Graduate Credit CoursesThe following is a complete listing of all mathematics courses which carry graduate credit at LSU. 4005 Geometry (3) S Prereq: MATH 2040. The foundations of geometry, including work in Euclidean and nonEuclidean geometries. 4023 Applied Algebra (3) S Prereq: MATH 2085 or equivalent. Credit will not be given for both this course and MATH 4200. Finite algebraic structures relevant to computers: groups, graphs, groups and computer design, group codes, semigroups, finitestate machines. 4024 Mathematical Models (3) S Prereq: MATH 1552 and credit or registration in MATH 2085; or equivalents. Construction, development, and study of mathematical models for real situations; basic examples, model construction, Markov chain models, models for linear optimization, selected case studies. 4025 Optimization Theory and Applications (3) F Prereq: MATH 2057 and credit or registration in MATH 2085; or equivalent. Basic methods and techniques for solving optimization problems; ndimensional geometry and convex sets; classical and search optimization of functions of one and several variables; linear, nonlinear, and integer programming. 4027 Differential Equations (3) Su Prereq: MATH 2057 and 2085. Ordinary differential equations, with attention to theory. 4031 Advanced Calculus I (3) F Prereq: MATH 2057 and 2085; or equivalent. Differential and integral calculus of real and vectorvalued functions of several real variables. 4032 Advanced Calculus II (3) S Prereq: MATH 4031 or equivalent. Vector integral calculus, Stokes' theorem, series, orthogonal functions, selected related topics. 4035 Advanced Calculus of Several Variables (3) S Prereq: MATH 4031 or equivalent, and 2085. Topology of ndimensional space, differential calculus in ndimensional space, inverse and implicit function theorems. 4036 Complex Variables (3) F,S,Su Prereq: MATH 2057. Analytic functions, integration, power series, residues, and conformal mapping. 4038 Mathematical Methods in Engineering (3) F,S Prereq: MATH 2065 or 2070 or 2090. Also offered as ME 4563. Vector analysis; solution of partial differential equations by the method of separation of variables; introduction to orthogonal functions using Bessel functions. 4039 Introduction to Topology (3) V Prereq: MATH 4031 or equivalent. Examples and classification of twodimensional manifolds, covering spaces, the Brouwer theorem, and other selected topics. 4050 Interest Theory (3) F, S Prereq: MATH 1550. Measurement of interest (including accumulated and present value factors), annuities certain, yield rates, amortization schedules and sinking funds, and bonds and related securities. 4055 Introduction to Probability (3) F Prereq: MATH 2057. Suggested for preparation for actuarial exams. Introduction to probability, emphasizing concrete problems and applications; combinatorial analysis, random variables, conditional probability, special distributions, law of large numbers, central limit theorem, and Markov chains. 4056 Mathematical Statistics (3) S Prereq: MATH 4055. Suggested for preparation for actuarial exams. Experimental design, sampling methods, nonparametric methods, hypothesis testing, and regression. 4058 Elementary Stochastic Process (3) Grad, S Prereq: MATH 3355 and 2085. Markov chains, Poisson process, and Brownian motion. 4065 Numerical Analysis I (3) F Prereq: MATH 2057. Some programming ability in Fortran, Pascal, or C. Newton's method, Lagrange interpolation, leastsquares approximation, orthogonal polynomials, numerical differentiation and integration, Gaussian elimination. 4066 Numerical Analysis II (3) S Prereq: MATH 4065 and one of the following: MATH 2065, 2070, 2090, 4027. Numerical solutions of initialvalue problems and boundaryvalue problems for ordinary and partial differential equations. 4153 Finite Dimensional Vector Spaces (3) S Prereq: MATH 2057 or 2085. Vector spaces, linear transformations, determinants, eigenvalues and vectors, and topics such as inner product spaces and canonical forms. 4158 Foundations of Mathematics (3) V Prereq: MATH 2057 or equivalent. Real number systems, sets, relations, product spaces, order, and cardinality. 4171 Theory of Graphs (3) S Prereq: MATH 2085 or equivalent. Fundamental concepts of undirected and directed graphs, trees, connectivity and traversability, planarity, colorability, network flows, matching theory, and applications. 4172 Combinatorics (3) F Prereq: MATH 2085 or equivalent. Topics selected from permutations and combinations, generating functions, principle of inclusion and exclusion, configurations and designs, matching theory, existence problems, applications. 