### Courses

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The online catalog includes the most recent changes to courses and degree
requirements that have been approved by the Faculty Senate, including changes
that are not yet effective.
Courses showing two entries of the same number
indicate that the course information is changing. The most recently approved
version is shown first, followed by the older version, in gray, with its
last-effective term preceding the course title. Courses shown in gray with only
one entry of the course number are being discontinued.
Course offerings by term can be accessed by clicking on the term links when viewing a specific campus catalog.
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#### Mathematics (MATH)

100 Basic Mathematics 2 Course Prerequisite: A minimum ALEKS math placement score of 1%. Review of basic arithmetic and elementary algebra. No credit earned toward degree. Typically offered Fall, Spring, and Summer. S, F grading.

101 Intermediate Algebra 3 Fundamental algebraic operations and concepts. No credit earned toward degree.

103 Algebra Methods and Introduction to Functions 3 Course Prerequisite: MATH 100 with an S, MATH 101 with a C or better, or a minimum ALEKS math placement score of 40%. Fundamental algebraic operations and concepts, linear systems and inequalities, polynomial and rational functions, introduction to exponential and logarithmic functions. Typically offered Fall, Spring, and Summer.

105 [QUAN] Exploring Mathematics 3 Course Prerequisite: MATH 101 with a C or better, MATH 103 with a C or better, or a minimum ALEKS math placement score of 45%. Nature and scope of modern mathematics, and its relationships to other disciplines. Typically offered Fall, Spring, and Summer.

106 College Algebra 3 Course Prerequisite: MATH 101 with a C or better, or MATH 103 with a C or better, or a minimum ALEKS math placement score of 70%. Graphs, properties and applications of polynomial, rational, exponential and logarithmic functions. Typically offered Fall, Spring, and Summer.

108 Trigonometry 2 Course Prerequisite: MATH 106 with a C or better. Graphs, properties and applications of trigonometric functions. Credit not normally granted for both MATH 108 and 107. Typically offered Fall, Spring, and Summer.

110 Mathematics Acceleration 1 (0-3) Course Prerequisite: A minimum ALEKS math placement score of 25%. Individualized instruction on mathematical skills to enhance the mathematical background necessary for success in one of MATH 103, 106, or 171. Typically offered Fall and Spring. S, F grading.

111 Mathematics Tutorial for MATH 201 1 Course Prerequisite: Concurrent enrollment MATH 107. Student-centered group tutorial focusing on skill improvement for success in MATH 201. Typically offered Fall and Spring. S, F grading.

115 Math 105 Tutorial 2 Tutorial for MATH 105 focusing on concept development and mastery; skill proficiency. Typically offered Fall and Spring. S, F grading.

116 Math 106 Tutorial 2 Tutorial for MATH 106 focusing on concept development and mastery; skill proficiency. Typically offered Fall and Spring. S, F grading.

140 [QUAN] Calculus for Life Scientists 4 (3-3) Course Prerequisite: MATH 106 with a C or better and MATH 108 with a C or better, or a minimum ALEKS math placement score of 80%. Enrollment not allowed if credit already earned for MATH 171, 202, or 206. Differential and integral calculus with emphasis on life science applications. Credit not granted for more than one of MATH 140, 171, 202, 206. Typically offered Fall, Spring, and Summer.

171 [QUAN] Calculus I 4 (3-3) Course Prerequisite: MATH 106 with a C or better and MATH 108 with a C or better, or a minimum ALEKS math placement score of 83%. Enrollment not allowed if credit already earned for MATH 140, 202, or 206. Differential and integral calculus of one variable with associated analytic geometry. Credit not normally allowed for more than one of MATH 140, 171, 202, 206. Typically offered Fall, Spring, and Summer.

172 Calculus II 4 (3-3) Course Prerequisite: MATH 171 with a C or better. Techniques and applications of one-variable calculus; estimations; series, derivative of a vector function. Credit not granted for both MATH 172 and 182. Typically offered Fall, Spring, and Summer.

182 Honors Calculus II 4 (3-3) Course Prerequisite: MATH 171 with a C or better; by department permission only. Single variable calculus, series, with emphasis on conceptual development and problem solving. Credit not granted for both MATH 172 and 182. Typically offered Fall.

201 Mathematics for Business and Economics 3 Course Prerequisite: MATH 101 with a C or better, MATH 103 with a C or better, or a minimum ALEKS math placement score of 65%. Mathematical analysis using polynomial, exponential, and logarithmic functions; linear systems, linear programming and probability, for business and economic applications. Typically offered Fall, Spring, and Summer.

202 [QUAN] Calculus for Business and Economics 3 Course Prerequisite: MATH 106 with a C or better, MATH 201 with a C or better, or a minimum ALEKS math placement score of 80%. Enrollment not allowed if credit already earned for MATH 140, 171, or 206. Differential and integral calculus of the polynomial, exponential, and logarithmic functions. Credit not granted for more than one of MATH 140, 171, 202, 206. Typically offered Fall, Spring, and Summer.

