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Courses

Catalog descriptions of mathematics courses offered at SLU.

These course descriptions are unofficial and may be out of date.  Please go to the Saint Louis University course information page and follow the directions there to see the official course listings.

Undergraduate Courses

MATH 0220 (previously MATH 092) - Basic Mathematics
Prep course designed to expose students to signed Numbers: common fraction, decimals and percentages; ratio and proportion; area and volume; powers and roots; algebraic expressions and operations; linear equations; basic trigonometric functions; factoring polynomials.  3 Credit Hours. 
MATH 0230 (previously MATH 093) - Intro Elementary Algebra
3 Credit Hours.  Mathematics (Ps) Department
MATH 0240 (previously MATH 094) - Introduction to Elementary Algebra I
MATH 0240 and MATH 0250 together cover the same material as MATH 0260, but in two semesters.  Credit not given for both MATH 0240 and MATH 0260.  Fall semester.  2 Credit Hours.
MATH 0250 (previously MATH 095) - Elementary Algebra II
MATH 0240 and MATH 0250 together cover the same material as MATH 0260, but in two semesters.  Credit not given for both MATH 0250 and MATH 0260.  Fall and spring semesters.  Prerequisite: Grade of “C−” or better in Math 0240.  2 Credit Hours.
MATH 0260 (previously MATH 096) - Intermediate Algebra
Radicals, exponents, first degree equations, simultaneous equations, quadratic equations, functions, graphs, logarithms, polynomials.  Credit not given for both MATH 0260 and any of the following: MATH 0240, MATH 0250.  Fall and spring semesters. Prerequisite: Math-Index at least 700.  3 Credit Hours.
MATH 1200 (previously MATH 120) - College Algebra
Polynomials; rational functions; exponential and logarithmic functions; conic sections; systems of equations; and inequalities.  Intended for students needing more preparation before taking MATH 1320 (Survey of Calculus), MATH 1400 (Precalculus).  Fall, spring, and summer.  Prerequisite: Math-Index at least 800, or a grade of “C−” or better in MATH 0260 (Intermediate Algebra).  3 Credit Hours.
MATH 1220 (previously MATH 122) - Finite Mathematics
Linear equations and straight lines, matrices, sets and counting, probability and statistics, the mathematics of finance, and logic.  Fall and spring semesters.  Prerequisite: Math-Index at least 750 or grade of “C−” or better in MATH 0260 (Intermediate Algebra).  3 Credit Hours.
MATH 1240 (previously MATH 124) - Mathematics and the Art of M.C. Escher
A SLU freshman seminar.  In this course we will discover how M.C. Escher created some of his artwork.  The art of M.C. Escher will be used to explore such topics as: polygons, transformations, tessellations, and wallpaper patterns.  Taught in a computer classroom.  Fall and spring semesters. 
Prerequisite: Math-Index at least 750 or grade of “C−” or better in MATH 1200 (College Algebra) or equivalent.  (An understanding beyond MATH 0260 is needed.)  3 Credit Hours. 

MATH 1250 (previously MATH 125) - Mathematical Thinking in Real World
A SLU freshman seminar.  In this course, aimed at students in the humanities and social sciences, we study some of the greatest ideas of mathematics that are often hidden from view in lower division courses.  Topics selected from number theory, the infinite, geometry, topology, chaos and fractals, and probability.  Taught in a computer classroom.  Fall and spring semesters. 
Prerequisite:
Math-Index at least 750 or a grade of “C−” or better in MATH 1200 (College Algebra) or equivalent.  (An understanding beyond MATH 0260 is needed.)  3 Credit Hours.
MATH/STAT 1260 (previously MATH 126) - Statistics Including Sports and Politics
A SLU freshman seminar.  Producing data through the use of samples and experiments; organizing data through graphs and numbers that describe the distribution of the data of one variable or the relationship between two variables; probability; statistical inference including confidence intervals and tests of significance.  Prerequisite: Math-Index at least 750 or a grade of “C−” or better in MATH 1200.  3 Credit Hours.
