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Undergraduate Studies Catalog

MATHEMATICS (MATH)

NOTES: (1) MATH 100, 117, and 118 are not part of the core curriculum. (2) A student who earns a grade below "C" in MATH 100, 117, 118, 131, 132, 161, 162, or 263 may not count such a course as a prerequisite for subsequent mathematical sciences courses.

099. Problem-Solving Methods in Mathematics. (0)
This non-credit math refresher course reviews those topics in arithmetic and basic algebra necessary for entrance to MATH 100. Topics include: percentages, decimals, fractions, basic algebraic operations, equations and inequalities, graphing, ratio and proportion, strategies for approaching word problems, applications to geometry, physics, and business. (Math 099 carries a tuition charge equivalent to one credit hour.)

100. Intermediate Algebra.
Prerequisite: Math Placement Test or MATH 099. Fundamentals of algebra. Graphs of linear equations, polynomials and factoring, first and second-degree equations and inequalities, radicals and exponents, and systems of equations. Word problems emphasized throughout the course.

108. Finite Mathematics.
Prerequisite: Math Placement Test or MATH 100.
An introduction to mathematical modeling. Topics chosen from linear programming, probability theory, Markov chains, scheduling problems, coding theory, social choice, voting theory, geometric concepts, game theory, graph theory, combinatorics, networks. Emphasis placed upon demonstrating the usefulness of mathematical models in other disciplines, especially the social sciences and business.

117. College Algebra.
Prerequisite: Math Placement Test or MATH 100.
Functions and their graphs, with emphasis on polynomials and rational functions. Complex numbers, synthetic division, binomial theorem, inverse functions, conic sections, the remainder and factor theorems, fundamental theorem of algebra. Word problems emphasized throughout the course.

118. Precalculus.
Prerequisite: Math Placement Test or MATH 117.
Exponential and logarithmic functions. Trigonometric functions, trigonometric identities and equations. Law of sines, law of cosines, area problems, and Heron’s formula. The complex plane and DeMoivre’s theorem. Vectors and parametric equations. Polar coordinates. Mathematical induction. Review of conic sections. Optimization problems. Gaussian elimination, partial fractions. Word problems emphasized throughout the course.

131. Elements of Calculus I.
Prerequisite: Math Placement Test or MATH 118.
An introduction to differenial and integral calculus, taught at the intuitive level, intended primarily for students in the life and social sciences, computer science, and business. Topics include: limits, continuity, differentiation, exponential growth and decay, integration, area, the fundamental theorem of calculus, chain-rule, curve-sketching including concavity, applied max/min problems. (Students may not receive credit for both MATH 131 and 161 without permission of the departmental chair.)

132. Elements of Calculus II.
Prerequisite: MATH 131.
A continuation of MATH 131. Topics include: properties of the integral, techniques of integration, numerical methods, improper integrals, applications to geometry, physics, economics, and probability theory, introduction to differential equations and mathematical modeling, systems of differential equations, and the Taylor series.

147. Mathematics for Teachers I. (CIEP 104)

148. Mathematics for Teachers II. (CIEP 105)

149. Introduction to Computer Science for Teachers. (COMP 120)

161. Calculus I. (4)
Prerequisite: Math Placement Test or Math 118.
A traditional introduction to differential and integral calculus. Functions, limits, continuity, differentiation, intermediate and mean-value theorems, curve sketching, optimization problems, related rates, definite and indefinite integrals, fundamental theorem of calculus, log and exponential functions. Applications to physics and other disciplines. (Students may not receive credit for both MATH 161 and MATH 131 without permission of the departmental chair.)

162. Calculus II. (4)
Prerequisite: MATH 161.
A continuation of MATH 161. Calculus of logarithmic, exponential, inverse trigonometric, and hyperbolic functions. Techniques of integration. Applications of integration to volume, surface area, arc length, center of mass, and work. Numerical sequences and series. Study of power series and the theory of convergence. Taylor’s theorem with remainder.

212. Linear Algebra.
Prerequisite: MATH 162 or 132.
An introduction to linear algebra in abstract vector spaces with particular emphasis on Rn. Topics include: Gaussian elimination, matrix algebra, linear independence, span, basis, linear transformations, determinants, eigenvalues, eigenvectors, and diagonalization. Some of the basic theorems will be proved rigorously; other results will be demonstrated informally. Software such as MAPLE may be utilized.

263. Multivariable Calculus. (5)
Prerequisite: MATH 162.
Vectors and vector algebra, vector-valued functions, functions of several variables, differential and integral calculus of functions of several variables, and advanced topics including change of variables in multiple integration, Green’s Theorem, the Divergence Theorem, and Stokes’ Theorem. Software such as MAPLE may be utilized.

264. Ordinary Differential Equations.
Prerequisite: MATH 263.
Techniques for solving linear and non-linear first and second-order differential equations, the theory of linear second-order equations with constant coefficients, power series solutions of second-order equation, and topics in systems of linear first-order differential equations. Software such as MAPLE may be utilized.