216 Discrete Structures 3 Course Prerequisite: MATH 108 with a C or better, or MATH 140, 171, 172, 182, or MATH 202 or concurrent enrollment. Discrete mathematics, trees, graphs, elementary logic, and combinatorics with application to computer science. Recommended preparation: Programming course. Typically offered Fall, Spring, and Summer.

220 Introductory Linear Algebra 2 Course Prerequisite: MATH 171 or concurrent enrollment. Solving linear systems, matrices, determinants, subspaces, eigenvalues, orthogonality. Credit not normally granted for more than one of MATH 220 and 230. Typically offered Fall, Spring, and Summer.

220 (Effective through Summer 2019) Introductory Linear Algebra 2 Course Prerequisite: MATH 171 or concurrent enrollment. Elementary linear algebra with geometric applications. Credit not normally granted for more than one of MATH 220 and 230. Typically offered Fall, Spring, and Summer.

230 Honors Introductory Linear Algebra 3 Course Prerequisite: MATH 171 or concurrent enrollment. An introduction to linear algebra with an emphasis on conceptual development. Credit not normally granted for more than one of MATH 220 and 230. Typically offered Spring.

251 Fundamentals of Elementary Mathematics I 3 (2-2) Course Prerequisite: MATH 101 with a C or better, MATH 103 with a C or better, MATH 106 with a C or better, or a minimum ALEKS math placement score of 45%. Comprehensive development of number systems emphasizing place-value, integers, rational numbers, and associated algorithms; methods of problem solving. Typically offered Fall and Spring.

252 [QUAN] Fundamentals of Elementary Mathematics II 3 (2-2) Course Prerequisite: MATH 251 with a C or better. Inquiry-based approach to fundamental concepts: measurement, geometrical constructions, similarity, congruence, symmetry, probability, counting principles, measures of central tendency, and distributions. Required preparation: One year of high school geometry. Typically offered Fall and Spring.

273 Calculus III 2 Course Prerequisite: MATH 172 with a C or better, or MATH 182 with a C or better. Calculus of functions of several variables. Credit not granted for both MATH 273 and 283. Typically offered Fall, Spring, and Summer.

283 Honors Calculus III 2 Course Prerequisite: MATH 182 or by department permission. Multivariable calculus with emphasis on conceptual development and problem solving. Credit not granted for both MATH 273 and 283. Typically offered Spring.

300 Mathematical Computing 3 Course Prerequisite: MATH 220 or MATH 230. Examination of some current computer software for solving mathematical problems. Recommended preparation: MATH 315. Typically offered Fall and Summer.

301 Introduction to Mathematical Reasoning 3 Course Prerequisite: MATH 220 with a C or better, or MATH 230 with a C or better. Mathematical arguments and the writing of proofs. Typically offered Fall, Spring, and Summer.

302 Theory of Numbers 3 Course Prerequisite: MATH 172 with a C or better, or MATH 182 with a C or better; MATH 301 with a C or better. Divisibility properties of integers; congruences; Diophantine equations; quadratic residues. Typically offered Spring.

303 [M] Geometry for the Middle School Teacher 3 Course Prerequisite: MATH 252. Topics in 2D and 3D geometry including technology-based reasoning and exploration, deductive arguments, transformational and proportional reasoning, and non-Euclidean geometries. Typically offered Fall and Summer.

315 Differential Equations 3 Course Prerequisite: MATH 273 with a C or better or Math 283 with a C or better; and MATH 220 with a C or better or concurrent enrollment, or MATH 230 with a C or better or concurrent enrollment. Linear differential equations and systems; series, numerical and qualitative approaches; applications. Typically offered Fall, Spring, and Summer.

320 [M] Elementary Modern Algebra 3 Course Prerequisite: MATH 220 with a C or better or MATH 230 with a C or better. Algebra as a deductive system; number systems; groups, rings, and fields. Typically offered Spring.

325 Elementary Combinatorics 3 Course Prerequisite: MATH 220 with a C or better or MATH 230 with a C or better. Introduction to combinatorial theory: counting methods, binomial coefficients and identities, generating functions, occurrence relations, inclusion-exclusion methods. Typically offered Fall and Spring.

330 Methods of Teaching Secondary School Mathematics 3 Course Prerequisite: MATH 301 or concurrent enrollment. New curricula and pedagogical techniques for secondary school mathematics. Typically offered Fall.

340 Introduction to Mathematical Biology 3 Course Prerequisite: MATH 140 with a C or better, or MATH 172 with a C or better, or MATH 182 with a C or better; BIOLOGY 101, BIOLOGY 102, BIOLOGY 106, or BIOLOGY 107. Mathematical biology and development of mathematical modeling for solutions to problems in the life sciences. (Crosslisted course offered as MATH 340, BIOLOGY 340). Typically offered Fall and Spring.