MATH/STAT 1300 (previously MATH 130) - Elementary Statistics w/ Computers
Data production and analysis; probability basics, distributions; sampling, estimation with confidence intervals, hypothesis testing, t-test; correlation and regression; crosstabulations and chi-square.  Students learn to use a statistical package such as SPSS.  Prerequisite: Math-Index at least 900 or a grade of "C−”" or better in MATH 1200 (College Algebra) or equivalent.  3 Credit Hours. 
MATH 1320 (previously MATH 132) - Survey of Calculus
Introductory differential and integral calculus, optimization and rate problems, calculus of rational, exponential and logarithmic functions, partial derivatives and applications.  Fall, spring, and summer.  Math-Index at least 900 or a grade of “C−” or better in MATH 1200 (College Algebra).  3 Credit Hours. 
MATH 1400 (previously MATH 141) - Pre-Calculus
Trigonometric functions, graphing, identities, solving triangles, inverse trigonometric functions, polar coordinates, complex numbers, and analytic geometry.  Fall and spring semesters.  Prerequisite: Math-Index at least 950 or a grade of “C−” or better in MATH 1200 (College Algebra).  3 Credit Hours. 
MATH 1510 (previously MATH 142) - Calculus I
Elementary functions; differentiation and integration from geometric and symbolic viewpoints; limits, continuity; applications.  Fall and spring semesters.  Prerequisite: Math-Index at least 1020 or a grade of “C−” or better in MATH 1400 (Pre-Calculus). 4 Credit Hours.   1818 Advanced College Credit
MATH 1520 (previously MATH 143) - Calculus II
Symbolic and numerical techniques of integration, indeterminate forms, infinite series, power series, Taylor series, differential equations; polar coordinates, applications.  Prerequisite: Score at least 4 on the Calculus AP Test (AB), Math-Index at least 1050, or a grade of “C−” or better in MATH 1510 (Calculus I).  4 Credit Hours.  1818 Advanced College Credit
MATH 1650 (previously MATH 165) - Cryptology
A SLU freshman seminar.  Aimed at students who require a course at the level of calculus or higher and who are interested in the mathematical basis for cryptology systems.  Topics include premutation based codes, block cipher schemes and public key encryption.  Prerequisite: 4 years of high school mathematics.  3 Credit Hours. 
MATH 1660 (previously MATH 135) - Discrete Mathematics
Concepts of discrete mathematics used in computer science; sets, sequences, strings, symbolic logic, proofs, mathematical induction, sums and products, number systems, algorithms, complexity, graph theory, finite state machines.  Prerequisite: A grade of “C−” or better in MATH 1200 (College Algebra) or equivalent.  3 Credit Hours.  
MATH 1990 - Honors Course in Mathematics
Offered occasionally.  1 to 3 Credit Hours. 
MATH 2150 (previously MATH 215) - Computational Linear Algebra
Vectors, matrices and matrix operations, determinants, systems of linear equations, Gaussian elimination, direct factorization, finite-precision arithmetic and round-off, condition number, iterative methods, vector and matrix norms, eigenvalues and eigenvectors, CAS package.  3 Credit Hours. 
MATH 2530 (previously MATH 244) - Calculus III
Three-dimensional analytic geometry, vector-valued functions, partial differentiation, multiple integration, and line integrals.  Fall and spring semesters.  Prerequisite: A grade of “C−” or better in MATH 1520 (Calculus II).  4 Credit Hours. 
MATH 2660 (previously MATH 266) - Principles of Mathematics
Introduction to the basic techniques of writing proofs and to fundamental ideas used throughout mathematics.  Topics covered include formal logic, proof by contradiction, set theory, mathematical induction and recursion, relations and congruence, functions.  Fall and spring semesters.  Prerequisite: A grade of “C−” or better in MATH 1510 (Calculus I).  3.000 Credit Hours. 
