Undergraduate Catalog 2002 - 2003

Mathematics (MATH)

Head of Department: Professor Charles Vinsonhaler
Department Office: Room 102, Mathematical Sciences Building

Students must pass the Q-course Readiness Test or Mathematics 101 before taking any "Q" courses.
 

101. Basic Algebra with Applications Either semester. Three credits. This course does not meet distribution requirements or count toward the minimum credit requirement for graduation. Not open to students who have passed any Q-course.  Polynomials, exponents, Cartesian coordinate system, linear and quadratic equations, inequalities. This course is required of all students who fail the Q-course readiness exam.

102Q. Problem Solving Either semester. Three credits. Not eligible for course credit by examination. Not open for credit to students who have passed any mathematics course other than MATH 101, 103, 105, 107, 108 or 109. Vinsonhaler An introduction to the techniques used by mathematicians to solve problems. Skills such as Externalization (pictures and charts), Visualization (associated mental images), Simplification, Trial and Error, and Lateral Thinking learned through the study of mathematical problems. Problems drawn from combinatorics, probability, optimization, cryptology, graph theory, and fractals. Students will be encouraged to work cooperatively and to think independently.

103Q. Elementary Discrete Mathematics Either semester. Three credits. Not open for credit to students who have passed any MATH course other than MATH 101, 102, 105, 107, 108 or 109 Problem solving strategies, solutions of simultaneous linear equations, sequences, counting and probability, graph theory, deductive reasoning, the axiomatic method and finite geometries, number systems.

105Q. Mathematics for Business and Economics Either semester. Three credits.  Linear equations and inequalities, exponents and logarithms, matrices and determinants, linear programming. Applications.

106Q. Calculus for Business and Economics Either semester. Three credits. (One credit for students who have passed MATH 113, 115, or 120.) Recommended preparation: MATH 105. Not open for credit to students who have passed MATH 118.  Derivatives and integrals of algebraic, exponential and logarithmic functions. Functions of several variables. Applications.

108V. Mathematical Modeling in the Environment Either semester. Three credits. A solid background and good performance in high school algebra are highly recommended.  An interdisciplinary approach to environmental issues, such as: ground water contamination, air pollution, and hazardous materials handling. Emphasis on mathematical models, social and ethical implications, and physical and chemical principles. Includes a spread sheet program for water and air pollution data; a computer modeling package to analyze  hazardous materials emergencies; creative use of the internet and field research.

109Q. Algebra and Trigonometry Either semester. Three credits. Not open for credit to students who have passed MATH 107, 112, 115, or 120.  A review of algebra, simultaneous and quadratic equations, logarithms, the trigonometric functions, solution of triangles, trigonometric equations.

112Q. Introductory Calculus 1 Either semester. Four credits. Four class periods. Students cannot receive credit for MATH 112 and either MATH 115 or MATH 120. Students who have not passed the Calculus Readiness Test take this course rather than MATH 115 or MATH 120.  Limits, derivatives, and extreme values of algebraic functions, with supporting algebraic topics.

113Q. Introductory Calculus 2 Either semester. Four credits. Four class periods. Prerequisite: MATH 112. Students cannot receive credit for MATH 113 and either MATH 115 or MATH 120. May be used in place of MATH 107, 115, or 120 to fulfill any requirement satisfied by MATH 107, 115 or 120.  Limits, derivatives, and extreme values of trigonometric functions, with supporting trigonometric topics; anti-derivatives of algebraic and trigonometric functions; the definite integral and applications.

114Q. Introductory Calculus 3 Either semester. Four credits. Four class periods. Prerequisite: MATH 113. Note: MATH 115 is not adequate preparation for MATH 114. Not open for credit to students who have passed MATH 116 or 121. May be used in place of MATH 116 or 121 to fulfill any requirement satisfied by MATH 116 or 121.  The transcendental functions, formal integration, polar coordinates, infinite sequences and series, lines and planes in three dimensions, vector algebra.