351 Algebraic Thinking for the Middle School Teacher 3 Course Prerequisite: MATH 252 with a C or better. Algebraic reasoning, classes of functions, translation among models, analytical rule, tables of data, context and coordinate graphs. Typically offered Spring.

352 Probability and Data Analysis for Middle School Teachers 3 Course Prerequisite: MATH 251; MATH 252. Probability and statistics in relation to middle school mathematics and real world problems through visualization, hands-on activities, and technology. Typically offered Spring.

364 Principles of Optimization 3 Course Prerequisite: MATH 202, MATH 220, or MATH 230. Algebra of linear inequalities; duality; graphs, transport networks; linear programming; special algorithms; nonlinear programming; selected applications. Typically offered Fall and Spring.

375 Vector Analysis 3 Course Prerequisite: MATH 315. Line integrals, gradient, curl, divergence; Stokes' theorem, potential functions. Typically offered Fall and Spring.

398 Mathematical Snapshots 1 Course Prerequisite: MATH 172 or MATH 182. Character, life work, and historical importance of mathematicians from various eras and branches of mathematics. Typically offered Spring.

401 [M] Introduction to Analysis I 3 Course Prerequisite: MATH 301 with a C or better. Properties of sets and sequences of real numbers; limits, continuity, differentiation and integration of functions; metric spaces. Typically offered Fall.

402 [M] Introduction to Analysis II 3 Course Prerequisite: MATH 401. Sequences of functions, power series, multivariable calculus, inverse and implicit function theorems, Lagrange multipliers, change of variable in multiple integrations. Typically offered Spring.

403 Euclidean and Non-Euclidean Geometry 3 Course Prerequisite: MATH 301 with a C or better. Geometry as a deductive system of logic; postulational systems; projective and non-Euclidian geometries. Typically offered Fall.

403 (Effective through Summer 2019) Geometry for Secondary Teachers 3 Course Prerequisite: MATH 301 with a C or better. Geometry as a deductive system of logic; postulational systems; projective and non-Euclidian geometries. Typically offered Fall.

405 Introduction to Financial Mathematics 3 Course Prerequisite: MATH 172 or 182. Introduction to financial mathematics including the basics of annuities, stocks, bonds, and financial derivatives. Typically offered Fall.

415 Intermediate Differential Equations 3 Course Prerequisite: MATH 315. Linear systems; qualitative theory (existence, uniqueness, stability, periodicity); boundary value problems; applications. Typically offered Spring.

416 Numerical Simulations for Probabilistic Models 3 Course Prerequisite: STAT 360; CPT S 121, CPT S 251, or MATH 300. Efficient generation of random variables; statistical analysis and validation techniques; variance reduction; Markov Chain Monte Carlo methods; applications include complex systems, financial models, and Bayesian computation. Credit not granted for both MATH 416 and MATH 516. Required preparation must include probability and statistics and programming experience. Offered at 400 and 500 level. Typically offered Fall. Cooperative: Open to UI degree-seeking students.

416 (Effective through Summer 2019) Simulation Methods 3 Course Prerequisite: STAT 360; CPT S 121, CPT S 251, or MATH 300. Model formulation and simulation in business, industry, and government; simulation languages; analysis of simulation output; applications. Credit not granted for both MATH 416 and MATH 516. Required preparation must include probability and statistics and programming experience. Offered at 400 and 500 level. Typically offered Fall.

420 Linear Algebra 3 Course Prerequisite: MATH 220 with a C or better, or MATH 230 with a C or better; MATH 301 with a C or better. Vector spaces, linear transformations, diagonalizability, normal matrices, inner product spaces, orthogonality, orthogonal projections, least-squares, SVD. Typically offered Fall.

420 (Effective through Summer 2019) Linear Algebra 3 Course Prerequisite: MATH 220 with a C or better, or MATH 230 with a C or better; MATH 301 with a C or better. Advanced topics in linear algebra including similarity transformations, canonical forms, bilinear forms. Typically offered Fall.

421 [M] Algebraic Structures 3 Course Prerequisite: MATH 301 with a C or better. Properties of algebraic structures and their homomorphisms, semi-groups, groups, rings, unique factorization domains, fields. Typically offered Spring.

425 Conceptual Aspects of Mathematics 3 Course Prerequisite: By instructor permission. Exploration of conceptual models for thinking about mathematical ideas; activities and discussions of mathematical thinking and instruction. (Crosslisted course offered as TCH LRN 425, MATH 425).

431 Intersections of Culture and Mathematics 3 Course Prerequisite: MATH 301 with a C or better. Gender/race/ethnicity differences; social consequences; cultural influences on development and learning of mathematics; role of women, people of color in mathematics. Credit not granted for both MATH 431 and 531. Offered at 400 and 500 level. Typically offered Fall. Cooperative: Open to UI degree-seeking students.

432 [CAPS] Mathematics for College and Secondary Teachers 3 Course Prerequisite: MATH 301 with a C or better. Pre-algebra, algebra functions and geometry examined from an advanced perspective, for secondary and lower level college teachers. Typically offered Spring.