298. Mathematics Seminar. (2)
Prerequisite: MATH 162.
A sophomore-level seminar which may cover topics in number theory, logic, set theory, metric spaces, or history of mathematics.

304. Probability and Statistics I. (STAT 304)

305. Probability and Statistics II. (STAT 305)

306. Stochastic Processes. (STAT 306)

309. Numerical Methods. (COMP 309)
Prerequisites: COMP 170; MATH 212, 264.
Introduction to error analysis, numerical solution of equations, interpolation and approximation, numerical differentiation and integration, matrices and solution of systems of equations, numerical solution of ordinary and partial differential equations.

313. Abstract Algebra.
Prerequisite: MATH 212.
A rigorous introduction to the study of abstract algebraic systems with emphasis on the theory of groups. Equivalence relations, subgroups, homomorphisms, quotients, products, linear groups, permutation groups, and selected advanced topics.

314. Advanced Topics in Abstract Algebra.
Prerequisite: MATH 313.
Study of commutative and non-commutative rings, integral domains, and fields. Selected topics may include Galois theory, group representations, modules, and advanced group theory.

315. Advanced Topics in Linear Algebra.
Prerequisite: MATH 313.
An abstract approach to the study of vector spaces and transformations. Selected topics may include similarity, duality, canonical forms, inner products, bilinear forms, Hermitian and unitary spaces.

318. Combinatorics.
Prerequisite: MATH 162.
Induction, pigeon-hole principle, permutations, combinations, recurrence relations, generating functions, and inclusion-exclusion principle. Topics drawn from partitions, graph theory, graph coloring, and combinatorial design, Polya’s theory, Ramsey’s theorem, and optimization problems.

320. Mathematical Logic.
Prerequisite: MATH 313.
This course in modern mathematical logic begins with a study of propositional logic and leads to an examination of first-order predicate logic including quantifiers, models, syntax, semantics, and the completeness and compactness theorems. Additional topics include Gödel’s incompleteness theorems. Connections with abstract algebra and other areas of mathematics are explored.

322. Theory of Numbers.
Prerequisite: MATH 162.
An introduction to number theory including the Euclidean algorithm, congruences, Diophantine equations, quadratic residues, number-theoretic functions and the distribution of primes.

331. Cryptography. (COMP 331)

344. Projective Geometry.
Prerequisite: MATH 162.
Axiomatic systems which define geometries. Topics in synthetic and analytic projective geometry.

351. Introduction to Real Analysis I.
Prerequisites: MATH 212, 263.
A rigorous treatment of properties and applications of real numbers and real-valued functions of a real variable. Topics include: sequences, limits, the Bolzano-Weierstrass theorem, compactness and the Heine-Borel theorem, connectedness, topology, continuity, uniform continuity, fixed-point theorem, derivatives.

352. Introduction to Real Analysis II.
Prerequisite: MATH 351.
Continuation of 351. Differentiability and integrability on R1 and Rm. Topics such as Taylor’s theorem, the change of variable theorem, the inverse and implicit function theorems, and Lebesgue integration.

353. Introductory Complex Analysis.
Prerequisites: MATH 264, 351.
An introduction to the theory of functions of a complex variable. Topics include analytic functions, contour integrals, Cauchy integral formula, harmonic functions, Liouville’s theorem, Laurent series, residues and poles, and conformal mapping. Additional topics may include the Picard theorems, Rouché’s theorem, Schwarz-Christoffel transformations, and Riemann surfaces.

355. Methods of Applied Mathematics.
Prerequisite: MATH 264.
A wide spectrum of topics with applications to physics, engineering, economics, and the social sciences. Topics include Green’s functions and solutions to ordinary differential equations, integral equations, the calculus of variations and optimization, and partial differential equations.

358. Methods in Operations Research. (STAT 358)
Prerequisites: MATH 212 and STAT 203 or 335. An introduction to linear programming, integer and non-linear programming, queuing theory, and game theory. Emphasis will be placed upon mathematical modeling of problems in economics, business, finance, and the behavioral sciences.

386. Introduction to Topology.
Prerequisite: MATH 351.
Topological spaces, continuity, connectedness, path-connectedness, compactness, product spaces, Tychonoff’s theorem, and the Baire category theorem. Additional topics may include space-filling curves, quotient spaces, topological dimension, Hausdorff dimension, homotopy theory, and filters.

388. Special Topics in Mathematics. (1-3)
Advanced topics in mathematics, including analysis, topology, algebra, applied mathematics, and logic. Course title and content vary; prerequisites are established by the instructor. May be repeated for credit.

398. Independent Study. (1-3)
Prerequisite: permission of chair.
Independent study of selected topics in mathematics under the supervision of a faculty member. May be repeated for credit.

399H. Honors Tutorial. (1-3)
Prerequisite: permission of chair.
Independent study of selected topics in mathematics for students in the honors program. May be repeated for credit.

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