6. CR2 indicates that students may not receive credit for more than one of the courses including second-term topics 01:640: 136, 138, 152, 154, or 192.

7. CR3 indicates that students may not receive credit for more than one of the courses including third-term topics 01:640:251 or 291.

8. CR4 indicates that students may not receive credit for more than one of the fourth-term courses 01: 640:244, 252, or 292.

01:640:011Precalculus I Workshop (E2) Workshop to accompany 01:640:111. Corequisite: 01:640:111.

01:640:012Precalculus II Workshop (E2) Workshop to accompany 01:640:112. Corequisite: 01:640:112.

01:640:025Elementary Algebra (E3) Operations with polynomials, rational and square root expressions, exponents, solving linear and quadratic equations, basic applications�and graphing.

01:640:026Intermediate Algebra (E3) Absolute value equations and inequalities, radical expressions, rational exponents, quadratic equations and inequalities, introduction to functions, and topics in analytic geometry. Prerequisite: 01:640:025 or appropriate performance on the placement test in mathematics.

01:640:027Elements of Algebra (E3) Review of fundamentals of elementary and intermediate algebra. Exponents, polynomials, solution of linear and quadratic equations.�Focus on mathematical translation of verbal statements. Prerequisites: Acceptable performance on placement test and permission of department. Not for students preparing for calculus.

01:640:103Topics in Mathematics for the Liberal Arts (3) Topics emphasizing fundamental ideas of mathematics, selected from set theory, mathematical logic, game theory, number theory, algebra, and geometry. An elementary course for liberal arts majors. Prerequisite: 01:640:026 or 027 or appropriate performance on the placement test in mathematics. May not be used as an elective for the math major or minor.

01:640:104Elementary Combinatorics and Probability (3) Introduction to the basic concepts of combinatorial mathematics,�probability, and statistics. An elementary course for liberal arts majors. Prerequisite: 01:640:026 or appropriate performance on the placement test in mathematics. May not be used as an elective for the math major or minor.

01:640:105Introduction to Linear Mathematics (3) Systems of linear equations, matrices, linear algebra, and linear programming. An elementary course for liberal arts majors. Prerequisite: 01:640:026 or appropriate performance on the placement test in mathematics. May not be used as an elective for the math major or minor.

01:640:111-112Precalculus I,II (2,2) Math 111: Algebraic expressions, algebraic equations, inequalities, functions, and graphing. Math 112: Exponential, logarithmic, and trigonometric functions. Prerequisite: 01:640:026 or appropriate performance on the placement test in mathematics. Corequisites: 01:640:011 for 111; 01:640: 012 for 112. These two courses cover the same material as 01:640:115, but at a slower pace. Students may�not receive more than 4 normal credits for any combination of 01:640:111-112 �and 115.

01:640:115Precalculus College Mathematics (4) Algebraic expressions, algebraic equations, inequalities, functions, graphing. Exponential, logarithmic, and trigonometric functions. Prerequisite: 01:640:026 or appropriate performance on the placement test in mathematics. Students may not receive more than 4 normal credits for any combination of 01:640:111-112 and 115. Students who feel unprepared for this course (who have not had math for several years or whose mathematical background is weak) should consider taking 01:640:111-112, which covers the same material as 115 but at a slower pace and begins with an extensive review of intermediate algebra.

01:640:131Calculus I Practicum (1) Application of algorithms studied in 01:640:135 to problems. Corequisite: 01:640:135.

01:640:132Calculus II Practicum (1) Application of algorithms studied in 01:640:136 to problems. Corequisite: 01:640:136.

01:640:135-136Calculus I,II (4,4) Math 135: Analytic geometry, differential calculus with applications, logarithmic and exponential functions, introduction to the integral. Math 136: Continuation of Calculus I for students who do not intend to continue beyond 01:640:250. Survey of techniques and applications of calculus. Taylor series, differential equations, multivariate calculus. For liberal arts majors. Prerequisite for 135: 01:640: 112 or 115 or

01:640:138Calculus II for the Biological Sciences (4) Techniques of integration, elementary differential equations and their applications to biological sciences, and an introduction to linear algebra. For students who do not intend to continue beyond 01:640:250. For biological sciences majors. Prerequisite: CALC1. Credit restrictions: CR2.

