Courses
and Programs 1995-1997 Courses
and Programs 1995-1997Math 10. High School Algebra. (4-0) Cr. 0. F.S.SS. For students who do not have adequate facility with topics from high school algebra or do not meet the algebra admission requirement. All students should initially enroll in Math 10. The course is divided into tracks of one- and two-semester lengths. For most students a diagnostic exam will determine which track must be taken, while those not meeting the algebra admission requirement must take a two-semester track. Students will receive a grade in Math 25 or 30 respectively depending on the level of material covered. Satisfactory completion of Math 30 is recommended for students planning to take Math 140 or 151, while Math 25 is sufficient for Math 104, 105, 150, 195, Stat 101 or 105. Students must complete Math 30 to remove a deficiency. Topics include signed numbers, polynomials, rational and radical expressions, exponential and logarithmic expressions, and equations. Offered on a satisfactory-fail basis only. Developmental math fee.
Math 20. High School Geometry. (4-0) Cr. 0. S. For students who do not meet the geometry admission requirement. Elements of Euclidean geometry including congruence, parallel lines, circles, similar polygons, perimeters, areas, surface areas, and volumes. Offered on a satisfactory-fail basis only. Developmental math fee.
Math 25. High School Algebra. (4-0) Cr. 0. F.S.SS. For students who do not have adequate facility with topics from high school algebra or do not meet the algebra admission requirement. All students should initially enroll in Math 10. The course is divided into tracks of one- and two-semester lengths. For most students a diagnostic exam will determine which track must be taken, while those not meeting the algebra admission requirement must take a two-semester track. Students will receive a grade in Math 25 or 30 respectively depending on the level of material covered. Satisfactory completion of Math 30 is recommended for students planning to take Math 140 or 151, while Math 25 is sufficient for Math 104, 105, 150, 195, Stat 101 or 105. Students must complete Math 30 to remove a deficiency. Topics include signed numbers, polynomials, rational and radical expressions, exponential and logarithmic expressions, and equations. Offered on a satisfactory-fail basis only. Developmental math fee.
Math 30. High School Algebra. (4-0) Cr. 0. F.S.SS. For students who do not have adequate facility with topics from high school algebra or do not meet the algebra admission requirement. All students should initially enroll in Math 10. The course is divided into tracks of one- and two-semester lengths. For most students a diagnostic exam will determine which track must be taken, while those not meeting the algebra admission requirement must take a two-semester track. Students will receive a grade in Math 25 or 30 respectively depending on the level of material covered. Satisfactory completion of Math 30 is recommended for students planning to take Math 140 or 151, while Math 25 is sufficient for Math 104, 105, 150, 195, Stat 101 or 105. Students must complete Math 30 to remove a deficiency. Topics include signed numbers, polynomials, rational and radical expressions, exponential and logarithmic expressions, and equations. Offered on a satisfactory-fail basis only. Developmental math fee.
Math 100. Orientation in Mathematics. (1-0) Cr. R. F. For new majors. Issues to consider in planning a program of study. Sources of general information and perspectives concerning mathematics. Discussion of possible areas of study or careers. Offered on a satisfactory-fail basis only.
Math 104. Introduction to Probability and Matrices. (3-0). Cr. 3. F.S. Prereq: Satisfactory performance on placement exam, 2 years of high school algebra, 1 year of high school geometry. Permutations, combinations, probability, binomial and multinomial theorems, matrices, Markov chains, expected value. Either 104 or 150 may be counted toward graduation, but not both.
Math 105. Introduction to Mathematical Ideas. (3-0) Cr. 3. F.S. Prereq: Satisfactory performance on placement exam, 2 years of high school algebra, 1 year of high school geometry. Topics from mathematics and mathematical applications with emphasis on their nontechnical content.
Math 140. Fundamentals of Algebra for Science and Higher Mathematics. (4-0) Cr. 3. F.S.SS. Prereq: Satisfactory performance on placement exam, 2 years of high school algebra; 1 year of high school geometry. Coordinate geometry, complex numbers, quadratic and polynomial equations, functions, graphing, systems of equations, exponential and logarithmic functions, determinants. Students in the College of Liberal Arts and Sciences may not count Math 140, 141, 142, or 195 toward Group III of the General Education Requirements.
Math 141. Trigonometry. (2-0) Cr. 2. F.S.SS. Prereq: Satisfactory performance on placement exam, 2 years of high school algebra; 1 year of high school geometry, or enrollment in 140. May be taken concurrently with 140. Trigonometric functions and their inverses, solving triangles, trigonometric equations, polar coordinates, graphing. Students in the College of Liberal Arts and Sciences may not count Math 140, 141, 142, or 195 toward Group III of the General Education Requirements. Only one of 141, 142 may count toward graduation.