115Q or V. Calculus I Either semester. Four credits. Four class periods. Prerequisite: Passing score on the Calculus Readiness Test, or the former MATH 107. Students cannot receive credit for MATH 115 and either MATH 112, MATH 113, or MATH 120. Suitable for students with some prior calculus experience. May be used in place of MATH 112 or 120 to fulfill any requirement satisfied by MATH 112 or 120.  Limits, continuity, differentiation, antidiffer-entiation, definite integrals, with applications to the physical and engineering sciences. Sections with V credit integrate computer-laboratory activity.

116Q or V. Calculus II Either semester. Four credits. Four class periods. Prerequisite: MATH 115 or 120, or advanced placement credit for calculus (a score of 4 or 5 on the Calculus AB exam or a score of 3 on the Calculus BC exam). Not open to students who have passed MATH 121. Substitutes for MATH 114 or 121 as a requirement.  Transcendental functions, formal integration, polar coordinates, infinite sequences and series, vector algebra and geometry, with applications to the physical sciences and engineering. Sections with V credit integrate computer-laboratory activity.

118Q. A Survey of Calculus with Applications I Either semester. Three credits. Not open for credit to students who have passed MATH 106, 113, 115, or 120.  Derivatives and integrals of elementary functions including the exponential and logarithm functions; applications include optimization, marginal functions, exponential growth and decay, compound interest.

120Q. Enhanced Calculus I Either semester. Four credits. Four class periods. Prerequisite: Passing score on the Calculus Readiness Test, or the former MATH 107. Students cannot receive credit for MATH 120 and either MATH 113 or 115. May be used in place of MATH 113 or 115 to fulfill any requirement satisfied by MATH 113 or 115. Intended to provide superior preparation for prospective mathematics, science and engineering majors. Recommended for those who have taken a semester of calculus in high school.  The subject matter of MATH 115 in greater depth, with emphasis on the underlying mathematical concepts.

121Q. Enhanced Calculus II Either semester. Four credits. Four class periods. Prerequisite: MATH 120 or advanced placement credit for calculus (a score of 4 or 5 on the calculus AB examination or a score of 3 on the Calculus BC examination) or consent of instructor. Not open for credit to students who have passed MATH 114 or 116. May be used in place of MATH 114 or 116 to fulfill any requirement satisfied by MATH 114 or 116. Intended to provide superior preparation for prospective mathematics, science and engineering majors. Recommended for those who have taken a semester of calculus in high school.  The subject matter of MATH 116 in greater depth, with emphasis on the underlying mathematical concepts.

193. Foreign Study Either or both semesters. Credits and hours by arrangement. May be repeated for credit (to a maximum of 15 for MATH 193 and 293 together). Consent of the Department Head or Undergraduate Coordinator required, normally before the student's departure.

204Q. Introduction to Mathematical Modeling Either semester. Three credits. Prerequisite: MATH 221; or MATH 211 and 227. Knowledge of a programming language is strongly recommended. Not open for credit to students who have passed MATH 304 or 305, CHEM 305, or PHYS 305.  Construction of mathematical models in the social, physical, life and management sciences. Linear programming, simplex algorithm, duality. Graphical and probabilistic modeling. Stochastic processes, Markov chains and matrices. Basic differential equations and modeling.

210Q. Multivariable Calculus Either semester. Four credits. Four class periods. Prerequisite: MATH 114, 116, or 121 or a score of 4 or 5 on the Advanced Placement Calculus BC exam. Not open for credit to students who have passed MATH 220. Open to sophomores.  Two- and three-dimensional vector algebra, calculus of functions of several variables, vector differential calculus, line and surface integrals.

211Q. Elementary Differential Equations Either semester. Three credits. Prerequisite: MATH 114, 116, or 121. Not open for credit to students who have passed MATH 221. Open to sophomores.  Introduction to ordinary differential equations and their applications, linear differential equations, systems of first order linear equations, numerical methods.

