Saint Louis University’s Department of Mathematics and Statistics offers undergraduate and graduate students a wide variety of courses on a diverse range of topics.

Be sure to check out the College of Arts and Sciences Academic Catalog for official course listings.

## Undergraduate Courses

**MATH 0225: Basic Mathematics**

Prep course designed to expose students to signed Numbers: common fractions, decimals
and percentages; ratio and proportion; area and volume; powers and roots; algebraic
expressions and operations; linear equations; basic trigonometric functions; factoring
polynomials. Three credit hours.

**MATH 0235: Introduction Elementary Algebra**

Three credit hours. Mathematics (Ps) Department

**MATH 0240: 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. Two credit
hours.

**MATH 0250: 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. Two credit hours.

**MATH 0260: 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. Three credit hours.

**MATH 1200: 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: Pre-calculus. Fall, spring,
and summer. Prerequisite: Math Index at least 800, or a grade of “C−” or better in
MATH 0260: Intermediate Algebra. Three credit hours.

**MATH 1220: 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.
Three credit hours.

**MATH 1240:Mathematics and the Art of M.C. Escher**

An inquiry course open to all undergraduates. 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. 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.) Thee credit hours.

**MATH 1240: Mathematics and the Art of M.C. Escher**

A SLU Inquiry Seminar. The art of M.C. Escher is used to explore topics in geometry
such as symmetry, tessellations, wallpaper patterns, the geometry of the sphere and
hyperbolic geometry. Taught in a computer classroom. Fall and spring. Prerequisites:
3.5 years of high school mathematics or a grade of C- or better in MATH 1200. Three
credit hours.

**MATH 1250: Mathematical Thinking in Real World**

An inquiry course open to all undergraduates. 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. 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.) Three credit hours.

**MATH/STAT 1260: Statistics Including Sports and Politics**

An inquiry course open to all undergraduates. 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. Three credit hours.

**MATH/STAT 1300: Elementary Statistics with 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. Three credit hours.

**MATH 1320: 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. Three credit hours.

**MATH 1400: 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. Three credit hours.

**MATH 1510: 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.
Four credit hours. 1818 Advanced College Credit

**MATH 1520: 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: Cryptology**

An inquiry course open to all undergraduates. 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 permutation based codes, block cipher schemes
and public key encryption. Prerequisite: Four years of high school mathematics. Three
credit hours.

**MATH 1660: 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. Three credit hours.

**MATH 1990: Honors Course in Mathematics**

Offered occasionally. One to three credit hours.

**MATH 2150: 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. Three credit hours.

**MATH 2530: 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 2530: Calculus III. Four credit hours.

**MATH 2660: 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. Three credit hours.

**MATH 2690: 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. One credit hour.

**MATH 2930: Special Topics**

One to four credit hours.

**MATH 2980: Independent Study**

Prior approval of sponsoring professor and chair required. Zero to three credit hours.
Independent study

**MATH 2990: Honors Course in Mathematics**

One to three credit hours.

**MATH 3110: 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. Three
credit hours.

**MATH 3120: 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. Three credit hours.

**MATH 3230: 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. Three
credit hours.

**MATH 3240: Numerical Analysis**

Review of calculus; root finding, nonlinear systems, interpolation and approximation;
numerical differentiation and integration. Alternate spring semesters. Prerequisite:
MATH 2530: Calculus III. Three credit hours.

**MATH 3270: 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. Three credit hours.

**MATH 3550: 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.
Three credit hours.

**MATH 3600: 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; combinatorial algorithms: resource scheduling,
bin-packing: algorithmic analysis and NP completeness. Three credit hours.

**MATH 3760: 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 2530: Calculus III. Three credit hours.

**MATH 3800: 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 3800 and either MATH 3810 or MATH 4800. Fall semester. Prerequisite:
MATH 2530: Calculus III. Three credit hours.

**MATH 3810: 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. Three credit hours.

**MATH 3850: Foundations of Statistical Analysis**

Descriptive statistics, probability distributions, random variables, expectation,
independence, hypothesis testing, confidence intervals, regression and ANOVA. Applications
and theory. Taught using statistical software. Credit not given for both MATH/STAT
3810 and MATH/STAT 3850. Fall and Spring semesters. Prerequisite: MATH 2530: Calculus
III. Three credit hours.

**MATH 4050: 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. Three credit hours.

**MATH 4110: 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. Three credit hours.

**MATH 4120: 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. Three credit hours.

**MATH 4150: 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. Three credit hours.

MATH 4210: Introduction to Analysis

Real number system, functions, sequences, limits, continuity, differentiation, integration
and series. Fall semester. Prerequisite: MATH 2530 and MATH 3120. Three credit hours.

**MATH 4220: Metric Spaces**

Set theory, metric spaces, completeness, compactness, connected sets, category. Spring
semester. Prerequisite: MATH 4210. Three credit hours.

**MATH 4230: 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. Three credit hours.

**MATH 4310: 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. Three credit hours.

**MATH 4320: 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. Three credit hours.

**MATH 4360: 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. Three credit hours.

**MATH 4410: 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 2530: Calculus III. Three credit hours.

**MATH 4430: 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. Three
credit hours.

**MATH 4480: 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. Three credit hours.

**MATH 4550: 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. Three credit hours.

**MATH 4570: 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. Three credit hours.

**MATH 4630: 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. Three credit hours.

**MATH 4650: Cryptography**

Classical cryptographic systems, public key cryptography, symmetric block ciphers,
implementation issues. Related and supporting mathematical concepts and structures.
Prerequisite: MATH 2530: Calculus III. Three credit hours.