Math 142. Trigonometry and Analytic Geometry. (3-0) Cr. 3. F.S.SS. Prereq: Satisfactory performance on placement exam, 2 years of high school algebra, 1 year of high school geometry, or enrollment in 140. May be taken concurrently with 140. Trigonometric functions and their inverses, solving triangles, trigonometric equations, polar coordinates, standard equations of lines and conic sections, conics in polar form, graphing of rational functions, quadric surfaces. Students in the College of Liberal Arts and Sciences may not count Math 140, 141, 142, or 195 toward Group III of the General Education Requirements. Only one of 141, 142 may count toward graduation.
Math 150. Discrete Mathematics for Business and Social Sciences. (3-0) Cr. 3. F.S.SS. Prereq: Satisfactory performance on placement exam, 2 years of high school algebra, 1 year of high school geometry. Linear equations and inequalities, linear programming, matrix algebra, discrete probability. Either 104 or 150 may be counted toward graduation, but not both.
Math 151. Calculus for Business and Social Sciences. (3-0) Cr. 3. F.S.SS. Prereq: Satisfactory performance on placement exam, 2 years of high school algebra, 1 year of high school geometry. Differential calculus, integral calculus, introduction to max-min theory for functions of two variables. Will not serve as prerequisite for 265 or 266. Only one of 151 or 160 or the sequence 165-166 may be counted toward graduation.
Math 160. Calculus for Economics and Biological Sciences. (4-0) Cr. 4. F.S. Prereq: Satisfactory performance on placement exam, 2 years of high school algebra, 1 year of geometry, 1 semester of trigonometry or enrollment in 141 or 142. Analytic geometry, differentiation and integration of elementary functions. Will not serve as a prerequisite for 265 or 266. Only one of 151 or 160 or the sequence 165-166 may be counted toward graduation.
Math 161. Intermediate Analytic Methods in Biology, (4-0) Cr. 4. S. Prereq: 160 or 166. Modeling growth and population by means of differential equations, multivariate analysis, matrix, and other discrete methods.
Math 165. Calculus I. (4-0) Cr. 4 each. F.S.SS. Prereq: Satisfactory performance on placement exam, 2 years of high school algebra, 1 year of geometry, 1 semester of trigonometry or enrollment in 141 or 142; 165H: High math placement scores recommended but not required. Functions, limits and continuity, differentiation, integration, polar coordinates, series.165H, 166H: Preference will be given to students in the University Honors Program. Only one of 151 or 160 or the sequence 165-166 may be counted toward graduation.
Math 165H. Calculus I. (4-0) Cr. 4 each. F. Prereq: High math placement scores recommended but not required. Functions, limits and continuity, differentiation, integration, polar coordinates, series.165H, 166H: Preference will be given to students in the University Honors Program. Only one of 151 or 160 or the sequence 165-166 may be counted toward graduation.
Math 166. Calculus II. (4-0) Cr. 4 each. F.S.SS. Prereq: Grade of C- or better in 165 or 165H or high math placement scores. Functions, limits and continuity, differentiation, integration, polar coordinates, series.165H, 166H: Preference will be given to students in the University Honors Program. Only one of 151 or 160 or the sequence 165-166 may be counted toward graduation.
Math 166H. Calculus II. (4-0) Cr. 4 each. F.S. Prereq: Permission of the instructor; and 165, 165H, or high math placement scores. Functions, limits and continuity, differentiation, integration, polar coordinates, series.165H, 166H: Preference will be given to students in the University Honors Program. Only one of 151 or 160 or the sequence 165-166 may be counted toward graduation.
Math 195. Mathematics for Elementary Education I. (4-0) Cr. 4. F.S. Prereq: Satisfactory performance on placement exam, 2 years of high school algebra, 1 year of high school geometry, enrollment in programs elementary education or child development. Language of sets, systems of whole numbers, numeration and algorithms for whole numbers, topics from number theory, geometric concepts. Students in the College of Liberal Arts and Sciences may not count Math 140, 141, 142, or 195 toward Group III of the General Education Requirements.
Math 196. Mathematics for Elementary Education II. (2-0) Cr. 2. S. Prereq: 195. Topics in mathematics of current importance to prospective elementary teachers.
Math 205. Computer Programming in FORTRAN. Same as Com S 205. See Computer Science.
Math 215. Numerical Methods and FORTRAN Programming. Same as Aer E 215. See Aerospace Engineering.