01:640:151-152Calculus for Mathematical and Physical Math 151: Same topics as 01:640:135, with additional theory and numerical applications. Math 152: Techniques of integration, elementary differential equations, sequences, infinite series, Taylor series, parametric equations, polar coordinates. For mathematics, physics, computer science, statistics, chemistry, or engineering majors. Prerequisite for 151: 01:640: 112 or 115 or appropriate performance on the placement test in mathematics. Prerequisite for 152: CALC1. Credit restrictions: CR1, CR2.

01:640:153-154Intensive Calculus I,II (6,6) Math 153: Intensive study of analytic geometry, differential calculus of elementary functions, applications, and introductory integral calculus with emphasis on the analysis and solution of problems and on mathematical exposition. Math 154: Intensive study, techniques of integration, polar coordinates, and series, with emphasis on solution of problems and on mathematical exposition. For students satisfying the prerequisites for first-term calculus who are invited by the department. Credit restrictions: CR1, CR2.

01:640:157Calculus I for Mathematical and Physical Sciences Practicum (1) Application of algorithms studied in 01:640:151 to problems. Corequisite: 01:640:151.

01:640:158Calculus II for Mathematical and Physical Application of algorithms studied in 01:640:152 to problems. Corequisite: 01:640:152.

01:640:171Honors Introduction to Discrete Math (4) Introduction to the principal elementary problems, methods, and proof techniques of discrete mathematics. Prerequisite: Permission of department.

01:640:191-192Honors Calculus I,II (4,4) These courses cover the same material as 01:640: 151-152 but in a more thorough and demanding fashion. For students with a serious interest in mathematics. Credit restrictions: CR1, CR2. Grades of B or better are required to continue in the honors sequence.

01:640:195,196Seminar in Mathematics I,II (1,1) Discussion of selected topics in mathematics. For first- and second- year students. Prerequisite: Permission of department. Corequisite: Enrollment in a calculus course.

01:640:244Differential Equations for Engineering and Physics (4) First- and second-order ordinary differential equations; introduction to linear algebra and to systems of ordinary differential equations. Prerequisite: CALC3. Credit restriction: CR4.

01:640:250Introductory Linear Algebra (3) Systems of linear equations, Gaussian elimination, matrices and determinants, vectors in two- and three-dimensional Euclidean space, vector spaces, introduction to eigenvalues and eigenvectors. Possible additional topics: systems of linear inequalities and systems of differential equations. Prerequisite: CALC2 or 01:640:136 or 138.

01:640:251Multivariable Calculus (4) Analytic geometry of three dimensions, partial derivatives, optimization techniques, multiple integrals, vectors in Euclidean space, and vector analysis. Prerequisite: CALC2. Credit restriction: CR3.

01:640:252Elementary Differential Equations (3) First- and second-order ordinary differential equations; systems of ordinary differential equations. Prerequisites: 01:640:250 and CALC3. Credit restriction: CR4.

01:640:291-292Honors Calculus III,IV (4,4) Covers the same material as 01:640:251 and 252 in a more thorough and demanding fashion. Prerequisites: 01:640:191-192 or permission of department. Prerequisite for 292: 01:640:250. Credit restrictions: CR3, CR4. Grades of B or better are required to continue in the honors sequence.

01:640:293Honors Mathematics for the Physical Sciences I (4) Selected topics from linear algebra and ordinary differential equations with illustrations of their use in the physical sciences and engineering. Prerequisites: CALC3 and 01:750:227 or 272, or permission of department. Primarily for students majoring in the physical sciences or engineering. Credit not given for this course and 01: 640:244, 250, and 252.

