Warren Wilson College Catalog 05-06

Go to the current College Catalog

Courses in Mathematics and Computer Science (MAT)

MAT 111 Mathematics for Liberal Arts 4cr

An introductory investigation of mathematics from historical, philosophical, computational and aesthetic points of view; 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

MAT 112 Mathematics of Form and Design 4cr

This introductory course approaches mathematical ideas from visual and conceptual points of view with numerous construction projects assigned. Topics include geometric constructions, Golden Mean, Fibonacci numbers, mosaics, symmetry, polyhedra, geodesic domes, sacred geometry, concepts of space and time, 3-D and 4-D geometry, fractals, randomness, and forms in nature.
Triad: Mathematics

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

Functions and their graphs: linear, quadratic, polynomial, rational, exponential, logarithmic, and trigonometric. The workshop method emphasizes interactive exploration. Graphing calculators are used extensively. Course can serve as preparation for MAT 241 Calculus I but also as a stand-alone providing grounding in basic functions useful in applications to the sciences, environmental studies, and finance.
Triad: Mathematics
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, techniques 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 * (2005-06)

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 * (2006-07)

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 * (2005-06)

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 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 250 Linear Algebra.

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.

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.

MAT 341 History and Philosophy of Mathematics 4cr **

This course includes history and philosophy of mathematics through the study of the original proofs of great mathematical theorems; discussion of mathematics in historical context; understanding the significance of mathematics; and analysis of mathematical creativity and abstraction from Greek times to the present.

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.
Triad: Mathematics
Prerequisite: MAT 242 Calculus II.

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 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