440 Applied Mathematics I: PDEs 3 Course Prerequisite: MATH 315. Applied partial differential equations; Fourier series; Bessel functions and Legendre polynomials as harmonics for disks and balls; Laplace, heat, and wave equations; separation of variables and D'Alambert's formula. Credit not granted for both MATH 440 and MATH 540. Required preparation must include differential equations. Offered at 400 and 500 level. Typically offered Fall, Spring, and Summer. Cooperative: Open to UI degree-seeking students.

441 Applied Mathematics II: Complex Variables 3 Course Prerequisite: MATH 315. Complex numbers and complex-valued functions of one complex variable; analytic functions and Cauchy-Riemann equations; differentiation and contour integration; Cauchy integral theorem; Taylor and Laurent series; residues; conformal mapping; applications to potential theory. Credit not granted for both MATH 441 and MATH 541. Required preparation must include differential equations. Offered at 400 and 500 level. Typically offered Spring. Cooperative: Open to UI degree-seeking students.

441 (Effective through Summer 2019) Applied Mathematics II 3 Course Prerequisite: MATH 315. Complex variable theory including analytic functions, infinite series, residues, and conformal mapping; Laplace transforms; applications. Credit not granted for both MATH 441 and MATH 541. Required preparation must include differential equations. Offered at 400 and 500 level. Typically offered Spring.

448 Numerical Analysis 3 Course Prerequisite: MATH 315 with a C or better; one of CPT S 121, 131, or MATH 300, with a C or better. Fundamentals of numerical computation; finding zeroes of functions, approximation and interpolation; numerical integration (quadrature); numerical solution of ordinary differential equations. (Crosslisted course offered as MATH 448, MATH 548, CPT S 430, CPT S 530). Required preparation must include differential equations and a programming course. Offered at 400 and 500 level. Typically offered Fall, Spring, and Summer.

453 Graph Theory 3 Course Prerequisite: MATH 220 or MATH 230. Graphs and their applications, directed graphs, trees, networks, Eulerian and Hamiltonian paths, matrix representations, construction of algorithms. (Crosslisted course offered as MATH 453, MATH 553, CPT S 453, CPT S 553). Required preparation must include linear algebra. Required preparation must include linear algebra. Offered at 400 and 500 level. Typically offered Fall. Cooperative: Open to UI degree-seeking students.

456 Introduction to Statistical Theory 3 Course Prerequisite: STAT 430 or 443. Sampling distributions; hypothesis testing and estimation; maximum likelihood; likelihood ratio tests; theory of least squares; nonparametrics. (Crosslisted course offered as STAT 456, MATH 456). Recommended preparation: One 3-hour 400-level STAT or probability course. Offered at 400 and 500 level. Typically offered Spring.

464 [CAPS] Linear Optimization 3 Course Prerequisite: MATH 273 or MATH 283. Linear and integer programming; optimization problems; applications to economic and military strategies; rectangular games; minimax theory. Typically offered Spring.

466 Optimization in Networks 3 Course Prerequisite: MATH 364. Formulation and solution of network optimization problems including shortest path, maximal flow, minimum cost flow, assignment, covering, postman, and salesman. Credit not granted for both MATH 466 and MATH 566. Required preparation must include linear programming. Offered at 400 and 500 level. Typically offered Even Years - Fall. Cooperative: Open to UI degree-seeking students.

486 Mathematical Methods in Natural Sciences 3 Course Prerequisite: MATH 315. Introduction to mathematical modeling of natural processes; methods include dimensional and scaling analysis, perturbation theory, field theory of continuum mechanics, calculus of variations, and Markov chains; applications to physics, chemistry, biology, and engineering. Credit not granted for both MATH 486 and MATH 586. Required preparation must include differential equations. Offered at 400 and 500 level. Typically offered Even Years - Fall. Cooperative: Open to UI degree-seeking students.

486 (Effective through Summer 2019) Mathematical Modeling in the Natural Science 3 Course Prerequisite: MATH 315. Development of mathematical models for solutions of problems in the physical and life sciences. Credit not granted for both MATH 486 and MATH 586. Required preparation must include differential equations. Offered at 400 and 500 level. Typically offered Fall.

490 Topics in Mathematics V 1-3 May be repeated for credit; cumulative maximum 9 hours. Course Prerequisite: By instructor permission. Special topics in mathematics. Typically offered Fall, Spring, and Summer.

494 Seminar in Mathematical Biology 1 May be repeated for credit; cumulative maximum 4 hours. Course Prerequisite: MATH 140 with a C or better, or MATH 172 with a C or better, or MATH 182 with a C or better; BIOLOGY 101, BIOLOGY 102, BIOLOGY 106, or BIOLOGY 107. Oral presentation of research approaches, research results and literature review of mathematical biology including mathematical modeling of biological systems. (Crosslisted course offered as MATH 494, BIOLOGY 494). Typically offered Spring. Cooperative: Open to UI degree-seeking students. S, F grading.