01:640:300Introduction to Mathematical Reasoning (3) Fundamental abstract concepts common to all branches of mathematics. Special emphasis placed on ability to understand and construct rigorous proofs. Prerequisite: CALC2 or permission of department.

01:640:311Advanced Calculus I (4) Introduction to language and fundamental concepts of analysis. The real numbers, sequences, limits, continuity, differentiation in one variable. Prerequisites: CALC4 and 01:640:300 or permission of department.

01:640:312Advanced Calculus II (3) Series of numbers and functions, integration of functions of one variable, pointwise and uniform convergence, differential calculus in several variables, implicit and inverse function theorems. Prerequisite: 01:640:311.

01:640:321Introduction to Applied Mathematics (3) Mathematical models of mechanical vibrations, population dynamics, and traffic flow, involving ordinary differential equations�and nonlinear first-order partial differential equations. Prerequisite: CALC4.

01:640:336Differential Equations in Biology (3) Models for biological processes based on ordinary and partial differential equations. Topics selected from models of population growth, predator-prey dynamics, biological oscillators, reaction-diffusion systems, pattern formation, neuronal and blood flow physiology, neural networks, and biomechanics. Prerequisites: CALC4 and 01:640:250.

01:640:338Discrete and Probabilistic Models in Biology (3) Models for biological processes based on discrete mathematics (graphs, combinatorics), probabilistic and optimization methods, Markov chains and Markov fields, Monte-Carlo simulation, maximum-likelihood estimation, entropy, and information. Applications selected from epidemiology, inheritance and genetic drift, conbinatorics and sequence alignment of nucleic acids, energy optimization in protein structure prediction, and topology of biological molecules. Prerequisites: 01:640:250, 251, and either 01:640:477, 01:960:381, 01:198:206, 14:540:210, or 14:332:321. Only one of 01:640:338 and 339 may count for credit toward any math major or minor option.

01:640:339Mathematical Models in the Social Sciences (3) Introduction to the modeling process and survey of mathematical models from such areas as economics, sociology, psychology, and urban and policy science. Models dealing with energy use, air pollution, currency transfer, transportation, bargaining, voting, auctions, ecommerce, learning, and allocation of scarce resources. Models use graphs, signed graphs, Markov chains, n-person games, consensus functions, and differential equations. Prerequisites: 01:640:250 and either 01:640:477, 01: 198:206, or 01:960:381. Only one of 01:640:338 and 339 may count for credit toward any math major or minor option.

01:640:348Cryptography (3) Applications of algebra and number theory to cryptography (encryption/decryption) and cryptanalysis (attacking encrypted messages). Topics include congruences, finite fields, finding large primes, pseudoprimes, and primality testing, as well as the Vigenere and Hill ciphers, the Data Encryption Standard, probabilistic, and trapdoor attacks on encrypted messages, and public key ciphers. Prerequisites: 01:640:250; one of 01:640:300, 356, or 477, or permission of department.

01:640:350Linear Algebra (3) Continuation of 01:640:250. Abstract vector spaces and linear transformations, inner product spaces, diagonalization, and canonical forms. Possible additional topics: systems of ordinary differential equations and numerical techniques. Prerequisites: CALC4, 01:640:250, and 300, or permission of department.

01:640:351-352Introduction to Abstract Algebra I,II (4,3) Abstract algebraic systems, including groups, rings, fields, polynomials, and some Galois theory. Prerequisites: CALC3, 01:640:250, and 300, or permission of department.

01:640:354Linear Optimization (3) Linear programming problems, the simplex method, duality theory, sensitivity analysis, introduction to integer programming, the transportation problem, network flows, and other applications. Prerequisite: 01:640:250. Credit not given for both this course and 01:640:453 or 01:711:453.

01:640:355Game Theory (3) Introduction to two-person and n-person game theory, with applications to economics, politics, strategic studies, and other areas. Pure and mixed strategies, the minimax theorem, cooperative and noncooperative games, and bargaining models. Prerequisite: 01:640:354. Credit not given for both this course and 01:220:406.

