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| ADMISSIONS | BURSAR | FINANCIAL AID | GRADUATE SCHOOL | RESIDENTIAL LIFE | STUDENT ADMINISTRATION | UNDERGRADUATE CATALOG | |
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Mathematics (MATH)Head of Department: Professor Michael Neumann For major requirements, see the College of Liberal Arts and Sciences section of this Catalog. 1010. Basic Algebra with Applications (101) Either semester. Three credits. Not open to students who have passed any Q-course. Strongly recommended as preparation for Q-courses for students with a weak algebra background. This course does not count toward the minimum credit requirement for graduation. Polynomials, exponents, Cartesian coordinate system, linear and quadratic equations, inequalities. 1011Q. Introductory College Algebra and Mathematical Modeling (104Q) Both semesters. Three credits. Five class periods. Not open for credit to students who have passed MATH 1010, or any Q course. Strongly recommended as preparation for Q courses for students whose high school algebra needs reinforcement. The course emphasizes two components necessary for success in 1000-level courses which employ mathematics. The first component consists of basic algebraic notions and their manipulations. The second component consists of the practice of solving multi-step problems from other disciplines, called mathematical modeling. The topics include: lines, systems of equations, polynomials, rational expressions, exponential and logarithmic functions. Students will engage in group projects in mathematical modeling. (102Q) Either semester. Three credits. Recommended preparation: MATH 1010, 1011 or the equivalent. Not eligible for course credit by examination. Not open for credit to students who have passed any mathematics course other than MATH 1010, 1011, 1030, 1040, 1050, 1060 or 1070. 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. 1030Q. Elementary Discrete Mathematics (103Q) Either semester. Three credits. Recommended preparation: MATH 1010, 1011 or the equivalent. Not open for credit to students who have passed any mathematics course other than MATH 1010, 1011, 1020, 1040, 1050, 1060 or 1070. Problem solving strategies, solutions of simultaneous linear equations, sequences, counting and probability, graph theory, deductive reasoning, the axiomatic method and finite geometries, number systems. 1040Q. Elementary Mathematical Modeling (107Q) Either semester. Three credits. Recommended preparation: MATH 1010, 1011 or the equivalent. Not open to students who have passed any mathematics course other than MATH 1010, 1011, 1020, 1030, 1050, or 1070. This course and MATH 1060 cannot both be taken for credit. This course should not be considered as adequate preparation for MATH 1071, 1120, 1131, or 1151. Use of algebraic and trigonometric functions with technology to analyze quantitative relationships and illustrate the role of mathematics in modern life; graphical numerical and symbolic methods. Most sections require a graphing calculator; some require work with a computer spreadsheet. 1050QC. Mathematical Modeling in the Environment (108QC) Either semester. Three credits. Recommended preparation: MATH 1010, 1011 or the equivalent. 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. CA 3. (109Q) Either semester. Three credits. Recommended preparation: MATH 1010, 1011 or the equivalent. Not open for credit to students who have passed MATH 1120, 1131, or 120. Students may not receive credit for this course and MATH 1040. Preparation for calculus. Review of algebra. Functions and their applications; in particular, polynomials, rational functions, exponentials, logarithms, and the trigonometric functions. 1070Q. Mathematics for Business and Economics (105Q) Either semester. Three credits. Recommended preparation: MATH 1010, 1011 or the equivalent. Linear equations and inequalities, exponents and logarithms, matrices and determinants, linear programming. Applications. 1071Q. Calculus for Business and Economics (106Q) Either semester. Three credits. (One credit for students who have passed MATH 1121, 1131, 120, or 1151. ) Recommended preparation: MATH 1010, 1011 or the equivalent and MATH 1070. Not open for credit to students who have passed MATH 1110. Derivatives and integrals of algebraic, exponential and logarithmic functions. Functions of several variables. Applications. 1110Q. A Survey of Calculus with Applications I (118Q) Either semester. Three credits. Recommended preparation: MATH 1010, 1011 or the equivalent. Not open for credit to students who have passed MATH 1071, 1121, 1131, or 120, or 1151. Derivatives and integrals of elementary functions including the exponential and logarithm functions; applications include optimization, marginal functions, exponential growth and decay, compound interest. 1120Q. Introductory Calculus 1 (112Q) Either semester. Four credits. Four class periods. Recommended preparation: MATH 1010, 1011 or the equivalent. Students cannot receive credit for MATH 1120 and either MATH 1131, 120, or 1151. Students who have not passed the Calculus Placement Survey take this course rather than MATH 1131 or 120. Limits, derivatives, and extreme values of algebraic functions, with supporting algebraic topics. 