
The following abbreviations are used in the course listing.
1. CALC1 indicates that the prerequisite is any one of 01:640:135, 151, 153, or 191.
2. CALC2 indicates that the prerequisite is any one of 01:640:152, 154, or 192.
3. CALC3 indicates that the prerequisite is any one of 01:640:251 or 291.
4. CALC4 indicates that the prerequisite is any one of 01:640:244, 252, or 292.
5. CR1 indicates that students may not receive credit for more than one
of the firstsemester calculus courses 01:640:135, 151, 153, or 191.
6. CR2 indicates that students may not receive credit for more than one
of the courses including secondsemester 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 thirdsemester topics 01:640:251
or 291.
8. CR4 indicates that students may not receive credit
for more than one of the fourthsemester courses 01:640:244, 252, or 292.

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

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

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

01:640:026
Intermediate 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.

01:640:103
Topics in Mathematics for the Liberal Arts (3)
Topics in mathematics including voting theory, apportionment, fair division, exponential growth in nature and finance, Euler circuits, Traveling Salesman Problem, and networks.
An elementary course for liberal arts majors. Prerequisite: 01:640:025 or appropriate performance on the placement test in mathematics. May not be used as an elective for the math major or minor.

01:640:104
Introduction to 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 027 or appropriate performance on the placement test in mathematics. May not be used as an elective for the math major or minor.

01:640:107
Mathematics for Elementary Teaching (3)
Reexamination of familiar mathematical ideas, primarily about number systems and arithmetic operations, in the context of mathematics as a whole and from the perspective of young students first learning them. Emphasis on reasoning and communication.
Prerequisites: 01:640:025 or appropriate performance on the placement test in mathematics, and permission of department. For students interested in pursuing a career in elementary school teaching. May not be used as an elective for the math major or minor.

01:640:108
Problem Solving and Reasoning with Discrete Mathematics (3)
Discrete mathematics as a tool for developing problemsolving and reasoning skills. Applications of vertexedge graphs and systematic counting, which can be introduced at K8 grade levels. For students interested in a career in teaching in elementary or middle schools.
Prerequisites: 01:640:025 or appropriate performance on the placement test in mathematics, and permission of department. May not be used as an elective for the math major or minor.

01:640:109
Geometry and Measurement for Elementary Teaching (3)
Math content course on geometry and measurement stressing
depth of understanding needed for effective teaching K8. Justifying procedures
and formulas. Multiple points of view in explanations. Geometric objects in two
and three dimensions. Transformations, symmetry, congruences, similarity,
scaling. Perimeter, area, volume. Error estimates in measurement. Changing units.
Prerequisites: 01:640:026 or 107 or placement into 01:640:111, and permission of department. Primarily for those intending to teach in grades K8.

01:640:111112
Precalculus 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 01:640:111112 and 115.

01:640:115
Precalculus College Mathematics (4)
Algebraic expressions, algebraic equations, inequalities, functions, and 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 01:640:111112 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 01:640:111112, which covers the same material as 115 but at a slower pace and begins with an extensive review of intermediate algebra.

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

01:640:135136
Calculus 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.
Primarily for majors in the social sciences, business, and pharmacy. Students in the life sciences should take 135138 or 151152. Students intending to take more than two semesters of calculus should take 151152. Prerequisite for 135: 01:640:112 or 115 or appropriate performance on the placement test in mathematics. Prerequisite for 136: CALC1. Credit restrictions: CR1, CR2.

01:640:138
Calculus 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 restriction: CR2.

01:640:151152
Calculus for Mathematical and Physical Sciences (4,4)
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.

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

01:640:158
Calculus II for Mathematical and Physical Sciences Practicum (1)
Application of algorithms studied in 01:640:152 to problems.
Corequisite: 01:640:152.

01:640:191192
Honors Calculus I,II (4,4)
These courses cover the same material as 01:640:151152 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.

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

01:640:197
Topics in Mathematics for K8 Teaching I (3)
Topics covered vary. Details available at registration.
Prerequisites: 01:640:026 or 027 or appropriate performance on the placement test in mathematics, and permission of the department. For students interested in a career in K8 teaching. May not be used as an elective for the math major or minor. May be repeated for credit, with permission of the department.

01:640:198
Topics in Mathematics II (3)
Topics covered vary. Details available at registration.
Prerequisite: 01:640:026 or 027 or appropriate performance on the placement test in mathematics, and permission of the department. For students interested in a career in K8 teaching. May not be used as an elective for the math major or minor. May be repeated for credit, with permission of the department.