Math 252. Topics in Optimization. (3-0) Cr. 3. F. Prereq: 104 or 150, and one of 151, 160, 165. Partial and total derivatives, optimization problems including the Lagrange multiplier rule, the Kuhn-Tucker conditions, second order conditions, post-optimal analysis.
Math 265. Elementary Multivariable Calculus. (4-0) Cr. 4. F.S.SS. Prereq: Grade of C- or better in 166 or 166H. Vectors, functions of several variables, gradients, multiple integrals.
Math 265H. Elementary Multivariable Calculus. (4-0) Cr. 4. F.S.SS. Prereq: Permission of the instructor; and 166 or 166H. Vectors, functions of several variables, gradients, multiple integrals. Preference will be given to students in the University Honors Program.
Math 266. Elementary Differential Equations. (3-0) Cr. 3. F.S.SS. Prereq: Grade of C- or better in 166. Elementary theory and applications of ordinary differential equations, matrices and solutions of linear equations, eigenvalue methods for systems of linear differential equations.
Math 267. Elementary Differential Equations and Laplace Transforms. (4-0) Cr. 4. F.S.SS. Prereq: Grade of C- or better in 166. Same as 266 but also including Laplace transforms and series solutions to ordinary differential equations.
Math 268. Laplace Transforms. (1-0) Cr. 1. F. Prereq: 266. Laplace transforms and series solutions to ordinary differential equations. Together, 266 and 268 are the same as 267.
Math 290. Special Problems. Cr. 1 to 3 each time taken.
H. Honors
Math 298. Cooperative Education. Cr. R. F.S.SS. Prereq: Permission of the department cooperative education coordinator; sophomore classification. Required of all cooperative education students. Students must register for these courses prior to commencing each work period.
Math 301. Introduction to Abstract Algebra. (3-0) Cr. 3 each. F.S. Prereq: 166 and 307 or 317. Introduction to the theory of groups and rings. Open to graduate students for minor graduate credit only.
Math 302. Introduction to Abstract Algebra. (3-0) Cr. 3 each. S. Prereq: 301. Theory of fields, abstract vector spaces, and linear algebra. Open to graduate students for minor graduate credit only.
Math 304. Introductory Combinatorics. (3-0) Cr. 3. F. Prereq: 166. Permutations, combinations, binomial coefficients, inclusion-exclusion principle, discrete probability, classical probability. Additional topics selected from recurrence relations, generating functions, random walks, and Markov chains. Open to graduate students for minor graduate credit only.
Math 307. Theory of Matrices. (3-0) Cr. 3. F.S.SS. Prereq: 2 semesters of calculus. The algebra of matrices including vector spaces, simultaneous linear equations, determinants, quadratic forms, eigenvalues, and diagonalization over the real and complex numbers. Open to graduate students for minor graduate credit only. Only one of 307, 317 may be counted toward graduation.
Math 308. Application of Linear Algebra to Discrete Optimization. (3-0) Cr. 3. S. Prereq: 307 or 317. Linear programming and topics chosen from game theory, transportation and assignment problems, discrete dynamic processes, and multiple objective linear programming. Open to graduate students for minor graduate credit only.
Math 314. Graphs and Networks. (3-0) Cr. 3. S. Prereq: 166. Graphs, directed graphs, and trees. Connectedness. Graph colorings. Eulerian and Hamiltonian chains. Matching and covering. Optimization for networks. Applications. Open to graduate students for minor graduate credit only.
Math 317. Theory of Linear Algebra. (4-0) Cr. 4. F.S. Prereq: 166. Systems of linear equations, determinants, vector spaces, inner product spaces, linear transformations, eigenvalues and eigenvectors. Emphasis on writing proofs and results. Open to graduate students for minor graduate credit only. Only one of 307, 317 may be counted toward graduation.
Math 331. Topology. (3-0) Cr. 3. S. Prereq: 307 or 317. Topological properties of metric spaces with emphasis on Rn, sequences, continuous functions, completeness, compactness. Open to graduate students for minor graduate credit only.
Math 341. Introduction to Theory of Probability and Statistics. Same as Stat 341. See Statistics.
Math 342. Introduction to Theory of Probability and Statistics. Same as Stat 342. See Statistics.
Math 365. Complex Variables with Applications. (3-0) Cr. 3. F.S. Prereq: 265. Functions of a complex variable, including differentiation, integration and series expansions, residues, evaluation of integrals, conformal mapping. Open to graduate students for minor graduate credit only. Only two of 365, 385, 395 may be counted toward graduation.
