cr

Topics include applications of integration, numerical integration, calculus of trigonometric functions, introduction to functions of more than one variable, elementary differential equations and applications, t echniques of integration, sequences, series, Taylor's Theorem with remainder, and approximations of transcendental functions.
Triad: Mathematics
Prerequisite: MAT 241 Calculus I.

MAT 243 Multivariable Calculus 4cr

Topics include vector algebra, lines and planes, partial derivatives, the gradient, graphing in three dimensions, multiple integrals, vector integral calculus, and Stokes' and Divergence Theorems. Software is used to graph surfaces.
Triad: Mathematics
Prerequisite: MAT 242 Calculus II.

MAT 250 Linear Algebra 4cr

Topics include systems of linear equations, Gaussian elimination, matrix algebra, geometry in three-dimensional Euclidean space, vector spaces, linear independence, spanning, linear transformations, eigenvalues and eigenvectors, and diagonalization. Appropriate technology is employed.
Triad: Mathematics
Prerequisite: MAT 242 Calculus II.

MAT 251 Differential Equations 4cr

Topics include classification, uniqueness and existence properties, analytic methods for solving first-order and second-order differential equations, series solutions, matrix methods, Laplace transforms, and numerical methods on computer and calculator. Emphasis is on the development of techniques for solving differential equations arising in applications.
Triad: Mathematics
Prerequisite: MAT 242 Calculus II.

MAT 253 Statistics for Natural Sciences 4cr

This course is designed to introduce students in the natural sciences to descriptive and inferential statistics. Topics include investigating and producing data, experimental design, and statistical inference. Upon successful completion of this course the student will be able to summarize data graphically and numerically, to produce data using surveys, observational studies and experiments, and to analyze data using confidence intervals and testing hypotheses. The student will also become familiar with how to read and comprehend statistics, how to distinguish and evaluate the validity of different statistical testing techniques, and how to use appropriate statistical technology. Students may not receive credit for this course and MAT 141 Statistics.
Triad: Mathematics
Prerequisite: Sophomore standing and a major/minor in BIO, CHEM, ENVS, or MATH (or consent of advisor/instrucor.

MAT 289 Introduction to Mathematical Rigor 1cr

This course is designed for the student with a desire to pursue mathematical knowledge past Calculus. The student will learn the language of mathematics through logic and proof techniques in the context of calculus, geometry, number theory, and graph theory. The successful student will be prepared for the study of introductory abstract and theoretical mathematics.
Prerequisite: MAT 242 Calculus II.
Prerequisite: MAT 242 Calculus II.

MAT 290-298 Special Topics in Mathematics 2-4cr

In-depth consideration of a topic in Mathematics. May be repeated for credit under different topics.

MAT 299 Independent Study 1-4cr

MAT 303 Data Structures 4cr

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.
Triad: Mathematics
Prerequisite: MAT 202 Computer Science II.

MAT 304 Computer Organization 4cr

Principles of computer organization are introduced: levels of computer organization, digital logic, microprocessing, machine language, assembly language, operating system processes, memory, interrupts, addressing, controls, paging, tasking, and linkage.
Triad: Mathematics
Prerequisite: MAT 202 Computer Science II.

MAT 310 Abstract Algebra 4cr

Topics include axiomatic structures, elementary number theory, groups and group representations, applications of groups, symmetry groups, permutation groups, homomorphisms, isomorphisms, rings, and fields. The emphasis is on theorem proving.
Triad: Mathematics
Prerequisite: MAT 242 Calculus II and MAT 289 Introduction to Mathematical Rigor.

MAT 320 Geometry 4cr

Topics include axiomatic foundations of Euclidean geometry, Euclidean rigid motions, isometry theorems, the Fifth Parallel Postulate and non-Euclidean geometries, Riemannian geometry, and the philosophy and history of geometry. The software package Geometer's Sketchpad and other appropriate technologies are employed. Theorem proving is stressed. A research paper is assigned.
Triad: Mathematics or College Composition II.
Prerequisite: MAT 242 Calculus II and MAT 289 Introduction to Mathematical Rigor.

MAT 330 Mathematical Modeling 4cr

Topics vary depending on instructor and student interest. Course content from past offerings includes probability and modeling random phenomena, dynamical systems, fractals, discrete mathematics, game theory, and mathematical methods in the physical sciences.
Triad: Mathematics
Prerequisite: MAT 242 Calculus II and MAT 289 Introduction to Mathematical Rigor.

MAT 341 History and Philosophy of Mathematics 4cr

In this course the successful student will, in a seminar setting, explore the history and philosophy of mathematics by studying original proofs of great mathematical theorems; study and discuss advanced mathematical results in their historical context; develop an appreciation for the significance of these contributions; gain a broader understanding of mathematics; and analyze mathematical creative thought, rigor and abstraction by studying mathematical thought from the Greek civilization through the twentieth century.
Triad: Mathematics or College Composition II.


Prerequisite: MAT 242 Calculus II and MAT 289 Introduction to Mathematical Rigor.

MAT 366 Number Theory 4cr

The study of numbers dates back to the ancient Greek mathematicians. In this course, we will investigate both the classical and modern theory of numbers. In particular, we will explore the intergers, and examine issues such as primes, divisibility, congruences, primitive roots, quadratic residules, and quadratic reciprocity, while considering questions about them that are simple to understand, but can be quite difficult to answer. Upon successful completion of this course the student will have gained proficiency in the variety of number theoretic techniques and computations as well as become skilled in some applications such as cryptography and coding theory.
Triad: Mathematics.

MAT 380 Discrete Mathematics 4cr

Topics include sets, propositional and predicate calculus, recursive definitions, and recurrence relations, combinatorial techniques, partially ordered sets, graphs, trees, Boolean algebra, algebraic systems. or
Prerequisite: MAT 242 Calculus II and MAT 289 Introduction to Mathematical Rigor.

MAT 389 Pre-Thesis Research 1cr

This course is designed for the student preparing to embark upon study for a senior thesis in mathematics (see MAT 489). The student will investigate several topics of interest and, in conference with his/her mathematics advisor, choose a particular topic for advanced study. The successful student will complete sufficient background study to develop a cohesive plane for future research. A synopsis of this study together with a written research proposal will be submitted to the mathematics faculty for approval. Junior standing is recommended.
Prerequisite: MAT 242 Calculus II and MAT 289 Introduction to Mathematical Rigor.

MAT 400 Real Analysis 4cr

Topics include sets, construction of the real numbers, topology of the real line, open and closed sets, limits, compactness, connectedness, continuity, metric spaces, continuity of functions on metric spaces, pathological sets and functions.
Triad: Mathematics
Prerequisite: MAT 242 Calculus II.

MAT 489 Thesis 2cr

This course is designed as the culminating course for the student completing a major in mathematics. The successful student will complete the research approved in MAT 389, submit a written report in the form of a thesis to the mathematics faculty for approval, and present his/her work in a public on-campus seminar.
Prerequisite: MAT 242 Calculus II and MAT 289 Introduction to Mathematical Rigor.
Prerequisite: MAT 389 Pre-Thesis Research.

MAT 490-498 Special Topics in Mathematics 2-4cr

The department offers other courses in addition to the above, depending on instructor and student interest. These have included Complex Analysis, Numerical Analysis, Logical Foundations of Mathematics, Topology, and History and Philosophy of Mathematics.

MAT 499 Independent Study 1-4cr