MATH 2690 (Previously MATH 269) - Mathematical Problem Solving
Intended primarily to train students for the William Lowell Putnam Mathematical Competition, this course covers a mélange of ingenious techniques for solving mathematics problems cutting across the entire undergraduate spectrum, including precalculus, calculus, combinatorics, probability, inequalities.  Coverage tailored to students’ interests.  May be repeated for credit.  Fall semester.  Prerequisite: None.  1 Credit Hour. 
MATH 2930 (Previously MATH 293)- Special Topics
1 to 4 Credit Hours.
MATH 2980 (Previously MATH 298)- Independent Study
Prior approval of sponsoring professor and chair required.  0 to 3 Credit Hours.  Independent Study
MATH 2990 (Previously MATH 299)- Honors Course in Mathematics
1 to 3 Credit Hours. 
MATH 3110 (previously MATH 311) - Linear Algebra for Engineers
Systems of linear equations, matrices, linear programming, determinants, vector spaces, inner product spaces, eigenvalues and eigenvectors, linear transformations, and numerical methods.  Credit not given for both MATH 3110 and MATH 3120.  Spring semester.  Prerequisite: A grade of “C−” or better in MATH  1520 (Calculus II) and a knowledge of vectors.  3 Credit Hours.
MATH 3120 (previously MATH 315) - Introduction to Linear Algebra
Matrices, row operations with matrices, determinants, systems of linear equations, vector spaces, linear transformations, inner products, eigenvalues and eigenvectors.  Credit not given for both MATH 3120 and MATH 3110. Fall and spring semesters.  Prerequisite: MATH 2530 (Calculus III) and MATH 2660 (Principles of Math).  3 Credit Hours. 
MATH 3230 (previously MATH 371) - Vector Analysis
Vector algebra, differential and integral calculus of vector functions, linear vector functions and dyadics, applications to geometry, particle and fluid mechanics, theory of vector fields.  Offered occasionally. Prerequisite: MATH 2530 (Calculus III).  3  Credit Hours. 
MATH 3240 (previously MATH 320) - Numerical Analysis
Review of calculus; root finding, nonlinear systems, interpolation and approximation; numerical differentiation and integration.  Alternate spring semesters. Prerequisite: MATH 1520 (Calculus II).  3 Credit Hours. 
MATH 3270 (previously MATH 370) - Advanced Mathematics for Engineers
Vector algebra; matrix algebra; systems of linear equations; eigenvalues and eigenvectors; systems of differential equations; vector differential calculus; divergence, gradient and curl; vector integral calculus; integral theorems; Fourier series with applications to partial differential equations.  Fall and spring semesters.   Prerequisite: MATH 3550 (Differential Equations).  3 Credit Hours. 
MATH 3550 (previously MATH 355) - Differential Equations
Solution of ordinary differential equations, higher order linear equations, constant coefficient equations, systems of first order equations, linear systems, equilibrium of nonlinear systems, Laplace transformations.  Prerequisite: MATH 2530 (Calculus III).  3 Credit Hours. 
MATH 3600 (previously MATH 360) - Combinatorics
Advanced counting methods: permutations and combinations, generalized permutations and combinations, recurrance relations, generating functions; algorithms: graphs and digraphs, graph algorithms: minimum-cost spanning trees, shortest path, network flows; depth first and breadth-first searches; combinational algorithms: resource scheduling, bin-packing: algorithmic analysis and NP completeness.  3 Credit Hours. 
MATH 3760 (previously MATH 363) - Financial Mathematics
Theory of interest material for the Financial Mathematics exam of the Society of Actuaries. Time permitting, supplemental material covering financial derivatives will be discussed.Prerequisite: MATH 1520 (Calculus II).  3 Credit Hours. 

MATH 4050 (previously MATH 405) - History of Mathematics
The development of several important branches of mathematics, including numeration and computation, algebra, non-Euclidean geometry, and calculus.  Offered every other Spring (even years).  Prerequisite: MATH 1520 (calculus II).  3 Credit Hours. 