497 Instructional Practicum V 1-2 May be repeated for credit; cumulative maximum 2 hours. Course Prerequisite: By instructor permission. Typically offered Fall and Spring. S, F grading.

499 Special Problems V 1-4 May be repeated for credit. Independent study conducted under the jurisdiction of an approving faculty member; may include independent research studies in technical or specialized problems; selection and analysis of specified readings; development of a creative project; or field experiences. Typically offered Fall, Spring, and Summer. S, F grading.

500 Proseminar 1 May be repeated for credit; cumulative maximum 2 hours. Typically offered Fall. S, F grading.

501 Real Analysis 3 Metric spaces, convergence, continuous functions, infinite series, differentiation and integration of functions of one and several variables. Required preparation must include advanced calculus or real analysis. Typically offered Fall.

502 Introduction to Functional Analysis 3 Course Prerequisite: MATH 501. Normed linear spaces, Banach spaces, introduction to Hilbert space, linear operators. Required preparation: Advanced linear algebra. Typically offered Spring.

503 Complex Analysis 3 Course Prerequisite: MATH 501. Analytic functions, complex integration, Taylor and Laurent series, conformal mapping, Riemann surfaces and analytic continuation. Cooperative: Open to UI degree-seeking students.

503 (Effective through Summer 2019) Complex Analysis 3 Course Prerequisite: MATH 501. Analytic functions, complex integration, Taylor and Laurent series, conformal mapping, Riemann surfaces and analytic continuation. Typically offered Fall. Cooperative: Open to UI degree-seeking students.

504 Measure and Integration 3 Course Prerequisite: MATH 501. Lebesque measure, Lebesque integration, differentiation, L spaces, general measure and integration, Radon-Nikodym Theorem, outer measure and product measures. Typically offered Odd Years - Fall. Cooperative: Open to UI degree-seeking students.

505 Abstract Algebra 3 Groups, rings, fields, and homological algebra. Required preparation must include abstract algebra. Typically offered Odd Years - Fall. Cooperative: Open to UI degree-seeking students.

507 Advanced Theory of Numbers 3 May be repeated for credit; cumulative maximum 6 hours. Analytic and algebraic number theory. Typically offered Spring. Cooperative: Open to UI degree-seeking students.

508 Advanced Mathematical Methods for Physics and Engineering 3 Advanced treatment of applications using techniques from fundamental analysis, convexity, analytic function theory, asymptotics, and differential equations. Typically offered Spring. Cooperative: Open to UI degree-seeking students.

508 (Effective through Summer 2019) Topics in Applied Analysis 3 Advanced treatment of applications using techniques from fundamental analysis, convexity, analytic function theory, asymptotics, and differential equations. Typically offered Spring.

511 Advanced Linear Algebra 3 Spectral theory, Schur's theorem, normality, Jordan canonical forms, hermitian matrices, variational inequalities, matrix norms, eigenvalue localization, matrix perturbation theory. Required preparation must include second level undergraduate linear algebra. Typically offered Spring. Cooperative: Open to UI degree-seeking students.

511 (Effective through Summer 2019) Advanced Linear Algebra 3 Vector spaces, inner products, unitary equivalence, similarity, Jordan forms, normality, spectral theory, singular value decomposition, norms and inequalities. Required preparation must include advanced linear algebra. Typically offered Spring.

512 Ordinary Differential Equations 3 Existence of solutions; linear systems; qualitative behavior, especially stability; periodic solutions. Required preparation must include a year-long sequence in advanced calculus or real analysis. Typically offered Even Years - Fall. Cooperative: Open to UI degree-seeking students.

516 Numerical Simulations for Probabilistic Models 3 Efficient generation of random variables; statistical analysis and validation techniques; variance reduction; Markov Chain Monte Carlo methods; applications include complex systems, financial models, and Bayesian computation. Credit not granted for both MATH 416 and MATH 516. Required preparation must include probability and statistics and programming experience. Offered at 400 and 500 level. Typically offered Fall. Cooperative: Open to UI degree-seeking students.

516 (Effective through Summer 2019) Simulation Methods 3 Model formulation and simulation in business, industry, and government; simulation languages; analysis of simulation output; applications. Credit not granted for both MATH 416 and MATH 516. Required preparation must include probability and statistics and programming experience. Offered at 400 and 500 level. Typically offered Fall.

524 Algebraic Topology 3 Algebraic techniques (groups, homomorphisms, etc) to study connectivity of spaces; topics include simplicial complexes, homology, relative homology, Meyer-Vietoris sequences, categories and functors, cohomology, and duality in manifolds. Recommended preparation: real analysis and abstract algebra. Typically offered Fall.

525 General Topology 3 Sets, metric spaces, topological spaces; continuous mappings, compactness, connectedness, local properties, function spaces, and fundamental groups. Required preparation must include a year-long sequence in advanced calculus or real analysis. Typically offered Even Years - Fall. Cooperative: Open to UI degree-seeking students.