01:640:356Theory of Numbers (3) Properties of the natural numbers, congruences, diophantine equations, and elementary arithmetical functions. Prerequisite: CALC3.

01:640:357Topics in Applied Algebra (3) Material relevant for various applications. Topics chosen from finite machines, languages, coding theory, Boolean algebras, graph theory, group-theoretic counting arguments, algebraic computational complexity. Prerequisites: CALC3 and 01:640:250.

01:640:361Set Theory (3) Introduction to set theory. The set-theoretic foundations of mathematics, including the construction of the real number system, countable and uncountable sets, cardinal numbers, and ordinals, the axiom of choice. Prerequisites: 01:640:300 and either 01:640:250 or CALC3, or permission of department.

01:640:373-374Numerical Analysis I,II (3,3) Analysis of numerical methods for the solution of linear and nonlinear equations, approximation of functions, numerical differentiation and integration, and the numerical solution of initial and boundary value problems for ordinary differential equations. Prerequisites: CALC4 and familiarity with a computer language. Credit not given for both these courses and 01:198:323,324.

01:640:393Honors Mathematics for the Physical Sciences II (4) The important partial differential equations of mathematical physics and an introduction to the theory of functions of a complex variable. Prerequisites: 01:640:293, or 250 and 252, or permission of department. Primarily for students majoring in the physical sciences or engineering. Credit not given for this course and 01: 640:403, 421, and 423.

01:640:395Studies in Mathematics (3) Topics vary from term to term. Details available at time of registration.

01:640:403Introductory Theory of Functions of a Complex Variable (3) First course in the theory of a complex variable. Cauchy's integral theorem and its applications. Taylor and Laurent expansions, singularities, conformal mapping. Prerequisite: CALC4.

01:640:411-412Mathematical Analysis I,II (3,3) Rigorous analysis of the differential and integral calculus of one and several variables. Prerequisites: Permission of department and instructor. For students preparing for graduate study in the mathematical sciences.

01:640:421Advanced Calculus for Engineering (3) Laplace transforms, numerical solution of ordinary differential equations, Fourier series, and separation of variables method applied to the linear partial differential equations of mathematical physics (heat, wave, and Laplace's equation). Primarily for mechanical engineering majors. Prerequisite: CALC4. Credit not given for both this course and 01:640:423.

01:640:423Elementary Partial Differential Equations (3) Linear partial differential equations of mathematical physics (heat, wave, and Laplace's equation), separation of variables, Fourier series. Prerequisite: CALC4. Credit not given for both this course and 01:640:421.

01:640:424Stochastic Models in Operations Research (3) Introduction to stochastic processes and their applications to problems in operations research: Poisson processes, birth-death processes, exponential models, continuous-time Markov chains, queuing theory, computer simulation of queuing models, and related topics in operations research. Prerequisites: CALC4 and 01:640:250 and 477.

01:640:426Topics in Applied Mathematics (3) Topics selected from integral transforms, calculus of variations, integral equations, Green's functions; applications to mathematical physics. Prerequisite: 01:640:421 or 423.

01:640:428Graph Theory (3) Colorability, connectedness, tournaments, eulerian and hamiltonian paths, orientability, and other topics from the theory of finite linear graphs, with an emphasis on applications chosen from social, biological, computer science, and physical problems. Prerequisites: CALC3 and 01:640:250.

01:640:429Industry-Oriented Mathematics: Case Studies (3) Introduces students to an actual industrial problem requiring mathematical techniques (including computer science and statistics) for its solution. Problem presented by an industry representative, who also discusses methodology; instructor covers relevant mathematical topics. Students expected to participate actively in discussion, research, bibliography search, and computer programming (if appropriate), and to prepare a detailed report describing the problem, approach, and conclusions. Prerequisites: Announced each year (including one or more of the following: CALC4, 01:640:250, 373, 477, 481); proficiency in computer programming.