**MATH 4800: Probability Theory**

Axioms of probability, conditional probability. Discrete and continuous random variables,
expectation, jointly defined random variables. Transformations of random variables
and limit theorems. Theory and applications, taught using statistical software. Credit
not given for any two of MATH 3800, MATH 4800 and MATH 4810. Prerequisites: MATH/STAT
3850, MATH 2530 and MATH 1660 or MATH 2660. Three credit hours.

**MATH 4840: Time Series**

Applied time series. Topics include exploratory data analysis, regression, ARIMA.
Spectral analysis, state- space models. Theory and applications, taught using statistical
software. Prerequisite: MATH/STAT 3850. Three credit hours.

**MATH 4850: Mathematical Statistics**

Theory of estimators, sampling distributions, hypothesis testing, confidence intervals,
regression, bootstrapping, and resampling. Theory and applications, taught using statistical
software. Credit not given for both MATH/STAT 3810 and MATH/STAT 3850. Prerequisite:
MATH 4800. Three credit hours.

**MATH 4860: Statistical Models**

Poisson processes, Markov chains, hidden Markov models, continuous time Markov chains,
queuing theory. Theory and applications, taught with statistical software. Prerequisite:
MATH 4800 . Three credit hours.

**MATH 4870: Applied Regression**

Linear regression, model selection, nonparametric regression, classification and graphical
models. Theory and applications using statistical software. Prerequisites: MATH/STAT
3850 and MATH 3110 or MATH 3120. Three credit hours.

**MATH 4950: Senior Residency**

Required for graduating seniors. 0 Credit Hours. Senior Residency

**MATH 4980: Advanced Independent Study**

Prior permission of sponsoring professor and chair required. Zero to six credit hours.
Independent Study.

**MATH 4WUI - Washington University Inter-U**

0 to 3 Credit Hours. Inter-University College

## Graduate Courses

**MATH 5102: 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. Three credit hours. (Cross-listed as MATH 4120)

**MATH 5202: Metric Spaces**

Set theory, real line, separation properties, compactness, metric spaces, metrization.
Offered every other spring semester. Prerequisite: MATH 4210. Three credit hours.
(Cross-listed as MATH 4220)

**MATH 5105: 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.
Three credit hours. (Cross-listed as MATH 4150)

**MATH 5203: 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. Three credit hours.
(Cross-listed as MATH 4230)

**MATH 5060: 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. Three credit hours.

**MATH 5070: 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. Three credit hours.

**MATH 5110: 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. Three
credit hours.

**MATH 5120: 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: Real Analysis I**

The topology of the reals, Lebesque and Borel measurable functions, properties of
the Lebesque integral, differential of the integral. Fall semester. Three credit hours.

**MATH 5220: 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. Three
credit hours. Offered occasionally.

**MATH 5230: 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. Three credit hours. Offered
occasionally.

**MATH 5240: 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. Three credit hours. Offered occasionally.

**MATH 5310: Topology I**

Topological spaces, convergence, nets, product spaces, metrization, compact spaces,
connected spaces. Fall semester. Three credit hours.

**MATH 5320: Topology II**

Compact surfaces, fundamental groups, force groups and free products, Seifert-van
Kampen theorem, covering spaces. Offered every spring semester. Prerequisite: MATH
5310. Three credit hours.

**MATH 5930: Special Topics in Mathematics**

One to three credit hours. Graduate.

**MATH 5950: Special Study for Examinations**

Zero Credit Hours. Graduate Special Study Exams.

**MATH 5980: Graduate Reading Course**

Prior permission of instructor and chairperson required. One to three credit hours.
Graduate independent study

**MATH 5990: Thesis Research**

Zero to six credit hours. Graduate research.

**MATH 5CR: Master’s Degree Study**

Zero credit hours. Graduate research.

**MATH 5WUI: Washington University Inter-University Course**

Zero to three credit hours. Graduate.

**MATH 6110: 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. Three credit
hours.

**MATH 6180: 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. Three credit hours.

**MATH 6210: 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. Three credit hours.

**MATH 6220: 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. Three credit
hours.

**MATH 6280: 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. Three credit hours.

**MATH 6310: 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. Three credit hours.

**MATH 6320: 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. Three credit hours.

**MATH 6380: 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. Three credit hours.

**MATH 6410: 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.
Three credit hours.

**MATH 6420: Differential Geometry II**

Continuation of MATH 641. Offered every spring semester. Three credit hours.

**MATH 6480: 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. Three credit hours.

**MATH 6950: Special Study for Examinations**

Zero credit hours. Graduate special study exams.

**MATH 6980: Graduate Reading Course**

Prior permission of instructor and chairperson required. One to three credit hours.
Graduate Independent study.

**MATH 6990: Dissertation Research**

Zero to six credit hours. Graduate Research.

**MATH 6CR: Doctor of Philosophy Degree Study**

Zero credit hours. Graduate.