529 Computational Topology 3 Topological techniques combined with algorithms to find structure in data; simplicial complexes from point clouds, algorithms for homology and persistent homology, mapper and topological data analysis, optimal homology problems. Recommended preparation: mathematical maturity at senior undergraduate level and some experience with computer programming. Typically offered Spring.

531 Intersections of Culture and Mathematics 3 Gender/race/ethnicity differences; social consequences; cultural influences on development and learning of mathematics; role of women, people of color in mathematics. Credit not granted for both MATH 431 and 531. Offered at 400 and 500 level. Typically offered Fall. Cooperative: Open to UI degree-seeking students.

532 Advanced Mathematical Thinking 3 Course Prerequisite: Graduate standing in mathematics. Current theories about how humans learn to think mathematically at the advanced level. Typically offered Even Years - Spring. Cooperative: Open to UI degree-seeking students.

533 Teaching College Mathematics 1 May be repeated for credit; cumulative maximum 3 hours. Course Prerequisite: Graduate standing in Mathematics. Theory and practice of mathematics instruction at the collegiate level. Typically offered Fall and Spring.

534 Theories of Learning in Mathematics 3 Math learning theories, including behaviorism, information processing, constructivism, situated cognition, communities of practice; influence on teaching and learning mathematics. Typically offered Odd Years - Fall. Cooperative: Open to UI degree-seeking students.

535 Research Paradigms in Mathematics Education 3 Course Prerequisite: MATH 534. Current research paradigms in math education research; critique research designs used in current mathematics education research article; design and carry out a research project. Typically offered Odd Years - Spring. Cooperative: Open to UI degree-seeking students.

536 Statistical Computing 3 (2-3) Generation of random variables, Monte Carlo simulation, bootstrap and jackknife methods, EM algorithm, Markov chain Monte Carlo methods. (Crosslisted course offered as STAT 536, MATH 536). Recommended preparation: One 3-hour 400-level probability or STAT course. Typically offered Fall. Cooperative: Open to UI degree-seeking students.

540 Applied Mathematics I: PDEs 3 Applied partial differential equations; Fourier series; Bessel functions and Legendre polynomials as harmonics for disks and balls; Laplace, heat, and wave equations; separation of variables and D'Alambert's formula. Credit not granted for both MATH 440 and MATH 540. Required preparation must include differential equations. Offered at 400 and 500 level. Typically offered Fall, Spring, and Summer. Cooperative: Open to UI degree-seeking students.

541 Applied Mathematics II: Complex Variables 3 Complex numbers and complex-valued functions of one complex variable; analytic functions and Cauchy-Riemann equations; differentiation and contour integration; Cauchy integral theorem; Taylor and Laurent series; residues; conformal mapping; applications to potential theory. Credit not granted for both MATH 441 and MATH 541. Required preparation must include differential equations. Offered at 400 and 500 level. Typically offered Spring. Cooperative: Open to UI degree-seeking students.

541 (Effective through Summer 2019) Applied Mathematics II 3 Complex variable theory including analytic functions, infinite series, residues, and conformal mapping; Laplace transforms; applications. Credit not granted for both MATH 441 and MATH 541. Required preparation must include differential equations. Offered at 400 and 500 level. Typically offered Spring.

543 Stable Numerical Methods Using Orthogonality 3 Computational methods for stabilizing difficult and ill-posed differential and integral equations problems by using systems of functions and regularization techniques; applications to forward and inverse problems; techniques include the use of wavelets and orthogonal polynomials. Required preparation must include numerical analysis. Typically offered Spring. Cooperative: Open to UI degree-seeking students.

543 (Effective through Summer 2019) Approximation Theory 3 Univariate polynomial and rational approximation techniques; approximation using splines and wavelets; selected topics in multivariate approximation; algorithms for approximation. Required preparation must include numerical analysis. Typically offered Spring. Cooperative: Open to UI degree-seeking students.

544 Advanced Matrix Computations 3 Advanced topics in the solution of linear systems and eigenvalue problems, including parallel matrix computations. (Crosslisted course offered as MATH 544, CPT S 531). Required preparation must include numerical analysis. Typically offered Spring. Cooperative: Open to UI degree-seeking students.

545 Numerical Analysis of Parabolic and Hyperbolic PDEs 3 Numerical solutions of parabolic and hyperbolic partial differential equations with emphasis on finite difference methods; topics include: finite difference; stability, consistency, and convergence; shocks; conservation of forms. Required preparation must include numerical analysis. Typically offered Odd Years - Spring. Cooperative: Open to UI degree-seeking students.

546 Numerical Analysis of Elliptic PDEs 3 Numerical solutions of elliptic partial differential equations with emphasis on finite element methods; finite difference; error analysis. Required preparation must include numerical analysis. Typically offered Even Years - Fall. Cooperative: Open to UI degree-seeking students.