1121Q. Introductory Calculus 2 (113Q) Either semester. Four credits. Four class periods. Prerequisite: MATH 1120. Recommended preparation: A grade of C- or better in MATH 1120. Students cannot receive credit for MATH 1121 and either MATH 1131, 120, or 1151. May be used in place of MATH 1131 or 120 to fulfill any requirement satisfied by MATH 1131 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. 1122Q. Introductory Calculus 3 (114Q) Either semester. Four credits. Four class periods. Prerequisite: MATH 1121. Recommended preparation: A grade of C- or better in MATH 1121. Note: MATH 1131 is not adequate preparation for MATH 1122. Not open for credit to students who have passed MATH 1132, 121, or 1152. The transcendental functions, formal integration, polar coordinates, infinite sequences and series, lines and planes in three dimensions, vector algebra. (115Q or QC) Either semester. Four credits. Four class periods. Prerequisite: Passing score on the Calculus Placement Survey. Students cannot receive credit for MATH 1131 and either MATH 1120, 1121, 120, or 1151. Suitable for students with some prior calculus experience. May be used in place of MATH 1120, 120, or 1151 to fulfill any requirement satisfied by MATH 1120, 120, or 1151. Limits, continuity, differentiation, antidifferentiation, definite integrals, with applications to the physical and engineering sciences. Sections with QC credit integrate computer-laboratory activity. (116Q or QC) Either semester. Four credits. Four class periods. Prerequisite: MATH 1121, 1131, or 1151, 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). Recommended preparation: A grade of C- or better in MATH 1121 and 1131. Not open to students who have passed MATH 1122, 121, or 1152. Substitutes for MATH 1122 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 QC credit integrate computer-laboratory activity. (135Q) (Formerly offered as MATH 120Q.) First semester. Four credits. Prerequisite: Passing score on the Calculus Placement Survey. Students cannot receive credit for MATH 1151 and either MATH 1121, 1131, or 120. May be used in place of MATH 1131 to fulfill any requirement satisfied by MATH 1131. The subject matter of MATH 1131 in greater depth, with emphasis on the underlying mathematical concepts. (136Q) (Formerly offered as MATH 121Q.) Both semesters. Four credits. Prerequisite: MATH 1151 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. Students cannot receive credit for MATH 1152 and either MATH 1122, 1132, or 121. May be used in place of MATH 1132 to fulfill any requirement satisfied by MATH 1132. The subject matter of MATH 1132 in greater depth, with emphasis on the underlying mathematical concepts. (193) Either or both semesters. Credits and hours by arrangement. May be repeated for credit (to a maximum of 15 for MATH 1793 and 3793 together). Consent of the Department Head or Undergraduate Coordinator required, normally before the student's departure. (195Q) Either semester. Credits, prerequisites, and hours as determined by the Senate Curricula and Courses Committee. Recommended preparation: MATH 1010 or equivalent. May be repeated for credit with a change in topic. 2010Q-2011Q. Fundamentals of Algebra and Geometry (247Q-248Q) Either semester. Three credits each semester. Prerequisite: PSYC 1100 and three credits of Mathematics other than MATH 1010. Not open for credit to students who have passed MATH 2110, 2410, 220, 2130, or 2143. 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. (210Q) Either semester. Four credits. Four class periods. Prerequisite: MATH 1132 or 1152 or a score of 4 or 5 on the Advanced Placement Calculus BC exam. Recommended preparation: A grade of C- or better in MATH 1132. Not open for credit to students who have passed MATH 220 or 2130 or 2143. Two- and three-dimensional vector algebra, calculus of functions of several variables, vector differential calculus, line and surface integrals. 2130Q. Honors Multivariable Calculus (230Q) (Formerly offered as MATH 220Q.) Both semesters. Four credits. Prerequisite: MATH 1152 or advanced placement credit for one year of calculus (a score of 4 or 5 on the Calculus BC examination) or consent of instructor. Not open to students who have passed MATH 2110 or 2143. May be used in place of MATH 2110 to fulfill any requirement satisfied by MATH 2110. The subject matter of MATH 2110 in greater depth, with emphasis on the underlying mathematical concepts. 2141Q-2142Q. Advanced Calculus I, II (243Q-244Q) Both semesters. 4 credits each semester. May be taken for honors credit but open to any qualified student. Prerequisite: A year of calculus (that may include high school) and instructor consent. MATH 2141Q may be used in place of MATH 1131 or 1151 to fulfill any requirement satisfied by MATH 1131 or 1151. MATH 2142Q may be used in place of MATH 1132 or 1152 to fulfill any requirement satisfied by MATH 1132 or 1152. A rigorous treatment of the mathematics underlying the main results of one-variable calculus. Intended for students with strong interest and ability in mathematics who are already familiar with the computational aspects of basic calculus. 