Math 385. Introduction to Partial Differential Equations. (3-0) Cr. 3. F.S.SS. Prereq: 265 and one of 266, 267. Fourier series, separation of variable methods, Bessel series and Legendre polynomials, introduction to Sturm-Liouville theory. Open to graduate students for minor graduate credit only. Only two of 365, 385, 395 may be counted toward graduation.
Math 395. Intermediate Engineering Mathematics. (4-0) Cr. 4. F.S.SS. Prereq: 265 and 267. Complex variables and analytic functions, complex integration techniques, complex series, Fourier series, separation of variables in partial differential equations, Fourier transforms. Open to graduate students for minor graduate credit only. Only two of 365, 385, 395 may be counted toward graduation.
Math 398. Cooperative Education. Cr. R. F.S.SS. Prereq: Permission of the department cooperative education coordinator; junior classification. Required of all cooperative education students. Students must register for these courses prior to commencing each work period.
Math 414. Advanced Calculus. (3-0) Cr. 3 each. F.SS. Prereq: 307 or 317. A careful development of calculus of functions of a real variable: limits, continuity, differentiation, integration, series. Open to graduate students for minor graduate credit only.
Math 415. Advanced Calculus. (3-0) Cr. 3 each. S. Prereq: 414. Calculus of functions from Rn to Rm, linear and topological properties of Rn, limits, continuity, differentiation, implicit functions, multiple integrals, line and surface integrals, Stokes' theorem. Open to graduate students for minor graduate credit only.
Math 421. Mathematical Logic. (3-0) Cr. 3. Alt. S., offered 1996. Prereq: 301 or 307 or 317. Validity, consistency, provability, completeness, definability, and decision problems for propositional calculus, predicate calculus, and generalized mathematical theories. Open to graduate students for minor graduate credit only.
Math 426. Mathematical Methods for the Physical Sciences. (3-0) Cr. 3. F. Prereq: 385. Primarily for first-year graduate students in physics and chemistry. (Not a substitute for Math 526-527.) Emphasis on techniques needed for quantum mechanics and electrodynamics. Fourier integrals, complex variables and contour integration, ordinary differential equations of hypergeometric type, Green's functions, Sturm-Liouville problems and orthogonal functions, boundary-value problems for partial differential equations. Open to graduate students for minor graduate credit only.
Math 435. Geometry. (3-0) Cr. 3 each. Yr. Prereq: 307 or 317. Euclidean geometry through properties invariant under similarity transformations, projective geometry by use of synthetic and analytic methods, topics chosen from finite geometry, non-Euclidean geometry and crystallography. Open to graduate students for minor graduate credit only.
Math 436. Geometry. (3-0) Cr. 3 each. Yr. Prereq: 435. Euclidean geometry through properties invariant under similarity transformations, projective geometry by use of synthetic and analytic methods, topics chosen from finite geometry, non-Euclidean geometry and crystallography. Open to graduate students for minor graduate credit only.
Math 439. Mathematics of Fractals. (3-0) Cr. 3. S. Prereq: 265; some knowledge of programming. Topology of metric spaces; iterated function systems; algorithms for generation of fractals; fractal dimension; Julia sets and the Mandelbrot set; applications to chaotic systems. Open to graduate students for minor graduate credit only.
Math 450. Number Theory. (3-0) Cr. 3 Alt. S., offered 1997. Prereq: 301. Properties of the integers. Diophantine equations, prime number distribution and representation problems. Open to graduate students for minor graduate credit only.
Math 465. Advanced Calculus for Applied Mathematics. (4-0) Cr. 4. F.SS. Prereq: 265. Certain frequently applied mathematical concepts presented with enough theory to promote understanding of applications. Calculus of functions of several variables, including vector calculus, line, surface, and multiple integrals, Stokes' theorem, divergence theorem, infinite series. Open to graduate students for minor graduate credit only.
Math 471. Computational Linear Algebra and Fixed Point Iteration. Same as Com S 471. (3-0) Cr. 3. F.S. Prereq: 265 and either 266, or 267; knowledge of FORTRAN or C. Computational error, solutions of linear systems, least square methods, similarity methods for eigenvalues, non-linear equations, fixed point iteration in one and several variables, Newton's method in several variables. Open to graduate students for minor graduate credit only.
Math 473. Introduction to Scientific Computation. (3-0) Cr. 3. F.S.SS. Prereq: 265 and either 266 or 267; knowledge of FORTRAN or C. Use of high quality software to solve systems of linear equations, solve nonlinear equations, interpolate data, integrate functions, integrate systems of differential equations, optimize functions of one and two variables. Emphasis on reasons for success or failure of programs. Open to graduate students for minor graduate credit only.