546 (Effective through Summer 2019) Numerical Analysis of Elliptic PDEs 3 Methods of discretizing elliptic partial differential equations and solving the resulting systems of equations; error analysis. Required preparation must include numerical analysis. Typically offered Fall. Cooperative: Open to UI degree-seeking students.

548 Numerical Analysis 3 Fundamentals of numerical computation; finding zeroes of functions, approximation and interpolation; numerical integration (quadrature); numerical solution of ordinary differential equations. (Crosslisted course offered as MATH 448, MATH 548, CPT S 430, CPT S 530). Required preparation must include differential equations and a programming course. Offered at 400 and 500 level. Typically offered Fall, Spring, and Summer.

553 Graph Theory 3 Graphs and their applications, directed graphs, trees, networks, Eulerian and Hamiltonian paths, matrix representations, construction of algorithms. (Crosslisted course offered as MATH 453, MATH 553, CPT S 453, CPT S 553). Required preparation must include linear algebra. Required preparation must include linear algebra. Offered at 400 and 500 level. Typically offered Fall. Cooperative: Open to UI degree-seeking students.

555 Topics in Combinatorics 3 May be repeated for credit; cumulative maximum 6 hours. Combinatorics, generating functions, recurrence relations, inclusion-exclusion, coding theory; experimental design, graph theory. Typically offered Odd Years - Spring. Cooperative: Open to UI degree-seeking students.

560 Partial Differential Equations I 3 Partial differential equations and other functional equations: general theory, methods of solution, applications. Required preparation must include a year-long sequence in advanced calculus or real analysis. Typically offered Even Years - Fall. Cooperative: Open to UI degree-seeking students.

561 Partial Differential Equations II 3 Course Prerequisite: MATH 560. Continuation of MATH 560. Typically offered Odd Years - Spring. Cooperative: Open to UI degree-seeking students.

563 Mathematical Genetics 3 Mathematical approaches to population genetics and genome analysis; theories and statistical analyses of genetic parameters. (Crosslisted course offered as MATH 563, BIOLOGY 566). Required preparation must include multivariate calculus, genetics, and statistics. Typically offered Odd Years - Fall. Cooperative: Open to UI degree-seeking students.

564 Convex and Nonlinear Optimization 3 Convex sets and functions; operations preserving convexity; linear, quadratic, and conic optimization; duality theory; unconstrained smooth optimization; interior point methods. Required preparation must include advanced multivariate calculus, and a programming language. Recommended preparation: Knowledge in linear optimization and numerical linear algebra. Typically offered Odd Years - Fall. Cooperative: Open to UI degree-seeking students.

564 (Effective through Summer 2019) Nonlinear Optimization I 3 Theory and algorithms for unconstrained nonlinear optimization problems, including line search, trust region, conjugate gradient, Newton and quasi-Newton methods. Required preparation must include advanced multivariate calculus, and a programming language. Recommended preparation: MATH 464, 544. Typically offered Fall.

565 Nonsmooth Analysis and Optimization with Applications 3 Course Prerequisite: MATH 564. Extended real-valued functions; continuity and convexity; subgradient, conjugate functions and optimality condition; alternating minimization; projected subgradient methods; alternating direction methods of multipliers; applications in statistical learning. Required preparation must include real analysis and command of a programming language. Typically offered Even Years - Spring. Cooperative: Open to UI degree-seeking students.

565 (Effective through Summer 2019) Nonlinear Optimization II 3 Course Prerequisite: MATH 564. Theory and algorithms for constrained linear and nonlinear optimization including interior point, quadratic programming, penalty, barrier and augmented Lagrangian methods. Typically offered Spring.

566 Optimization in Networks 3 Formulation and solution of network optimization problems including shortest path, maximal flow, minimum cost flow, assignment, covering, postman, and salesman. Credit not granted for both MATH 466 and MATH 566. Required preparation must include linear programming. Offered at 400 and 500 level. Typically offered Even Years - Fall. Cooperative: Open to UI degree-seeking students.

567 Integer and Combinatorial Optimization 3 Theory and applications of integer and combinatorial optimization including enumerative, cutting plane, basis reduction, relaxation and matching methods. Required preparation must include linear optimization. Typically offered Odd Years - Spring. Cooperative: Open to UI degree-seeking students.

568 Statistical Theory I 3 Probability spaces, combinatorics, multidimensional random variables, characteristic function, special distributions, limit theorems, stochastic processes, order statistics. (Crosslisted course offered as STAT 548, MATH 568). Recommended preparation: Calculus III and one 3-hour 400-level probability course. Typically offered Fall. Cooperative: Open to UI degree-seeking students.

569 Statistical Theory II 3 Continuation of STAT 548. Statistical inferences; estimation and testing hypotheses; regression analysis; sequential analysis and nonparametric methods. (Crosslisted course offered as STAT 549, MATH 569). Recommended preparation: STAT 548. Typically offered Spring. Cooperative: Open to UI degree-seeking students.