213Q. Transition to Advanced Mathematics Either semester. Three credits. Prerequisite: MATH 210 or 220 or consent of instructor. Open to sophomores. Not open for credit to students who have passed MATH 214 or CSE 254. Students intending to major in mathematics should ordinarily take this course or MATH 214 during the third or fourth semester.  Basic concepts, principles, and techniques of mathematical proof common to higher mathematics. Logic, set theory, counting principles, mathematical induction, relations, functions. Concepts from abstract algebra and analysis.

214Q. Introduction to Discrete Systems Either semester. Three credits. Prerequisite: CSE 111 or 130 or consent of the instructor. Open to sophomores. Not open for credit to students who have passed MATH 213 or CSE 254. Students who intend to major in mathematics should ordinarily take this course or MATH 213 during the third or fourth semester.  Mathematical methods for characterizing and analyzing discrete systems. Modern algebraic concepts, logic, set theory, grammars and formal languages, and graph theory. Applications to the analysis of computer systems and computational structures.

215Q. Linear Algebra Either semester. Three credits. (Two credits for students who have passed MATH 227.) Prerequisite: MATH 213 or 214.  Linear algebra and its applications; systems of equations, matrices, linear transformations, vector spaces, determinants, canonical forms, applications.

216Q. Abstract Algebra I Either semester. Three credits. Prerequisite: MATH 213 or 214. Recommended preparation: MATH 215 or 227.  The fundamental topics of modern algebra including elementary number theory, groups, rings, polynomials and fields.

217Q. Abstract Algebra II Either semester. Three credits. Prerequisite: MATH 216.  Topic chosen from modules, linear algebra, geometric algebra, extension fields, algebraic coding, algebraic combinatorics.

220Q. Enhanced Multivariable Calculus Either semester. Four credits. Prerequisite: MATH 114 or 116 or 121. Open to sophomores. Not open to students who have passed MATH 210. MATH 220 satisfies any requirement met by MATH 210, and provides superior preparation for prospective mathematics, science, and engineering majors.  The subject matter of MATH 210 in greater depth, with emphasis on the underlying mathematical concepts.

221Q. Enhanced Differential Equations Either semester. Three credits. Prerequisite: MATH 114 or 116 or 121. Open to sophomores. Not open to students who have passed MATH 211. MATH 221 satisfies any requirement met by MATH 211, and provides superior preparation for prospective mathematics, science, and engineering majors.  The subject matter of MATH 211 in greater depth, with emphasis on the underlying mathematical concepts.

223Q. Geometry Either semester. Three credits. Prerequisite: MATH 113 or 115 or 120. MATH 113 may be taken concurrently. Open to sophomores.  Deductive reasoning and the axiomatic method, Euclidean geometry, parallelism, hyperbolic and other non-Euclidean geometries, geometric transformations.

224Q. Projective Geometry Either semester. Three credits. Prerequisite: MATH 213Q.  Finite and infinite geometries as logical systems based on axioms. Synthetic and analytic projective geometry.

227Q. Applied Linear Algebra Either semester. Three credits. Prerequisite: MATH 114, 116, or 121. Not open for credit to students who have passed MATH 215. Open to sophomores.  Systems of equations, matrices, determinants, linear transformations on vector spaces, characteristic values and vectors, from a computational point of view. The course is an introduction to the techniques of linear algebra with elementary applications.

231Q. Probability Either semester. Three credits. Prerequisite: MATH 210 or 220, which may be taken concurrently with the consent of the instructor.  Introduction to the theory of probability. Discussion of some of the probability problems encountered in scientific and business fields.

232Q. Elementary Stochastic Processes (Also offered as STAT 235Q.) Either semester. Three credits. Prerequisite: STAT 220 or 224 or 230 or MATH 231. Not open for credit to students who have passed STAT 235Q.  Conditional distributions, discrete and continuous time Markov chains, limit theorems for Markov chains, random walks, Poisson processes, compound and marked Poisson processes, and Brownian motion. Selected applications from actuarial science, biology, engineering, or finance.