Math 481. Numerical Solution of Differential Equations and Interpolation. Same as Com S 481. (3-0) Cr. 3. S.SS. Prereq: 265 and either 266 or 267; knowledge of FORTRAN or C. Orthogonal polynomials, least square and spline methods, numerical differentiation and integration, Euler, Taylor, Runge-Kutta, and predictor-corrector methods for solution of systems of ordinary differential equations. Open to graduate students for minor graduate credit only.
Math 489. History of Mathematics. (3-0) Cr. 3. S. Prereq: 6 credits in mathematics at the 300 level or above. History of mathematical ideas found in the undergraduate curriculum. Topics and treatment may vary with instructor. Open to graduate students for minor graduate credit only.
Math 490. Independent Study. Cr. 1 to 3 each time taken. Prereq: 301 or 317; 6 credits in mathematics. No more than 9 credits of Math 490 may be counted toward graduation.
H. Honors
Math 491. Undergraduate Thesis. Cr. 2 or 3. Writing a formal mathematics paper. Upon approval by the department, the paper will satisfy the departmental advanced English requirement.
Math 497. Teaching Secondary School Mathematics. Same as SecEd 497. (3-0) Cr. 3. F. Prereq: 15 credits in college mathematics. Techniques for teaching secondary mathematics students, use of calculators in secondary schools.
Math 498. Cooperative Education. Cr. R. F.S.SS. Prereq: Permission of the department cooperative education coordinator; senior classification. Required of all cooperative education students. Students must register for these courses prior to commencing each work period.
Math 504. Abstract Algebra. (3-0) Cr. 3 each. Yr. Prereq: 302. Algebraic systems and their morphisms, including groups, rings, modules, and fields.
Math 505. Abstract Algebra. (3-0) Cr. 3 each. Yr. Prereq: 302. Algebraic systems and their morphisms, including groups, rings, modules, and fields.
Math 507. Numerical Solution of Ordinary Differential Equations. Same as Com S 507. (3-0) Cr. 3. F.SS. Prereq: 481 or 465 or 415; knowledge of FORTRAN or C. One step methods for initial value problems, one-step methods for systems, multistep methods, boundary-value problems. Examples using university computers.
Math 508. Numerical Solution of Partial Differential Equations. (3-0) Cr. 3. S. Prereq: 385 and one of 471 and 481; knowledge of FORTRAN or C. Analysis of error and stability of finite difference methods. Hyperbolic systems, characteristics, conservation laws, shocks. Applications to heat transfer and fluid mechanics. The finite element method. Direct and iterative solution of large linear systems.
Math 509. Computational Methods of Linear Algebra. Same as Com S 509. (3-0) Cr. 3. F. Prereq: 307 or 317; knowledge of FORTRAN or C. Numerical methods for solving linear systems of equations and linear least squares problems, and for computing eigenvalues and eigenvectors of matrices, symmetric or not. Matrix factorizations, iteration methods. Analysis of well- and ill-conditioning of computational problems, and stability of methods. Practical computing exercises.
Math 511. Functions of a Single Complex Variable. (3-0) Cr. 3 each. 511: F.; 512: S. Prereq: 465 or 415. Theory of analytic functions, integration, topology of the extended complex plane, singularities and residue theory.
Math 512. Functions of a Single Complex Variable. (3-0) Cr. 3 each. S. Prereq: 511. Conformal mappings, theory of meromorphic and entire functions, analytic continuation. Infinite products.
Math 513. Numerical Solution of Integral Equations. (3-0) Cr. 3. Alt. S., offered 1996. Prereq: 471 or 509 and a knowledge of FORTRAN or C. Collocation, Galerkin, expansion and product integration methods. First and second kind integral equations, Volterra equations, weakly singular integral equations.
Math 514. Measure Theory. (3-0) Cr. 3. F. Prereq: 414. Measure and integration, construction of measures (Lebesgue and Lebesgue-Stieltjes measures), LP spaces, Hilbert spaces, differentiation, Radon-Nikodym theory, product measures, finite measure spaces. Primarily for statistics students.
Math 515. Real Analysis I. (3-0) Cr. 3. F. Prereq: 414. Measure and integration, differentiation, topology of metric spaces, Lpspaces, Hilbert spaces.
Math 516. Real Analysis II. (3-0) Cr. 3. S. Prereq: 515. Elementary theory of Banach spaces. Product integration, Fubini's theorem. Decomposition of measures; differentiation theory. Fourier analysis, theory of distributions.