4181 Elementary Number Theory (3) F Prereq: MATH 2057 or 2085. Divisibility, Euclidean algorithm, prime numbers, congruences, and topics such as Chinese remainder theorem and sums of integral squares. 4200 Abstract Algebra I (3) F Prereq: MATH 2085 or equivalent. Credit will not be given for both this course and MATH 4023. Elementary properties of sets, relations, mappings, integers; groups, subgroups, normal subgroups, quotient groups, homomorphisms, automorphisms, and permutation groups; elementary properties of rings. 4201 Abstract Algebra II (3) S Prereq: MATH 4200 or equivalent. Ideals in rings, factorization in polynomial rings, unique factorization and Euclidean domains, field extensions, splitting fields, finite fields, Galois theory. 4325 Fourier Transforms (3) V Prereq: MATH 1552 and at least one of MATH 2057, 2065, 2070, 2085, or 2090. For students majoring in mathematics, physics, or engineering. Fourier analysis on the real line, the integers, and finite cyclic groups; the fast Fourier transform; generalized functions; attention to modern applications and computational methods. 4340 Partial Differential Equations (3) V Prereq: either MATH 2057, 2090, and knowledge of Laplace transforms; or MATH 2057, 2065 or 2070, and 2085. Firstorder partial differential equations and systems, canonical secondorder linear equations, Green's functions, method of characteristics, properties of solutions, and applications. 4345 Special Functions (3) V Prereq: either MATH 2057 and 2090; or MATH 2057, 2065 or 2070, and 2085. SturmLiouville problems, orthogonal functions (Bessel, Laguerre, Legendre, Hermite), orthogonal expansions including Fourier series, recurrence relations and generating functions, Chebychev polynomials, and other topics. 4470 ErrorCorrecting Codes (3) V Prereq: MATH 2085 or 2090 or equivalent knowledge of linear algebra. Vector spaces over finite fields, basic properties of codes, examples of important codes and decoding schemes, bounds on sizes and rates of codes, the weight enumerator polynomial, perfect codes, and other topics. 4700 History of Mathematics (3) Grad, V Prereq: MATH 2057, and 2085; students entering the course should have a firm sense of what constitutes a proof. This course will have substantial mathematical content; topics such as early Greek mathematics, from Euclid to Archimedes; algebra and number theory from Diophantus to the present; the calculus of Newton and Leibniz; the renewed emphasis on rigor and axiomatic foundations in the 19th and 20th centuries; interactions of mathematics with technology and the natural sciences; biographies of significant mathematicians. 4999 Selected Readings in Mathematics (1  3 ) Prereq: consent of department. May be repeated for a max. of 9 sem. hrs. credit. 6300 Topics in Mathematics for Secondary Teachers (13) Grad, V Prereq: 6 sem. hrs. of mathematics at or above the level of 2040 or equivalent. May be taken for a max. of 6 sem. hrs. credit when topics vary. Areas of current interest to teachers of secondary school mathematics. 6301 Implementing the NCTM Standards I (3) Grad, V Prereq: May be taken for a max. of 9 sem. hrs. credit when topics vary. Enrollment is restricted to participants in the teachertraining and grantsupported programs. Topics for mathematics teachers (K5) to be selected from those in the Principles and Standards of School Mathematics of the National Council of Teachers of Mathematics. 6302 Implementing the NCTM Standards II (3) Grad, V Prereq: May be taken for a max. of 9 sem. hrs. of credit when topics vary. Enrollment is restricted to participants in the teachertraining and grantsupported programs. Topics for mathematics teachers (68) to be selected from those in the Principles and Standards of School Mathematics of the National Council of Teachers of Mathematics. 7200 Geometric and Abstract Algebra (3) Prereq: MATH 2085 or equivalent. Linear algebra, rings, finite fields, groups, multilinear algebra, other topics. 7210, 7211 Algebra I, II (3,3) 7210 offered S; 7211 offered Prereq: MATH 7200 or equivalent. Groups: Sylow theorems, finitely generated abelian groups; rings and modules: exact sequences, projective modules; fields: algebraic, transcendental, normal, separable field extensions; Galois theory, valuation theory, Noetherian and Dedekind domains, topics from commutative rings. 7280 Seminar in Commutative Algebra (1  3) V Prereq: consent of department. May be repeated for credit with consent of department. Advanced topics such as commutative rings, homological algebra, algebraic curves, or algebraic geometry. 7290 Seminar in Algebra and Number Theory (1  3) V Prereq: consent of department. May be repeated for credit with the consent of the department. Advanced topics such as algebraic number theory, algebraic semigroups, quadratic forms, or algebraic Ktheory. 