2018-2019 Undergraduate Academic Catalog

Mathematics (MATH) MATH-1700 4 hours Calculus and Dynamical Systems for the Life Sciences –Fa, Sp An introductory calculus and dynamical systems course for majors in the life sciences. Discrete and continuous dynamical systems, limits and derivatives, including derivatives of trigonometric, exponential, logarithmic and inverse trigonometric functions, applications of derivatives and dynamical systems, including related rates and optimization, differential equations, integrals - both definite and indefinite - and their applications, and possibly analysis of autonomous differential equations. Prerequisite: GMTH-1030 Precalculus or equivalent; or permission of instructor. MATH-1710 Calculus I –Fa, Sp 5 hours First course of a two-course sequence covering basic concepts of analytic geometry and single variable calculus. Includes limits and single variable calculus. Includes limits and derivatives of algebraic and transcendental functions, applications of the derivative, single variable integration, including the Fundamental Theorem of Calculus and integration by substitution, and applications of integration, including solving differential equations and finding volumes of revolution. Prerequisite: GMTH-1030 Precalculus or equivalent; or permission of instructor. MATH-1720 Calculus II –Fa, Sp 5 hours The second course of a two-course sequence covering the basic concepts of analytic geometry and single variable calculus. Includes techniques of integration such as integration by parts, trigonometric substitution and partial fractions, improper integrals and L’Hopital’s rule, sequences, series, expansion of functions into Taylor and power series, conic sections, plane curves, calculus of parametric equations and polar coordinates, vectors and geometry in three-space, vector-valued functions and curvature. Prerequisite: MATH-1710 Calculus I or equivalent or permission of instructor. MATH-1880 Topics in Calculus –Fa, Sp, Su 1–3 hours This course is for students who are attempting to transfer credit for MATH-1710 or MATH-1720 Calculus I and II when those transferred courses lack some of the topics contained in MATH- 1710 or MATH-1720. It requires full participation in a MATH-1710 or MATH-1720 course during the sections in which the student’s transferred course is found to be deficient or in a stand-alone course offered during Summer School I. Prerequisite: GMTH-1030 Precalculus or equivalent; permission of instructor. Corequisite: partial transfer credit for MATH-1710 and/or MATH-1720 or approved transient credit for a Calculus I or II course that will provide less than full credit for MATH-1710 or MATH 1720. MATH-1990 3 hours Beautiful Math Structures and Thinking –Fa This course introduces freshmen math majors to interesting mathematical ideas and applications beyond the usual scope of standard math courses. Topics include an introduction to propositional logic, function theory, and infinite sets. Other topics will be chosen from elementary number theory, modular arithmetic, error-correcting codes, Fibonacci numbers and the golden ratio, fractals, discrete dynamical systems and chaos, Euler and Hamilton Circuits, democracy and impossibility theorems, game theory, the Platonic solids, n-dimensional space, and other topics up to the discretion of the instructor. MATH-2210 Logic and Methods of Proof –Fa 3 hours Introduction to formal mathematical logic; emphasis on preparing students for the abstraction of upper-division courses. Special attention is given to the development of students’ skills with a variety of methods of proof, using examples from numerous areas. Prerequisites: MATH-1720 Calculus II; MATH- 1990 Beautiful Math Structures and Thinking; or permission of instructor. MATH-2510 Discrete Math for Computer Science –Sp 3 hours An introduction to mathematical foundations of computer science, including propositional and predicate calculus, methods of proof, sets and relations, recurrences, graphs and trees, and program correctness and proofs. This course does not satisfy any requirements for the B.A. or B.S. in mathematics or the B.A. in integrated mathematics education. Prerequisite: MATH-1710 Calculus I. MATH-2520 3 hours Discrete Math and Probability Principles for Computer Science –Sp An introduction to mathematical foundations of computer science, including propositional and predicate calculus, methods of proof, sets and relations, recurrences, program correctness and proofs, probability models, random variables, probability distributions, estimation, and hypothesis testing. This course does not satisfy any requirements for the B.A. or B.S. in mathematics or the B.A. in integrated mathematics education Prerequisites: MATH-1720 Calculus II; EGCP-1010 Digital Logic Design. MATH-2710 Calculus III –Fa, Sp 3 hours Introduction to differential and integral calculus of several variables, multiple integrals, vector analysis, line integrals, and surface integrals. Prerequisite: MATH-1720 Calculus II or equivalent or permission of instructor. MATH-2740 Differential Equations –Fa, Sp 3 hours Study of the standard techniques employed in the solution of differential equations with emphasis on those arising from physical problems. Prerequisite: MATH-1720 Calculus II or equivalent. MATH-2800 LaTeX for Technical Documents –Sp 1 hour In this course students will be introduced to the typesetting language of LaTeX through the use of tutorials, example documents, and homework assignments. They will learn to easily prepare professional-looking theses, conference papers, and journal papers. They will also learn how to create professional- looking presentations, homework, quizzes, examinations, syllabi, resumés, and curriculum vitae. MATH-3050 4 hours Algebraic Structures for Secondary Education Majors –Fa An introduction to the basic ideas of number theory, abstract algebra, and linear algebra. Factorization of integers, congruence modulo m, Fermat’s Theorem, groups, rings, integral domains, fields, vector spaces, systems of linear equations, determinants and inverses, linear transformations, eigenvalues, and eigenvectors. Does not count toward B.A. or B.S. majors in mathematics. Prerequisites: MATH-2210 Logic and Methods of Proof. (even years) MATH-3110 Probability and Statistics –Sp 3 hours Probability models, random variables, probability distributions, estimation, and hypothesis tests are studied from theoretical and practical viewpoints. Prerequisite: MATH-1720 Calculus II. MATH-3120 Theory of Probability –Sp 3 hours Topics include combinatorial analysis, axioms of probability, conditional probability, independent events, Bayes’ Formula, random variables, expected value, variance, discrete distributions, continuous distributions, joint distributions, the Law of Large Numbers, and the Central Limit Theorem. Prerequisites: MATH- 2710 Calculus III; MATH-2210 Logic and Methods of Proof MATH-3240 Introduction to Operations Research –Fa 3 hours Formulation and analysis of mathematical models for the optimal solution of decision making problems under certainty. Course content includes linear programming; the simplex method, duality and sensitivity analysis. This course applies probabilistic analysis to such nondeterministic models as queueing models, elements of dynamic programming, and Markov decision analysis. Prerequisites: MATH-3610 Linear Algebra; or permission of the instructor. (even years) 2017–18 Undergraduate Academic Catalog Page 297 Course Descriptions MATH-1700 – MATH-3240 SCIENCE AND MATHEMATICS