Math 521. Partial Differential Equations of Applied Mathematics. (3-0) Cr. 3. S. Prereq: 365, 385. Solution methods for classical linear partial differential equations. Series methods, Laplace and Fourier transforms, Green's functions. Method of characteristics for first order equations.
Math 522. Perturbation Methods in Applied Mathematics. (3-0) Cr. 3. F. Prereq: 307; one of 365, 414. Asymptotic and perturbation methods, asymptotic evaluation of integrals, regular and singular perturbation expansions, WKB method, matched asymptotics and method of multiple scales.
Math 525. Numerical Analysis of High Performance Computing. Same as Com S 525, Cpr E 525. (3-0) Cr. 3. S. Prereq: Cpr E 308, or one of Math 471, 473 or 481; experience in scientific programming; knowledge of FORTRAN or C. Development, analysis, and testing of efficient numerical methods for use on current state-of-the-art high performance computers. Applications of the methods to the students' areas of research.
Math 527. Mathematics of Complex Physical Systems. (3-0) Cr. 3. S. Prereq: 365 or 426; 385. Classical "molecular" dynamics, stochastic modeling and Monte-Carlo techniques, random walks and diffusion processes, nonlinear dynamics, self-organization and pattern formation.
Math 528. Special Functions. (3-0) Cr. 3. S. Prereq: 365. A unified treatment of the special functions arising in applied mathematics. Topics chosen from: gamma and beta functions, orthogonal polynomials, Legendre and Bessel functions, elliptic integrals, and other functions of hypergeometric type.
Math 531. Introduction to Functional Analysis. (3-0) Cr. 3 each. Alt. yr., offered 1995-96. Prereq: Permission of instructor. Fundamental theory of normed linear spaces and algebras emphasizing aspects that provide a framework for study of boundary-value problems, eigenvalue problems, harmonic analysis, and analytic function theory. Hahn-Banach theorem, Banach-Steinhaus theorem, Gelfand representation, elementary spectral theory for operators in Hilbert space.
Math 532. Introduction to Functional Analysis. (3-0) Cr. 3 each. Alt. yr., offered 1995-96. Prereq: Permission of instructor. Fundamental theory of normed linear spaces and algebras emphasizing aspects that provide a framework for study of boundary-value problems, eigenvalue problems, harmonic analysis, and analytic function theory. Hahn-Banach theorem, Banach-Steinhaus theorem, Gelfand representation, elementary spectral theory for operators in Hilbert space.
Math 534. Topology. (3-0) Cr. 3. F. Prereq: Permission of instructor. Introduction to general topology. Emphasizes topics useful in analysis.
Math 537. Algebraic Topology. (3-0) Cr. 3. Alt. S., offered 1997. Prereq: 331 or 534; 301. Foundations of algebraic topology. Simplicial complexes. Simplicial and singular homology groups.
Math 540. Seminar in Mathematics Education. (3-0) Cr. 3. Offered on a 3-year cycle, offered SS. 1996. Prereq: Enrollment in the master of school mathematics program or professional studies in education. Research studies in mathematics learning and teaching, exemplary practices in mathematics education, and current state and national trends in the mathematics curriculum in grades K-12.
Math 545. Intermediate Calculus. (4-0) Cr. 4. Offered on a 3-year cycle, offered SS. 1998. Prereq: 3 semesters of calculus and enrollment in the master of school mathematics program. Further develop-ment of the fundamental concepts of calculus and their applications with an emphasis on a constructivist approach to learning, cooperative groups, problem solving, the use of technology.
Math 546. Algorithms in Analysis and Their Computer Implementation. (2-2) Cr. 3. Offered on a 3-year cycle, offered SS. 1998. Prereq: 3 semesters in calculus or concurrent enrollment in 545 and enrollment in the master of school mathematics program. The use of technology in secondary mathematics with an emphasis on the exploration and implementation of algorithms.
Math 547. Discrete Mathematics and Applications. (4-0) Cr. 4. Offered on a 3-year cycle, offered SS. 1997. Prereq: Enrollment in the master of school mathematics program. Applications of graph theory, game theory, linear programming, recursion, combinatorics and algebraic structures. Issues in integrating discrete topics into the secondary curriculum. Use of the computer to explore discrete mathematics.
Math 549. Intermediate Geometry. (3-0) Cr. 3. Offered on a 3-year cycle, offered SS. 1997. Prereq: 435 or equivalent and enrollment in the master of school mathematics program. A study of geometry with emphasis on metrics, the group of isometries, the group of similarities, and the affine group. Specific spaces studied normally include the Euclidean plane, the 2-sphere, and projective 2-space. Emphasis on analytical methods.