MATH 4110 (previously MATH 411) - Introduction to Abstract Algebra
Elementary properties of the integers, sets and mappings, groups, rings, integral domains, division rings and fields.  Fall semester.  Prerequisite: MATH 3120 (Intro to Linear Algebra).  3 Credit Hours. 
MATH 4120 (previously MATH 412) - Linear Algebra
Advanced linear algebra, including linear transformations and duality, elementary canonical forms, rational and Jordan forms, inner product spaces, unitary operators, normal operators and spectral theory.  Alternate spring semesters.  Prerequisite: MATH 4110.  3 Credit Hours. 
MATH 4150 (previously MATH 415) - Number Theory
Introduction to algebraic number theory.  Topics will include primes, Chinese remainder theorem, Diophantine equations, algebraic numbers and quadratic residues.  Additional topics will vary from year to year.  Alternate spring semesters.  Prerequisite: MATH 4110.  3 Credit Hours. 
MATH 4210 (previously MATH 421) - Introduction to Analysis
Real number system, functions, sequences, limits, continuity, differentiation, integration and series.  Fall semester.  Prerequisite: MATH 2530 and MATH 3120.  3 Credit Hours
MATH 4220 (previously MATH 422) - Metric Spaces
Set theory, metric spaces, completeness, compactness, connected sets, category.  Spring semester.  Prerequisite: MATH 4210.  3 Credit Hours. 
MATH 4230 (previously MATH 423) - Multivariable Analysis
Introduction to analysis in multidimensional Euclidean space.  Sequences and Series of functions, Differentiability, Integrability, Inverse and Implicit function theorems, Fundamental Theorems of Multivariable Calculus (Green's Theorem, Stokes Theorem, Divergence Theorem).  Spring semester.  Prerequisite: MATH 4210.  3 Credit Hours. 
MATH 4310 (previously MATH 451) - Introduction to Complex Variables
Complex number system and its operations, limits and sequences, continuous functions and their properties, derivatives, conformal representation, curvilinear and complex integration, Cauchy integral theorems, power series and singularities.  Fall semester.  Prerequisite: MATH 2530 (Calculus III).  3 Credit Hours.  
MATH 4320 (previously MATH 452) - Complex Variables II
This course is a continuation of MATH 4310.  Topics covered include series, residues and poles, conformal mapping, integral formulas, analytic continuation, and Riemann surfaces.  Spring semester.  Prerequisite: MATH 4310.  3 Credit Hours. 
MATH 4360 (previously MATH 453) - Geometric Topology
An introduction to the geometry and topology of surfaces and three dimensional spaces.  Topics covered Include Euclidean, spherical and hyperbolic geometry, topology of surfaces, knot theory, and the fundamental group.  Prerequisite: MATH 4310.  3 Credit Hours.  
MATH 4410 (previously MATH 441) - Foundations of Geometry
Historical background of the study of Euclidean geometry; development of two-dimensional Euclidean geometry from a selected set of postulates.  Offered occasionally.  Prerequisite: MATH 1520 (Calculus II).  3 Credit Hours.  
MATH 4430 (previously MATH 447) - Non-Euclidean Geometry
The rise and development of the non-Euclidean geometries with intensive study of plane hyperbolic geometry.  Offered occasionally.   Prerequisite: MATH 1510 (Calculus I).  3 Credit Hours.  
MATH 4480 (previously MATH 448) - Differential Geometry
Classical theory of smooth curves and surfaces in 3-space.  Curvature and torsion of space curves, Gaussian curvature of surfaces, the Theorema Egregium of Gauss.  Offered occasionally.  3 Credit Hours.  
 
MATH 4550 (previously MATH 455) - Nonlinear Dynamics and Chaos
Bifurcation in one-dimensional flows.  Two-dimensional flows, fixed points and linearization, conservative systems, index theory, limit cycles.  Poincaré-Bendixson theory, bifurcations.  Chaos, the Lorenz equation, discrete maps, fractals, and strange attractors.  Prerequisite: MATH 3550 (Differential Equations).  3 Credit Hours. 
