
 Info
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These course descriptions are unofficial and may be out of date.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 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 093  Intro Elementary Algebra

3 Credit Hours.
Mathematics (Ps) Department
 MATH 94  Introduction to Elementary Algebra I

MATH 94 and MATH 95 together cover the same material as MATH 96, but in two semesters. Credit not given for both MATH 94 and MATH 96. Fall semester.
2 Credit Hours.
 MATH 95  Elementary Algebra II

MATH 94 and MATH 95 together cover the same material as MATH 96, but in two semesters. Credit not given for both MATH 95 and MATH 96. Fall and spring semesters. Prerequisite: Grade of “C−” or better in Math 94.
2 Credit Hours.
 MATH 96  Intermediate Algebra

Radicals, exponents, first degree equations, simultaneous equations, quadratic equations, functions, graphs, logarithms, polynomials. Credit not given for both MATH 96 and any of the following: MATH 94, MATH 95. Fall and spring semesters.
3 Credit Hours.
 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 132, MATH 141. Fall, spring, and summer. Prerequisite: Two years of high school mathematics or grade of “C−” or better in MATH 96.
3 Credit Hours.
 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: Two years of high school mathematics or grade of “C−” or better in MATH 96.
3 Credit Hours.
 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: Three years of high school mathematics or grade of “C−” or better in MATH 120. (An understanding beyond MATH 96 is needed.)
3 Credit Hours.
 MATH 125  Math 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: Three years of high school mathematics or a grade of “C−” or better in MATH 120. (An understanding beyond MATH 96 is needed.)
3 Credit Hours.
 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: 3.5 years of high school mathematics or a grade of “C−” or better in MATH 120. 3 Credit Hours.
 MATH 130  Elementary Stats w/ Computers

Data production and analysis; probability basics, distributions; sampling, estimation with confidence intervals, hypothesis testing, ttest; correlation and regression; crosstabulations and chisquare. Students learn to use a statistical package such as SPSS. Prerequisite: MATH 120 or equivalent.
3 Credit Hours.
 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. Prerequisite: 3.5 years of high school mathematics or a grade of “C−” or better in MATH 120.
3 Credit Hours.
 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 120 or equivalent.
3 Credit Hours.
 MATH 141  PreCalculus

Trigonometric functions, graphing, identities, solving triangles, inverse
trigonometric functions, polar coordinates, complex numbers, and analytic
geometry. Fall and spring semesters. Prerequisite: 3.5 years of high school mathematics or a grade of “C−” or better in MATH 120.
3 Credit Hours.
 MATH 142  Calculus I

Elementary functions; differentiation and integration from geometric and
symbolic viewpoints; limits, continuity; applications. Fall and spring semesters. Prerequisite: 4 years of high school mathematics or a grade of “C−” or better in MATH 141. 4 Credit Hours.
1818 Advanced College Credit
 MATH 143  Calculus II

Symbolic and numerical techniques of integration, indeterminate forms,
infinite series, power series, Taylor series, differential equations; polar
coordinates, applications. Prerequisite: A grade of “C−” or better in MATH 142.
4 Credit Hours.
1818 Advanced College Credit
 MATH 160  Computer Prob and Stat

Elements of statistics: presenting data, mean, median, and mode; standard deviation; counting methods, the binomial theorem, probability, conditional probability, distributions, and hypothesis testing. Prerequisite: A grade of “C−” or better in MATH 120 or MATH 142.
3 Credit Hours.
 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 199  Honors Course in Mathematics

Offered occasionally. 1 to 3 Credit Hours.
 MATH 215  Computational Linear Algebra

Vectors, matrices and matrix operations, determinants, systems of linear equations, Gaussian elimination, direct factorization, finiteprecision arithmetic and roundoff, condition number, iterative methods, vector and matrix norms, eigenvalues and eigenvectors, CAS package.
3 Credit Hours.
 MATH 244  Calculus III