Math 551. Design Theory and Association Schemes. (3-0) Cr. 3. F. Prereq: 301 or 304 or 307 or 317. Combinatorial designs and Latin squares. Construction methods including finite fields. Error-correcting codes. Adjacency matrices and algebraic combinatorics.
Math 552. Enumerative Combinatorics and Ordered Sets. (3-0) Cr. 3. S. Prereq: 301 or 304 or 307 or 317. Ordered sets and lattices. Generating functions. Möbius inversion and other enumerative methods.
Math 554. Introduction to Stochastic Processes. Same as Stat 554. (3-0) Cr. 3. S. Prereq: Stat 542. Markov chains on discrete spaces in discrete and continuous time (random walks, Poisson processes, birth and death processes) and their long-term behavior. Elementary introduction to Brownian motion and second order processes. Optional topics may include branching processes.
Math 555. Theory of Stochastic Processes. Same as Stat 555. (3-0) Cr. 3. F. Prereq: 514 or 515 , Stat 542. Martingales. Markov processes on continuous spaces and their qualitative behavior. Wiener processes. Optional topics may include elementary theory of Ito calculus and diffusions, linear stochastic systems, advanced topics in branching process.
Math 557. Ordinary Differential Equations. (3-0) Cr. 3 each. F. Prereq: 266 or 267; 307 or 317; 415 or 465. The initial-value problem, existence and uniqueness theorems, continuous dependence on parameters, linear systems, stability and asymptotic behavior of solutions, dynamical systems, two-point boundary-value problems.
Math 558. Ordinary Differential Equations. (3-0) Cr. 3 each. Alt. S., offered 1997. Prereq: 266 or 267; 307 or 317; 415 or 465. The initial-value problem, existence and uniqueness theorems, continuous dependence on parameters, linear systems, stability and asymptotic behavior of solutions, dynamical systems, two-point boundary-value problems.
Math 561. Dynamical Systems. (3-0) Cr. 3. Alt. S., offered 1997. Prereq: 414. Smooth mappings and flows on manifolds. Fixed points, stable, unstable and center manifolds, normal forms. Structural stability, bifurcations. Horseshoe maps, introduction to chaotic behavior.
Math 562. Manifolds, Tensors and Differential Geometry. (3-0) Cr. 3. Alt. S., offered 1996. Prereq: 414. Geometry of curves and surfaces. Manifolds, coordinate systems. Tensors, differential forms, Riemannian metrics. Connections, covariant differentiation, curvature tensors.
Math 564. Theory of Groups. (3-0) Cr. 3. Alt. S., offered 1997. Prereq: 504. Commutators, p-groups, nilpotent groups, solvable groups, permutation groups, free groups, semidirect products, introduction to representation theory.
Math 567. Boolean Algebras. (3-0) Cr. 3. Alt. S., offered 1997. Prereq: 302 or 421. Structure of Boolean algebras and their representations. Stone spaces and duality. Atomicity, completeness, distributivity, operators, extensions of homomorphisms. Examples and applications from mathematical logic and topology.
Math 568. Theory of Rings. (3-0) Cr. 3. Alt. S., offered 1996. Prereq: 504. Selected topics from the structure theory for various classes of rings, including the theory of radicals and rings with chain conditions.
Math 571. Mathematical Logic. (3-0) Cr. 3 each. Alt. yr., offered 1996-97. Prereq: 421. Algebraic structures in logical systems, recursive functions, consistency, undecidability and incompleteness of axiomatic theories, results of Gentzen and Gödel, theory of models, ultraproducts and ultralimits, nonstandard analysis.
Math 572. Mathematical Logic. (3-0) Cr. 3 each. Alt. yr., offered 1996-97. Prereq: 421. Algebraic structures in logical systems, recursive functions, consistency, undecidability and incompleteness of axiomatic theories, results of Gentzen and Gödel, theory of models, ultraproducts and ultralimits, nonstandard analysis.
Math 573. Random Signal Analysis and Kalman Filtering. Same as Aer E 573, E E 573, M E 573. (3-0) Cr. 3. F. Prereq: 341 or 395 or Aer E 431 or M E 360 or 411. Elementary notions of probability. Random processes. Autocorrelation and spectral functions. Estimation of spectrum from finite data. Response of linear systems to random inputs. Discrete and continuous Kalman filter theory and applications. Smoothing and prediction. Linearization of nonlinear dynamics.