MATH 4570 (previously MATH 457) - Partial Differential Equations
Fourier series, Fourier Integrals, the heat equation, Staum-Liouville problems, the wave equation, the potential equation, problems in several dimensions, Laplace transforms numerical methods.  Prerequisite: MATH 3550 (Differential Equations).  3 Credit Hours. 
MATH 4630 (previously MATH 463) - Graph Theory
Basic definitions and concepts, undirected graphs (trees and graphs with cycles), directed graphs, and operation on graphs, Euler's formula, and surfaces.  Offered occasionally.  Prerequisite: MATH 2530 (Calculus III).  3 Credit Hours. 
MATH 4650 (previously MATH 465) - Cryptography
Classical cryptographic systems, public key cryptography, symmetric block ciphers, implementation issues.  Related and supporting mathematical concepts and structures.  Prerequisite: MATH 1520 (Calculus II).  3 Credit Hours.  

MATH 4810 (previously MATH 401) - Elementary Theory of Probability
Counting theory; axiomatic probability, random variables, expectation, limit theorems.  Applications of the theory of probability to a variety of practical problems.  Credit not given for both MATH 4810 and MATH 4880.  Fall and Spring semester.   Prerequisite: MATH 2530 (Calculus III).  3  Credit Hours.  
MATH 4820 (previously MATH 402) - Intro Mathematical Statistics
Probability and random sampling; distributions of various statistics; statistical procedures, such as estimation of parameters, hypothesis testing, and simple linear regression.  Credit not given for both MATH 4820 and MATH 4880.  Spring semester.  Prerequisite: MATH 4810 (Elem. Theory of Probability).  3 Credit Hours.  
MATH 4880 (previously MATH 403) - Probability and Statistics for Engineers
Analyzing and producing data; probability; random variables; probability distributions; expectation; sampling distributions; confidence intervals; hypothesis testing; experimental design; regression and correlation analysis.  Credit not given for both MATH 4880 and either MATH 4810 or MATH 4820.  Fall and spring semesters.  Prerequisite: MATH 2530 (Calculus III).  3 Credit Hours. 
 
MATH 4930 (Previously MATH 493)- Special Topics
3 Credit Hours. 
MATH 4950 (Previously MATH 495)- Senior Residency
Required for graduating seniors.  0 Credit Hours.  Senior Residency
MATH 4980 (Previously MATH 498)- Advanced Independent Study
Prior permission of sponsoring professor and chair required.  0 to 6 Credit Hours.  Independent Study.
MATH 4WUI - Washington Univeristy Inter-U
0 to 3 Credit Hours.  Inter-University College

Graduate Courses

MATH 5102 (previously MATH 501) - Linear Algebra
Advanced linear algebra including linear transformations and duality, elementary canonical forms, rational and Jordan forms, inner product spaces, unitary operators, normal operators, and spectral theory.  Offered every other spring semester.  Prerequisite: MATH 4110.  3 Credit Hours.  (Cross-listed as MATH 4120)
MATH 5202 (previously MATH 502) - Metric Spaces
Set theory, real line, separation properties, compactness, metric spaces, metrization.  Offered every other spring semester.  Prerequisite: MATH 4210.  3 Credit Hours.  (Cross-listed as MATH 4220)
MATH 5105 (previously MATH 503) - Number Theory 
Introduction to algebraic number theory.  Topics will include primes, Chinese remainder theorem, Diophantine equations, algebraic numbers and quadratic residues.  Additional topics will vary from year to year.  Offered every other year.  Prerequisite: MATH 4110.  3 Credit Hours.  (Cross-listed as MATH 4150)
MATH 5203 (previously MATH 504) - Multivariable Analysis
Sequences and Series of functions, Differentiability, Integrability, Inverse and Implicit function theorems, Fundamental Theorems of Multi-variable Calculus (Green’s Theorem, Stokes Theorem, Divergence Theorem).  Prerequisite: MATH 4210.  3 Credit Hours.  (Cross-listed as MATH 4230)
MATH 5060  (previously MATH 506) - Math Methods Engineering I
Review of vector analysis, curvilinear coordinates, introduction to partial differential equations, Cartesian tensors, matrices, similarity transformations, variational methods, Lagrange multipliers, Cauchy-Riemann conditions, geometry of a complex plane, conformal mapping, and engineering applications. Only offered occasionally.  Prerequisite: Permission of Instructor.  3 Credit Hours. 