235Q. Introduction to Mathematical Logic Either semester, alternate years. Three credits. Prerequisite: MATH 213 or 214 or CSE 207. PHIL 211 is recommended.  Formalization of mathematical theories, elementary model theory with applications to algebra, number theory, and non-standard analysis. Additional topics: Elementary recursion theory and axiomatic set theory. Emphasis on the applications of logic to mathematics rather than the philosophical foundations of logic.

237Q. Theory of Computability Either semester, alternate years. Three credits. Prerequisite: MATH 213 or 214 or CSE 254.  Finite automata and regular languages, pushdown automata and context-free languages and grammars. Turing machines, recursively enumerable sets and grammars, Church's thesis, the halting problem, and other undecidable problems. Computational complexity and NP-completeness.

242W. History of Mathematics Either semester, alternate years. Three credits. Prerequisite: MATH 210 and 211, or 221. This course may not be counted in any of the major groups described in the Mathematics Departmental listing.  A historical study of the growth of the various fields of mathematics.

247Q-248Q. Fundamentals of Algebra and Geometry Either semester. Three credits each semester. Prerequisite: PSYC 132 and three credits of Mathematics other than MATH 101. Not open for credit to students who have passed MATH 210 or 211 or 220. This course may not be counted in any of the major groups described in the Mathematics Departmental listing.  The development of the number system with applications to elementary number theory and analytic geometry. This course is recommended for students in elementary education.

250Q. Elements of Topology Either semester, alternate years. Three credits. Prerequisite: MATH 213 or 214.  Metric spaces, topological spaces and functions, topological properties, surfaces, elementary topics in geometric topology.

252Q. Introduction to Complex Variables (Also offered as MATH 352.) Either semester. Three credits. Prerequisite: MATH 210 and 211, or 221. MATH 252Q not open for credit to students who have passed MATH 352.  Functions of a complex variable, integration in the complex plane, conformal mappings.

255Q. Principles of Computer Graphics Either semester. Three credits. Prerequisite: CSE 111 or 130C, MATH 227 or 215, MATH 210, and consent of instructor. Not open for credit to students who have passed CSE 275.  Representation of two- and three-dimensional data, internal representation of data structures, transformations, mapping of functions to graphics screen, graphics hardware. Programming projects assigned.

258Q. Introduction to Number Theory Either semester, alternate years. Three credits. Prerequisite: MATH 213 or 214.  Congruences, unique factorization, primitive roots, numerical functions, quadratic reciprocity and other selected topics, with emphasis on problem solving.

272Q. Differential Equations for Applications Either semester. Three credits. Prerequisite: MATH 210 and 211, or 221. Not open for credit to students who have passed MATH 279Q.  Series solutions of differential equations, Bessel functions, Fourier series, partial differential equations and boundary value problems, nonlinear differential equations.

273Q-274Q. Analysis Either semester. Three credits each semester. Prerequisite: MATH 213 or 214, and 211 or 221.  Introduction to the theory of functions of one and several real variables.

277Q. Applied Analysis (Also offered as Mathematics 377.) Either semester. Three credits. Prerequisite: MATH 272. Offered in alternate years. MATH 277Q not open for credit to students who have passed MATH 377.  Convergence of Fourier Series, Legendre and Hermite polynomials, existence and uniqueness theorems, two point boundary value problems, and Green's functions.

278Q. Partial Differential Equations (Also offered as Mathematics 378.) Either semester, alternate years. Three credits. Prerequisite: MATH 272 or its equivalent. MATH 278Q not open for credit to students who have passed MATH 378.  Solution of first and second order partial differential equations with applications to engineering and the sciences.

279Q. Introduction to Field Theory Either semester. Three credits. Prerequisite: MATH 210 and 211. Not open for credit to students who have passed MATH 272Q.  Vector analysis in rectangular, circular-cylindrical and spherical coordinates, postulational derivation of the partial differential equations of classical physics, Fourier series, Bessel and Legendre functions, solutions of Laplace, Poisson, diffusion and scalar and vector wave equations.