Math 574. Optimal Control. Same as Aer E 574, E E 574, M E 574. (3-0) Cr. 3. S. Prereq: 577. The optimal control problem. Variational approach. Pontryagin's principle. Hamilton-Jacobi equation. Dynamic programming. Time-optimal, minimum fuel, minimum energy control systems. The regulator problem. Structures and properties of optimal controls.
Math 575. Introduction to Robust Control. Same as E E 575. See Electrical Engineering.
Math 576. Digital Feedback Control Systems. Same as Aer E 576, E E 576, M E 576. (3-0) Cr. 3. F. Prereq: 415 or Aer E 432 or E E 475 or M E 411 or 414; and Math 267. Sampled-data, discrete data, and the z-transform. Design of digital control systems using transform methods: root locus, frequency response and direct design methods. Design using state-space methods. Controllability, observability, pole placement, state estimators. Digital filters in control systems. Microcomputer implementation of digital filters. Finite wordlength effects. Linear quadratic optimal control in digital control systems. Simulation of digital control systems.
Math 577. Modern Control Systems I. Same as Aer E 577, E E 577, M E 577. (3-0) Cr. 3. F. Prereq: 415 Aer E 431 or M E 414; and Math 307 or 317. State variable and input-output descriptions of linear continuous-time and discrete-time systems. Solution of linear dynamical equations. Controllability and observability of linear dynamical systems. Canonical descriptions of linear equations. Irreducible realizations of rational transfer function matrices. Canonical form dynamical equations. State feedback. State estimators. Decoupling by state feedback. Design of feedback systems. Stability of linear dynamical systems.
Math 578. Modern Control Systems II. Same as Aer E 578, E E 578, M E 578. (3-0) Cr. 3. S. Prereq: 577. Well-posedness of nonlinear control systems. Approximate analysis methods. Krylov-Boguliubov method. Poincaré perturbation method and describing function method. Lyapunov stability theory. Absolute stability of feedback systems. Input-output stability. Large-scale systems.
Math 579. Adaptive Control. Same as E E 579. See Electrical Engineering.
Math 581. Axiomatic Set Theory. (3-0) Cr. 3 . Alt. S., offered 1996. Prereq: Permission of instructor. Axiomatic considerations, model and proof theory, Zermelo-Frćnkel axioms, classical theorems, transfinite methods, ordinal and cardinal numbers and their arithmetic. Von Neumann-Bernays-Gödel axioms and inaccessible cardinals. Survey of consistency and independence results.
Math 584. Category Theory. (3-0) Cr. 3. Alt. F., offered 1996. Prereq: 302. Categories and functors and their applications.
Math 585. Partial Differential Equations. (3-0) Cr. 3 each. Alt. yr., offered 1995-96. Prereq: 415 or 515 or 521. First order equations and systems; wave, heat and potential equations, Huygen's principle, fundamental solutions; maximum principle; variational methods.
Math 586. Partial Differential Equations. (3-0) Cr. 3 each. Alt. yr., offered 1995-96. Prereq: 415 or 515 or 521. First order equations and systems; wave, heat and potential equations, Huygen's principle, fundamental solutions; maximum principle; variational methods.
Math 588. General Theory of Algebraic Structures. (3-0) Cr. 3 each. Alt. Yr., offered 1995-96. Prereq: 504. Subalgebras, homomorphisms, congruence relations, and direct products. Lattices and closure operators. Varieties and quasivarieties of algebras, free algebras, Birkhoff's theorems, clones, Mal'cev conditions. Advanced topics.
Math 589. General Theory of Algebraic Structures. (3-0) Cr. 3 each. Alt. Yr., offered 1995-96. Prereq: 504. Subalgebras, homomorphisms, congruence relations, and direct products. Lattices and closure operators. Varieties and quasivarieties of algebras, free algebras, Birkhoff's theorems, clones, Mal'cev conditions. Advanced topics.
Math 590. Special Topics. Cr. var.
Math 599. Creative Component. Cr. var.
Math 610. Seminar. Cr. var.
Math 690. Advanced Topics. Cr. var. Prereq: Permission of instructor.
A. Algebra
B. Functional Analysis
C. Measure Theory
D. Approximation Theory
E. Linear Algebra
F. Calculus of Variations
H. Harmonic Analysis
L. Logic and Foundations
M. Complex Analysis
N. Numerical Analysis
O. Ordinary Differential Equations
P. Partial Differential Equations
S. Set Theory
T. Topology
U. Automata Theory
V. Optimization Theory
W. Probability and Stochastic Processes
Y. Special Functions
Math 699. Research.