2143Q-2144Q. Advanced Calculus III, IV (245Q-246Q) Both semesters. 4 credits each semester. May be taken for honors credit but open to any qualified student. Prerequisite: MATH 2142Q or consent of instructor. MATH 2143 may be used in place of MATH 2110 to fulfill any requirement satisfied by MATH 2110. MATH 2144 may be used in place of MATH 2410 to fulfill any requirement satisfied by MATH 2410. A rigorous treatment of more advanced topics, including vector spaces and their application to multivariable calculus and first-order, second-order and systems of differential equations. (202W) Either semester. One credit. Corequisite: MATH 2110. Prerequisite: ENGL 1010 or 1011 or 3800. Weekly seminars and short essays reflecting on the learning experiences and content of MATH 2110. (227Q) Either semester. Three credits. Prerequisite: MATH 1132, 1152, or 2142. Recommended preparation: A grade of C- or better in MATH 1132. Not open for credit to students who have passed MATH 2144 or 3210. 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. (223Q) Either semester. Three credits. Prerequisite: MATH 1121, 1131, 1151, or 2142. MATH 1121 may be taken concurrently. Deductive reasoning and the axiomatic method, Euclidean geometry, parallelism, hyperbolic and other non-Euclidean geometries, geometric transformations. 2410Q. Elementary Differential Equations (211Q) Either semester. Three credits. Prerequisite: MATH 1132, 1152 or 2142. Recommended preparation: A grade of C- or better in MATH 1132; and MATH 2110, 220 or 2130. Not open for credit to students who have passed MATH 2144 or 2420. Introduction to ordinary differential equations and their applications, linear differential equations, systems of first order linear equations, numerical methods. 2420Q. Honors Differential Equations (221Q) Either semester. Three credits. Prerequisite: MATH 1152 or instructor consent. Not open to students who have passed MATH 2144 or 2410. MATH 2420 satisfies any requirement met by MATH 2410, and provides superior preparation for prospective mathematics, science, and engineering majors. The subject matter of MATH 2410 in greater depth, with emphasis on the underlying mathematical concepts. 2610. Introduction to Actuarial Science (236) Both semesters. Three credits. Prerequisite: Consent of instructor. An introduction to actuarial science, covering many of the topics in the first Foundations of Actuarial Practice module, Role of the Actuary, of the Society of Actuaries. Topics include: what an actuary is and does; external forces that influence actuarial work; and the framework and processes actuaries use to perform actuarial work using Microsoft Excel. (285) (Also offered as MATH 5620.) First semester. Three credits. Prerequisite: MATH 1132, 1152, or 2142. Fundamental concepts of financial mathematics, with applications in calculating present and accumulated values for various streams of cash flows as a basis for future use in: reserving, valuation, pricing, duration calculation, asset/liability management, investment income, capital budgeting and valuing contingent cash flows. 2710. Transition to Advanced Mathematics (213) Either semester. Three credits. Prerequisite: MATH 2110 or 2130. Students intending to major in mathematics should ordinarily take this course 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. (242W) Either semester, alternate years. Three credits. Prerequisite: Either (i) MATH 2110 or 2130, and 2410, or (ii) 2144 or 2420;and ENGL 1010 or 1011 or 3800. 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. (200) Either semester. Two credits. Prerequisite: Either MATH 2110, 2130, or 2143; and either MATH 2144, 2410, or 2420; ENGL 1010 or 1011 or 3800. The student will attend talks during the semester, and choose a mathematical topic from one of them to investigate in detail. The student will write a well-revised, comprehensive paper on this topic, including a literature review, description of technical details, and a summary and discussion. 2794W. Undergraduate Seminar II (201W) Either semester. Two credits. Prerequisite: MATH 2784; ENGL 1010 or 1011 or 3800. The student will attend talks during the semester, and choose a mathematical topic from one of them to investigate in detail. The student will write a well-revised, comprehensive paper on this topic, including a literature review, description of technical details, and a summary and discussion, building upon the writing experience in MATH 2784. (297) Either semester. Three credits. Open only with consent of instructor. This course, with a change of topic, may be repeated for credit. 