281Q. Numerical Analysis I Either semester. Three credits. Prerequisite: MATH 210Q, 211Q, and either 215Q or 227Q; and knowledge of at least one programming language.  Analysis of numerical methods associated with linear systems, eigenvalues, inverses of matrices, zeros of non-linear functions and polynomials. Roundoff error and computational speed.

282Q. Numerical Analysis II Either semester. Three credits. Prerequisite: MATH 281.  Approximate integration, difference equations, solution of ordinary and partial differential equations.

283Q. Calculus and Probability Problems Either semester. One or two credits. Hours by arrangement. Prerequisite: MATH 210 and 231.  Problems in calculus and probability designed to help students prepare for the first actuarial examination.

285Q. Financial Mathematics I (Also offered as MATH 365.) Either semester. Three credits. Prerequisite:MATH114, 116, or 121.  The mathematics of measurement of interest, accumulation and discount, present value, annuities, loans, bonds, and other securities.

286Q. Introduction to Operations Research (Also offered as STAT 286Q and STAT 356.) Either semester. Three credits. Prerequisite: MATH 231 or STAT 220 or 230. Not open for credit to students who have passed STAT 286 or 356.  Introduction to the use of mathematical and statistical techniques to solve a wide variety of organizational problems. Topics include linear programming, network analysis, queueing theory, decision analysis.

287Q-288Q. Actuarial Mathematics (Also offered as MATH 387-388.) Either semester. Three credits each semester. Prerequisite: MATH 231 or STAT 230; and MATH 285, which may be taken concurrently.  Survival distributions, claim frequency and severity distributions, life tables, life insurance, life annuities, net premiums, net premium reserves, multiple life functions, and multiple decrement models.

289. Financial Mathematics II Either semester. Three credits. Prerequisite: MATH 285. Also ACCT 131, which may be taken concurrently.  The continuation of MATH 285Q. Measurement of financial risk, the mathematics of capital budgeting, mathematical analysis of financial decisions and capital structure, and option pricing theory.

290. Field Study Internship Students taking this course will be assigned a final grade of S (satisfactory) or U (unsatisfactory). Either or both semesters. One to three credits. May be repeated for credit (to a maximum of 6 credits). Consent of the Department Head, Director of the Actuarial Program, or the Undergraduate Coordinator required. Prerequisite: Completion of Freshman - Sophomore level requisite courses in the major.

292W. Senior Thesis in Mathematics Either semester. Three credits. Open only by consent of Department Head or Departmental Honors Committee.  The student should define a general subject area for the thesis before choosing a thesis advisor and seeking consent at the time of registration. The student should submit a written proposal for the senior thesis to the advisor by the end of the semester preceding enrollment for thesis credit.

293. Foreign Study Either or both semesters. Credit and hours by arrangement. May be repeated for credit (to a maximum of 15 for MATH 193 and 293 together). Consent of the Department Head or Undergraduate Coordinator required, normally before the student's departure. May count toward the major with consent of the Advisor and either the Department Head or Undergraduate Coordinator.

295. Variable Topics Either semester. Three credits. With a change in topic, may be repeated for credit. Prerequisites and recommended preparation vary.

296. Problem Seminar Either semester. One credit. One class period. Prerequisite: MATH 114, 116, or 121. Open to sophomores. This course, with a change of topic, may be repeated for credit.  Problem sequences selected from algebra, geometry, calculus, combinatorics, and other branches of mathematics, designed to introduce mathematical concepts and to give experience in problem solving.

297. Undergraduate Seminar Either semester. Three credits. Open only with consent of instructor. This course, with a change of topic, may be repeated for credit.

298. Special Topics Either semester. Credits and hours by arrangement. With a change in content, may be repeated for credit. Prerequisites and recommended preparation vary.

299. Independent Study Either semester. Credits and hours by arrangement. Open only with consent of instructor. This course, with a change of topic, may be repeated for credit.