MATH 5070  (previously MATH 507) - Math Methods Engineering II
Calculus of residues, contour integration, multi-valued functions, series solutions of differential equations, Sturm-Liouville theory, special functions, integral transforms, discrete Laplace and Fourier transforms, basic numerical methods, finite difference methods, and their applications to partial differential equations.  Only offered occasionally.  Prerequisite: Permission of Instructor.  3 Credit Hours. 
MATH 5110 (previously MATH 511) - Algebra
Simple properties of groups, groups of transformations,subgroups, homomorphisms and isomorphisms, theorems of Schreier and Jordan-Hölder, mappings into a group, rings, integral domains, fields, polynomials, direct sums and modules.  Fall semester.  3 Credit Hours. 
MATH 5120 (previously MATH 512) - Algebra II
Rings, fields, bases and degrees of extension fields, transcendental elements, normal fields and their structures.  Galois theory, finite fields; solutions of equations by radicals, general equations of degree n.  Offered every spring semester.  Prerequisite: MATH 5110. 3 Credit Hours. 
MATH 5210 (previously MATH 521) - Real Analysis I
The topology of the reals, Lebesque and Borel measurable functions, properties of the Lebesque integral, differential of the integral.  Fall semester.  3 Credit Hours. 
MATH 5220 (previously MATH 522) - Complex Analysis
Holomorphic and Harmonic functions and power series expansions.  Complex integration.  Cauchy’s theorem and applications.  Laurent series, singularities, Runge’s theorem, and the calculus of residues.  Additional topics may include Analytic continuation, Riemann surfaces, and conformal mapping.  Prerequisite: MATH 5210 and MATH 5310.  3 Credit Hours.  Offered occasionally. 
MATH 5230 (previously MATH 523) - Functional Analysis
Banach and Hilbert spaces.  Linear functionals and linear operators.  Dual spaces, weak and weak-* topologies.  Hahn-Banach, Closed Graph and Open Mapping Theorems.  Topological Vector spaces.  Prerequisite: MATH 5210 and MATH 5310.  3 Credit Hours.  Offered occasionally. 
MATH 5240 (previously MATH 524) - Harmonic Analysis
Fourier Series on the circle, Convergence of Fourier series, Conjugate and maximal functions, Interpolation of Linear Operators, Lacunary Sequences, Fourier Transform on the line, Fourier transform on locally compact Abelian groups.  Prerequisite: MATH 5210.  3.000 Credit Hours.  Offered occasionally. 
MATH 5310 (previously MATH 531) - Topology I
Topological spaces, convergence, nets, product spaces, metrization, compact spaces, connected spaces.  Fall semester.  3 Credit Hours. 
MATH 5320 (previously MATH 532) - Topology II
Compact surfaces, fundamental groups, force groups and free products, Seifert-van Kampen theorem, covering spaces.  Offered every spring semester.  Prerequisite: MATH 5310. 3 Credit Hours. 
MATH 5930 (previously MATH 593) - Special Topics in Mathematics
1 to 3 Credit Hours.  Graduate.