3146. Introduction to Complex Variables (252) (Also offered as MATH 5046.) Either semester. Three credits. Prerequisite: MATH 2110 and 2410, or 2144 or 2420. Not open for credit to students who have passed MATH 5046. Functions of a complex variable, integration in the complex plane, conformal mappings. (273-274) Either semester. Three credits each semester. Prerequisite: MATH 2144 or 2410 or 2420; MATH 2142 or 2710. Introduction to the theory of functions of one and several real variables. (231) Either semester. Three credits. Prerequisite: MATH 2110, 2130 or 2143 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. 3170. Elementary Stochastic Processes (232) (Also offered as STAT 3965.) Either semester. Three credits. Prerequisite: STAT 3025 or 3345 or 3375 or MATH 3160. 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. (215) ither semester. Alternate years. Three credits. Prerequisite: MATH 2144 or 2210; and MATH 2710. Vector spaces and linear transformations over fields. (216) Either semester. Three credits. Prerequisite: MATH 2142 or 2710. Recommended preparation: MATH 2144 or 2210. The fundamental topics of modern algebra including elementary number theory, groups, rings, polynomials and fields. (217) Either semester. Three credits. Prerequisite: MATH 3230. Recommended preparation: MATH 3210. Topics from ring theory, Galois theory, linear and multilinear algebra, or algebraic geometry. 3240. Introduction to Number Theory (258) Either semester, alternate years. Three credits. Prerequisite: MATH 2142 or 2710. Euclid's algorithm, modular arithmetic, Diophantine equations, analogies between integers and polynomials, and quadratic reciprocity, with emphasis on developing both conjectures and their proofs. (251) Either semester. Three credits. Prerequisite: MATH 2142 or 2710. Analysis of combinatorial problems and solution methods. Topics include: Enumeration, generating functions, bijective proofs, sieve methods, recurrence relations, graphs, partially ordered sets, and extremal combinatorics. 3260. Introduction to Mathematical Logic (235) Either semester, alternate years. Three credits. Prerequisite: MATH 2142 or 2710 or CSE 207. PHIL 2211 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. (237) Either semester, alternate years. Three credits. Prerequisite: MATH 2142 or 2710 or CSE 2500. 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. (250) Either semester, alternate years. Three credits. Prerequisite: MATH 2142 or 2710. Metric spaces, topological spaces and functions, topological properties, surfaces, elementary topics in geometric topology. (225) Either semester, alternate years. Three credits. Prerequisite: Either (i) MATH 2110 or 2130, and 2410, and MATH 2142 or 2710, or (ii) MATH 2144. The in-depth study of curves and surfaces in space. 3410. Differential Equations for Applications (272) Either semester. Three credits. Prerequisite: MATH 2110 and 2410, or 2144 or 2420. Not open for credit to students who have passed MATH 3412. Series solutions of differential equations, Bessel functions, Fourier series, partial differential equations and boundary value problems, nonlinear differential equations. 3412. Introduction to Field Theory (279) Either semester. Three credits. Prerequisite: Either (i) MATH 2110 or 2130, and 2410 or 2420 or (ii) MATH 2144. Not open for credit to students who have passed MATH 3410. 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. (277) (Also offered as Mathematics 5430.) Either semester. Three credits. Prerequisite: MATH 3410. Offered in alternate years. Not open for credit to students who have passed MATH 5430. Convergence of Fourier Series, Legendre and Hermite polynomials, existence and uniqueness theorems, two point boundary value problems, and Green's functions. 3435. Partial Differential Equations (278) (Also offered as Mathematics 5435.) Either semester, alternate years. Three credits. Prerequisite: MATH 3410 or its equivalent. Not open for credit to students who have passed MATH 5435. Solution of first and second order partial differential equations with applications to engineering and the sciences. (281) Either semester. Three credits. Prerequisite: Either (i) MATH 2110 or 2130, 2410, and either 2210 or 3210 or (ii) MATH 2144; 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. (282) Either semester. Three credits. Prerequisite: MATH 3510. Approximate integration, difference equations, solution of ordinary and partial differential equations. (283) Either semester. One credit. Two class periods. Prerequisite: MATH 2110, 2130 or 2143; and MATH 3160. Preparation through problem solving for the probability actuarial examination, which tests a student's knowledge of the fundamental probability tools for quantitatively assessing risk. Recommended prior knowledge: a thorough command of probability, as well as basic concepts in insurance and risk management. 