570 Mathematical Foundations of Continuum Mechanics I 3 The basic mathematical theory of continuum mechanics and its relation to perturbation techniques and stability methods. Required preparation must include differential equations and advanced calculus or real analysis. Typically offered Odd Years - Fall. Cooperative: Open to UI degree-seeking students.

571 Mathematical Foundations of Continuum Mechanics II 3 Course Prerequisite: MATH 570. Continuation of MATH 570. Typically offered Even Years - Spring. Cooperative: Open to UI degree-seeking students.

574 Topics in Optimization 3 May be repeated for credit; cumulative maximum 12 hours. Advanced topics in the theory and computing methodology in optimization with emphasis on real-life algorithmic implementations. Required preparation must include advanced multivariable calculus and a programming language. Typically offered Even Years - Fall. Cooperative: Open to UI degree-seeking students.

575 Asset Pricing in Financial Engineering 3 Mathematical methods for various models on valuation of stocks and options, with rigorous mathematical analysis on pricing and hedging techniques. Recommended preparation: Advanced calculus and some knowledge on differential equations. Typically offered Odd Years - Fall. Cooperative: Open to UI degree-seeking students.

576 Quantitative Risk Management 3 Fundamental concepts in modern risk theory and mathematical methods in quantitative risk management; coherent risk measures, volatility modeling, multivariate dependence analysis using copulas, risk aggregation and allocation, and extreme value theory. Typically offered Even Years - Spring. Cooperative: Open to UI degree-seeking students.

579 Mathematical Modeling in the Biological and Health Sciences 3 Techniques, theory, and current literature in mathematical modeling in the biological and health sciences, including computational simulation. (Course offered as BIOLOGY 579, MATH 579). Typically offered Odd Years - Fall. Cooperative: Open to UI degree-seeking students.

581 Topics in Mathematics V 1-3 May be repeated for credit. Topics in mathematics. Typically offered Fall, Spring, and Summer. Cooperative: Open to UI degree-seeking students.

583 Topics in Applied Mathematics V 1-3 May be repeated for credit. Topics in applied mathematics. Typically offered Fall and Spring. Cooperative: Open to UI degree-seeking students.

586 Mathematical Methods in Natural Sciences 3 Introduction to mathematical modeling of natural processes; methods include dimensional and scaling analysis, perturbation theory, field theory of continuum mechanics, calculus of variations, and Markov chains; applications to physics, chemistry, biology, and engineering. Credit not granted for both MATH 486 and MATH 586. Required preparation must include differential equations. Offered at 400 and 500 level. Typically offered Fall. Cooperative: Open to UI degree-seeking students.

586 (Effective through Summer 2019) Mathematical Modeling in the Natural Science 3 Development of mathematical models for solutions of problems in the physical and life sciences. Credit not granted for both MATH 486 and MATH 586. Required preparation must include differential equations. Offered at 400 and 500 level. Typically offered Fall.

590 Topics in Mathematics Education V 1-3 May be repeated for credit; cumulative maximum 6 hours. Topics in mathematics education. Typically offered Fall and Spring.

591 Seminar in Mathematical Biology 1 May be repeated for credit; cumulative maximum 10 hours. Current research in mathematical biology. Typically offered Fall, Spring, and Summer. S, F grading.

592 Seminar in Analysis 1 May be repeated for credit; cumulative maximum 10 hours. Current research in analysis. Typically offered Fall and Spring. S, F grading.

593 Seminar in Combinatorics, Linear Algebra, and Number Theory 1 May be repeated for credit; cumulative maximum 10 hours. Current research in combinatorics, linear algebra, and number theory. Typically offered Fall, Spring, and Summer. S, F grading.

594 Mathematics Education Seminar 1 May be repeated for credit; cumulative maximum 10 hours. Current research in mathematics education. Typically offered Fall, Spring, and Summer. S, F grading.

597 Mathematics Instruction Seminar 1 May be repeated for credit; cumulative maximum 5 hours. Introduction to the teaching of university mathematics. Typically offered Fall and Spring. S, F grading.

600 Special Projects or Independent Study V 1-18 May be repeated for credit. Independent study, special projects, and/or internships. Students must have graduate degree-seeking status and should check with their major advisor before enrolling in 600 credit, which cannot be used toward the core graded credits required for a graduate degree. Typically offered Fall, Spring, and Summer. S, F grading.

702 Master's Special Problems, Directed Study, and/or Examination V 1-18 May be repeated for credit. Independent research in special problems, directed study, and/or examination credit for students in a non-thesis master's degree program. Students must have graduate degree-seeking status and should check with their major advisor/committee chair before enrolling for 702 credit. Typically offered Fall, Spring, and Summer. S, U grading.

800 Doctoral Research, Dissertation, and/or Examination V 1-18 May be repeated for credit. Course Prerequisite: Admitted to the Mathematics PhD program. Independent research and advanced study for students working on their doctoral research, dissertation and/or final examination. Students must have graduate degree-seeking status and should check with their major advisor/committee chair before enrolling for 800 credit. Typically offered Fall, Spring, and Summer. S, U grading.