7311 Real Analysis I (3) Prereq: Math 4032 or equivalent.Axiom of choice, Lebesgue measure and integration, convergence theorems, bounded variation and absolute continuity, differentiation, MinkowskiHolder inequalities, RieszFischer theorem. 7312 Measure and Integration (3) Prereq: Math 7311 or equivalent. Ascoli theorem, StoneWeierstrass theorem, HahnBanach theorem, uniform boundedness theorem, Hilbert spaces, weak topologies, general measure and integration, Riesz representation theorem, other related topics. 7320 Ordinary Differential Equations (3) S Prereq: MATH 2085 and 4031; or equivalent. Existence and uniqueness theorems, approximation methods, linear equations, linear systems, stability theory, other topics such as boundary value problems. 7330 Functional Analysis (3) V Prereq: Math 7312 or equivalent. Banach spaces and their generalizations; Baire category, BanachSteinhaus, open mapping, closed graph, and HahnBanach theorems; duality in Banach spaces, weak topologies; other topics such as commutative Banach algebras, spectral theory, distributions, and Fourier transforms. 7350 Complex Analysis (3) V Prereq: MATH 7311 or equivalent. Theory of holomorphic functions of one complex variable; path integrals, power series, singularities, mapping properties, normal families, other topics. 7360 Probability Theory (3) F Prereq: MATH 7311 or equivalent. Probability spaces, random variables and expectations, independence, convergence concepts, laws of large numbers, convergence of series, law of iterated logarithm, characteristic functions, central limit theorem, limiting distributions, martingales. 7370 Lie Groups and Representation Theory (3) V Prereq: MATH 7312, 7200, and 7510 or equivalent. Lie groups, Lie algebras, subgroups, homomorphisms, the exponential map. Also topics in finite and infinite dimensional representation theory. 7380 Seminar in Functional Analysis (1  3) V Prereq: consent of department. May be repeated for credit with consent of department. Advanced topics such as topological vector spaces, Banach algebras, operator theory, or nonlinear functional analysis. 7390 Seminar in Analysis (1  3) V Prereq: consent of department. May be repeated for credit with consent of department. Advanced topics such as harmonic analysis, partial differential equations, Lie group representation theory, several complex variables, or probability theory. 7400 Combinatorial Theory (3) S Prereq: MATH 7200 or equivalent. Problems of existence and enumeration in the study of arrangements of elements into sets; combinations and permutations; other topics such as generating functions, recurrence relations, inclusionexclusion, P'olya's theorem, graphs and digraphs, combinatorial designs, incidence matrices, partially ordered sets, matroids, finite geometries, Latin squares, difference sets, matching theory. 7490 Seminar in Combinatorics, Graph Theory, and Discrete Structures (1  3) V Prereq: consent of department. May be repeated for credit with consent of department. Advanced topics such as combinatorics, graph theory, automata theory, or optimization. 7510 Topology I (3) Prereq: MATH 2057 or equivalent. Basic notions of general topology, with emphasis on Euclidean and metric spaces, continuous and differentiable functions, inverse function theorem and its consequences. 7512 Topology II (3) Prereq: MATH 7510. Theory of the fundamental group and covering spaces including the SeifertVan Kampen theorem; universal covering space; classification of covering spaces; selected areas from algebraic or general topology. 7520 Algebraic Topology (3) S Prereq: MATH 7200 and 7510; or equivalent. Basic concepts of homology, cohomology, and homotopy theory. 7550 Differential Geometry and Topology (3) F Prereq: MATH 7200 and 7510; or equivalent. Manifolds, vector fields, vector bundles, transversality, Riemannian geometry, other topics. 7590 Seminar in Geometry and Algebraic Topology (1  3) V Prereq: consent of department. May be repeated for credit with consent of department. Advanced topics such as advanced algebraic topology, transformation groups, surgery theory, sheaf theory, or fiber bundles. 7690 Seminar in Topological Algebra (1  3) V Prereq: consent of department. May be repeated for credit with consent of department. Advanced topics such as topological groups, topological semigroups, or topological lattices. 7999 Selected Readings in Mathematics (1  3) Prereq: consent of department. May be repeated for credit with consent of department. 8000 Thesis Research (112 per sem.) ``S"/``U" grading. 9000 Dissertation Research (112 per sem.) ``S"/``U" grading.