MATH 5950 (previously MATH 595) - Special Study for Examinations
0 Credit Hours.  Graduate Special Study Exams.
MATH 5980 (previously MATH 598) - Graduate Reading Course
Prior permission of instructor and chairperson required.  1 to 3 Credit Hours.  Graduate Independent Study
MATH 5990 (previously MATH 599) - Thesis Research
0 to 6 Credit Hours.  Graduate Research.
MATH 5CR - Master’s Degree Study
0 Credit Hours.  Graduate Research.
MATH 5WUI - Washington University Inter-Univerisity Course
0 to 3 Credit Hours.  Graduate.
MATH 6110 (previously MATH 611) - Algebra III
Categories and functors, properties of hom and tensor, projective and injective modules, chain conditions, decomposition and cancellation of modules, theorems of Maschke, Wedderburn, and Artin-Wedderburn, tensor algebras.  Offered occasionally.  3 Credit Hours. 
MATH 6180 (previously MATH 618) - Topics in Algebra
Various topics are discussed to bring graduate students to the forefront of a research area in algebra.  Times of offering in accordance with research interests of faculty.  Offered occasionally.  3 Credit Hours. 
MATH 6210 (previously MATH 621) - Lie Groups and Lie Algebras
Lie groups and Lie algebras, matrix groups, the Lie algebra of a Lie group, homogeneous spaces, solvable and nilpotent groups, semisimple Lie groups.  Offered every other year.  3 Credit Hours. 
MATH 6220 (previously MATH 622) - Representation Theory of Lie Groups
Representation theory of Lie groups, irreducibility and complete reducibility, Cartan subalgebra and root space decomposition, root system and classification, coadjoint orbits, harmonic analysis on homogeneous spaces.  Offered every other year.  3 Credit Hours.
MATH 6280 (previously MATH 628) - Topics in Analysis
Various topics are offered to bring graduate students to the forefront of a research area in analysis.  Times of offering in accordance with research interests of faculty.  Offered occasionally.  3 Credit Hours. 
MATH 6310 (previously MATH 631) - Algebraic Topology
Homotopy theory, homology theory, exact sequences, Mayer-Victoris sequences, degrees of maps, cohomology, Kunneth formula, cup and cap products, applications to manifolds including Poincare-Lefshetz duality.  Offered every other year.  3 Credit Hours.  
MATH 6320 (previously MATH 632) - Topology of Manifolds
Examples of manifolds, the tangent bundle, maps between manifolds, embeddings, critical values, transversality, isotopies, vector bundles and bubular neighborhoods, cobordism, intersection numbers and Euler characteristics.  May be taught in either the piecewise linear or differentiable categories.  Offered every other year.  3 Credit Hours. 
MATH 6380 (previously MATH 638) - Topics in Topology
Various topics are offered to bring graduate students to the forefront of a research area in topology.  Times of offering in accordance with research interests of faculty.  Offered occasionally.  3 Credit Hours. 
MATH 6410 (previously MATH 641) - Differential Geometry I
The theory of differentiable manifolds, topological manifolds, differential calculus of several variables, smooth manifolds and submanifolds, vector fields and ordinary differential equations, tensor fields, integration and de Rham cohomology.  Fall semester.  3 Credit Hours. 
MATH 6420 (previously MATH 642) - Differential Geometry II
Continuation of MATH 641.  Offered every spring semester.  3 Credit Hours. 
MATH 6480 (previously MATH 648) - Topics in Geometry
Various topics are offered to bring graduate students to the forefront of a research area in geometry.  Times of offering in accordance with research interests of faculty.  Offered occasionally.  3 Credit Hours. 
MATH 6950 (previously MATH 695) - Special Study for Examinations
0 Credit Hours.  Graduate Special Study Exams.
MATH 6980 (previously MATH 698) - Graduate Reading Course
Prior permission of instructor and chairperson required.  1 to 3 Credit Hours.  Graduate Independent Study.
MATH 6990 (previously MATH 699) - Dissertation Research
0 to 6 Credit Hours.  Graduate Research.
MATH 6CR - Doctor of Philosophy Degree St
0 Credit Hours.  Graduate.
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