01:640:432Introduction to Differential Geometry (3) Investigation of the properties of curves and surfaces using methods of analysis. Prerequisite: 01:640:311.

01:640:435Geometry (3) Various geometries, including projective and non-Euclidean geometries, and geometric axiom systems. Prerequisites: CALC3, 01:640:250, and 300, or permission of department.

01:640:436History of Mathematics (3) Selected topics from the history of mathematics including number systems; Euclidean geometry; the development of algebra in India, Arabia, and the West; and calculus. Prerequisites: 01:640:250, 251; recommended to be taken after Geometry (01:640:435).

01:640:441-442Introductory Topology I,II (3,3) Math 441: Introduction to topology with emphasis on the foundations of analysis; Euclidean spaces, metric spaces, topological spaces, and their properties; applications to analysis. Math 442: Basic concepts of algebraic topology, including the fundamental group, plane curves, homotopy, and a brief introduction to homology. Prerequisites: CALC4 and either 01:640:300 or permission of department.

01:640:451-452Abstract Algebra I,II (3,3) Rigorous study of abstract algebraic systems including groups, rings, and fields. Prerequisites: Permission of department and instructor. For students preparing for graduate study in the mathematical sciences.

01:640:453Theory of Linear Optimization (3) Emphasis on the theory of linear optimization. Topics include convex sets, polyhedra, Farkas lemma, canonical forms, simplex algorithm, duality theory, revised simplex method, primal-dual methods, complementary slackness theorem, maximal flows, transportation problems, 2-person game theory. Prerequisite: 01:640:250. Credit not given for both this course and 01:640:354 or 01:711:453.

01:640:454Combinatorics (3) Existence and enumeration of designs and patterns such as codes, graphs, and block designs, and extremal problems related to such objects. Emphasis on applications to computer, biological, physical, and social problems. Prerequisites: CALC2 and 01:640:250.

01:640:457-458Computational Methods in Abstract Algebra (1.5,1.5) Computer techniques for the study of particular algebraic objects such as finite groups, finitely generated abelian groups, and vector spaces over finite fields. APL programming language used. Pre- or corequisites: 01:640:351-352. No prior computing experience is assumed.

01:640:461Mathematical Logic (3) Intuitive and formal development of the sentential and predicate calculus. Special emphasis given to questions of consistency, completeness, and independence. Formal systems; incompleteness and undecidability; theorems of G�del. Exploration of which properties of structures can be defined in the first-order language. Prerequisite: CALC3 and either 01:640:300 or permission of department.

01:640:477Mathematical Theory of Probability (3) Basic probability theory in both discrete and continuous sample spaces, combinations, random variables and their distribution functions, expectations, law of large numbers, central limit theorem. Prerequisite: CALC3. Credit not given for both this course and 01:198:206, 14:332:331, or 01:960:381.

01:640:478Probability II (3) Sums of independent random variables, moments and moment- generating functions, characteristic functions, uniqueness and continuity theorems, law of large numbers, conditional expectations,�Markov chains, random walks. Prerequisites: 01:640:250 and either 01:640:477 or both 01:640:251 and 01:960:381.

01:640:481Mathematical Theory of Statistics (3) Fundamental principles of mathematical statistics, sampling distributions, estimation, testing hypotheses, correlation analysis, regression, analysis of variance, nonparametric methods. Prerequisites: 01:640:250 and either 01:640:477 or both 01:640:251 and 01:960:381. Credit not given for both this course and 01:960:382.

01:640:491,492Undergraduate Mathematics Seminar (1,1) Reading, presentation, and discussion of mathematical topics.

01:640:493,494Individual Study in Mathematics (1-3 BA,1-3 BA) Prerequisite: Permission of department.

01:640:495Selected Topics in Mathematics (3)

01:640:496Research in Mathematics (3)

01:640:497,498Honors in Mathematics (3,3)