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

01:640:250
Introductory Linear Algebra (3)
Systems of linear equations, Gaussian elimination, matrices and determinants, vectors in two and threedimensional 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.

01:640:251
Multivariable 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.

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

01:640:291
Honors Calculus III (4)
Covers the same material as 01:640:251 and 252 in a more thorough and demanding fashion.
Prerequisites: 01:640:191192 or permission of department. Credit restrictions: CR3, CR4. Grades of B or better are required to continue in the honors sequence.

01:640:292
Honors Calculus IV (4)
First and secondorder ordinary differential equations;
systems of ordinary differential equations. A more thorough and demanding
alternative to 01:640:244 or 252.
Prerequisite: 01:640:291 or permission of department. Pre or corequisite: 01:640:250.
Credit restrictions: CR4. Grades of B or better are required to continue in the honors sequence.

01:640:300
Introduction 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.

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

01:640:312
Advanced 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.

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

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

01:640:338
Discrete 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, MonteCarlo simulation, maximumlikelihood estimation, entropy, and information. Applications selected from epidemiology, inheritance and genetic drift, combinatorics and sequence alignment of nucleic acids, energy optimization in protein structure prediction, and topology of biological molecules.
Prerequisites: 01:640:250, 251; and either 01:198:206, 01:640:477, 01:960:381, 14:332:321, or 14:540:210. Only one of 01:640:338 and 339 may count for credit toward any math major or minor option.

01:640:339
Mathematical 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, nperson 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.

01:640:348
Cryptography (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, 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.

01:640:350
Linear 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.

01:640:351352
Introduction 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.

01:640:354
Linear 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.

01:640:356
Theory of Numbers (3)
Properties of the natural numbers, congruences, diophantine equations, and elementary arithmetical functions.
Prerequisites: CALC3 and 01:640:300, or permission of department.

01:640:357
Topics in Applied Algebra (3)
Material relevant for various applications. Topics chosen from finite Fourier and wavelet transforms for signal and image processing, coding theory, algebraic graph theory, algebraic combinatorics, and algebraic computational complexity. Details available at time of registration.
Prerequisites: CALC3 and 01:640:250.

01:640:361
Set Theory (3)
Introduction to set theory. The settheoretic 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.

01:640:373374
Numerical 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.

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

01:640:403
Introductory 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.

01:640:411412
Mathematical 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.

01:640:421
Advanced 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.

01:640:423
Elementary 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.

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

01:640:428
Graph 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.

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

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

01:640:436
History 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, CALC3; recommended to be taken after Geometry (01:640:435).

01:640:441442
Introductory 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 01:640:311 or permission of department.

01:640:451452
Abstract 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.

01:640:453
Theory 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, primaldual methods, complementary slackness theorem, maximal flows, transportation problems, and twoperson game theory.
Prerequisite: 01:640:250. Credit not given for both this course and 01:640:354 or 01:711:453. Crosslisted with 01:711:453.

01:640:454
Combinatorics (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.

01:640:461
Mathematical 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 Gödel. Exploration of which properties of structures can be defined in the firstorder language.
Prerequisites: CALC3 and either 01:640:300 or permission of department.

01:640:468
Connecting Advanced Mathematics to High School Content (3)
Connects math major course content to curricular content
of grades 9 through 12. Shows how advanced mathematics justifies and elucidates
high school material taught without full justification. Provides connections
between concepts and procedures to facilitate recall and application of content
knowledge both for exposition and for response to student misconceptions. Focus
on applications of reasoning, real analysis, and abstract algebra to high
school topics.
Prerequisite: Permission of instructor. Primarily for fifthyear students in the HS Mathematics Certification Program.

01:640:477
Mathematical 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, 14:332:321, or 01:960:381.

01:640:478
Probability II (3)
Sums of independent random variables, moments and momentgenerating 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.

01:640:481
Mathematical 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.

01:640:485
Introduction to Mathematical Finance (3)
Study of the mathematical theory and financial concepts used to model and analyze financial derivatives. Topics include martingales, Brownian motion, and stochastic differentials, with applications to discrete and continuous time stochastic models of asset prices, option pricing, the BlackScholes pricing model, and hedging.
Prerequisites: 01:640:250, CALC4, and 01:640:477 or 01:960:381 or 14:332:226.
Recommended for students interested in economics, statistics, finance, or actuarial mathematics.

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

01:640:493,494
Individual Study in Mathematics (13 BA,13 BA)
Prerequisite: Permission of department.

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

01:640:496
Research in Mathematics (3)

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