3615. Financial Mathematics Problems (280) Both semesters. One credit. Two class periods. Prerequisite: MATH 2620 and 3660, which may be taken concurrently. Preparation for the financial mathematics actuarial examinaton, which tests a student's knowledge of the theory of interest and financial economies at an introductory level. (238) First semester. Three credits. Prerequisite: MATH 3160 and STAT 3375. Regression and time series applied to actuarial science. Covers the learning objectives established by the Society of Actuaries for Validation by Educational Experience in Applied Statistics. (287) (Also offered as MATH 5630.) First semester. Four credits. Prerequisite: MATH 3160 or STAT 3375; and MATH 2620. MATH 3630 is not open to students who have passed MATH 5630. Provides the theoretical basis of actuarial models and the application of those models to insurance and other financial risks. The concept of “model” in an actuarial context, how and why models are used, their advantages and their limitations. Extracting important results from models for the purpose of making business decisions, and approaches to determining these results. 3631. Actuarial Mathematics II (288) (Also offered as MATH 5631.) Second semester. Four credits. Prerequisite: MATH 3630. MATH 3631 is not open to students who have passed MATH 5631. A continuation of Actuarial Mathematics I. This course, along with MATH 3630, helps students prepare for the actuarial examination on models for quantifying risk . (276) Either semester. Three credits. Prerequisite: MATH 3160 or STAT 3025 or 3375; and MATH 2620. Introduction to the design of computerized simulations for analyzing and interpreting actuarial and financial problems. This course, together with MATH 392, 393, and 395, helps the student prepare for the actuarial examination on the construction and evaluation of risk models. 3650. Financial Mathematics II (289) Either semester. Three credits. Prerequisite: MATH 2620 and ACCT 2001, which may be taken concurrently. Not open for credit to students who have passed MATH 5621. The continuation of MATH 2620. Measurement of financial risk, the mathematics of capital budgeting, mathematical analysis of financial decisions and capital structure, and option pricing theory. 3660. Advanced Financial Mathematics (284) Either semester. Three credits. Prerequisite: MATH 2620 and 3160. Advanced topics in financial mathematics such as single period, multi-period and continuous time financial models; Black-Scholes formula; interest rate models; and immunization theory. 3670W. Technical Writing for Actuaries (291W) Second semester. Three credits. Prerequisite: ENGL 1010 or 1011 or 3800. Consent of Director of Actuarial Science required. Students will write a technical report on an advanced topic in actuarial science. 3710. Introduction to Mathematical Modeling (204) Either semester. Three credits. Prerequisite: MATH 2144 or 2420; or MATH 2210 and 2410. Knowledge of a programming language is strongly recommended. Not open for credit to students who have passed MATH 5530 or 5540, CHEM 305, or PHYS 5350. 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. (290) 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. Students taking this course will be assigned a final grade of S (satisfactory) or U (unsatisfactory). (293) Either or both semesters. Credit and hours by arrangement. May be repeated for credit (to a maximum of 15 for MATH 1793 and 3793 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. (296) Either semester. One credit. One class period. Prerequisite: MATH 1122, 1132, or 1152. 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. (298) Either semester. Credits and hours by arrangement. With a change in content, may be repeated for credit. Prerequisites and recommended preparation vary. 3796W. Senior Thesis in Mathematics (292W) Either semester. Three credits.Prerequisite: ENGL 1010 or 1011 or 3800. 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. (295) Either semester. Three credits. With a change in topic, may be repeated for credit. Prerequisites and recommended preparation vary. (299) 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. 4110. Introduction to Modern Analysis (261) (Also offered as MATH 5110.) First semester. Three credits. Prerequisite: Consent of instructor. Not open for credit to students who have passed MATH 5510. Metric spaces, sequences and series, continuity, differentiation, the Riemann-Stieltjes integral, functions of several variables. 4210. Advanced Abstract Algebra (265) (Also offered as MATH 5210.) First semester. Three credits. Prerequisite: Consent of instructor. Not open for credit to students who have passed MATH 5210. Group theory, ring theory and modules, and universal mapping properties. 4310. Introduction to Geometry and Topology (267) (Also offered as MATH 5310.) First semester. Three credits. Prerequisite: Consent of instructor. Not open for credit to students who have passed MATH 5310. Topological spaces, connectedness, compactness, separation axioms, Tychonoff theorem, compact-open topology, fundamental group, covering spaces, simplicial complexes, differentiable manifolds, homology theory and the De Rham theory, intrinsic Riemannian geometry of surfaces. 4735. Introduction to Operations Research (286) Also offered as STAT 4535 and STAT 5535.) Either semester. Three credits. Prerequisite: MATH 3160 or STAT 3025 or 3375. Not open for credit to students who have passed MATH 5635, STAT 4535 or 5535. 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.
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