Threedimensional analytic geometry, vectorvalued functions, partial
differentiation, multiple integration, and line integrals. Fall and spring semesters. Prerequisite: A grade of “C−” or better in MATH 143.
4 Credit Hours.
 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 142.
3.000 Credit Hours.
 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 293  Special Topics

1 to 4 Credit Hours.
 MATH 298  Independent Study

Prior approval of sponsoring professor and chair required. 0 to 3 Credit Hours.
Independent Study
 MATH 299  Honors Course in Mathematics

1 to 3 Credit Hours.
 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 MATH311 and
MATH315. Spring semester. Prerequisite: A grade of “C−” or better in MATH 143 and a knowledge of vectors.
3 Credit Hours.
 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 315 and MATH 311. Fall and
spring semesters. Prerequisite: MATH 244 and MATH 266.
3 Credit Hours.
 MATH 320  Numerical Analysis

Review of calculus; root finding, nonlinear systems, interpolation and approximation; numerical differentiation and integration. Alternate spring semesters. Prerequisite: MATH 143.
3 Credit Hours.
 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 244.
3 Credit Hours.
 MATH 360  Combinatorics

Advanced counting methods: permutations and combinations, generalized permutations and combinations, recurrance relations, generating functions; algorithms: graphs and digraphs, graph algorithms: minimumcost spanning trees, shortest path, network flows; depth first and breadthfirst searches; combinational algorithms: resource scheduling, binpacking: algorithmic analysis and NP completeness.
3 Credit Hours.
 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 143. 3 Credit Hours.
 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 355.
3 Credit Hours.
 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 244.
3 Credit Hours.
 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 401 and MATH 403. Fall semester. Prerequisite: MATH 244.
3 Credit Hours.
 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 402 and MATH 403. Spring semester.
Prerequisite: MATH 401. 3 Credit Hours.
 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 403 and either MATH 401 or MATH 402. Fall and spring semesters.
Prerequisite: MATH 244. 3 Credit Hours.
 MATH 405  History of Mathematics

The development of several important branches of mathematics, including numeration and computation, algebra, nonEuclidean geometry, and calculus. Offered every other Spring (even years). Prerequisite: MATH 143.
3 Credit Hours.
 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 315.
3 Credit Hours.
 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 411.
3 Credit Hours.
 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 411.
3 Credit Hours.
 MATH 421  Intro to Analysis

Real number system, functions, sequences, limits, continuity, differentiation,
integration and series. Fall semester. Prerequisite: MATH 244.
3 Credit Hours.
 MATH 422  Metric Spaces

Set theory, metric spaces, completeness, compactness, connected sets,
category. Spring semester. Prerequisite: MATH 421.
3 Credit Hours.
 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 421.
3 Credit Hours.
 MATH 441  Foundations of Geometry

Historical background of the study of Euclidean geometry; development of
twodimensional Euclidean geometry from a selected set of postulates. Offered
occasionally. Prerequisite: MATH 142.
3 Credit Hours.
 MATH 447  NonEuclidean Geometry

The rise and development of the nonEuclidean geometries with intensive study
of plane hyperbolic geometry. Offered occasionally. Prerequisite: MATH 142.
3 Credit Hours.
 MATH 448  Differential Geometry

Classical theory of smooth curves and surfaces in 3space. Curvature and
torsion of space curves, Gaussian curvature of surfaces, the Theorema Egregium
of Gauss. Offered occasionally.
3 Credit Hours.
 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 244.
3 Credit Hours.
 MATH 452  Complex Variables II

This course is a continuation of MATH 451. Topics covered include series, residues and poles, conformal mapping, integral formulas, analytic continuation, and Riemann surfaces. Spring semester. Prerequisite: MATH 451.
3 Credit Hours.
 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 451.
3 Credit Hours.
 MATH 455  Nonlinear Dynamics and Chaos

Bifurcation in onedimensional flows. Twodimensional flows, fixed points and
linearization, conservative systems, index theory, limit cycles. PoincaréBendixson theory, bifurcations. Chaos, the Lorenz equation, discrete maps, fractals, and strange attractors. Prerequisite: MATH 355.
3 Credit Hours.
 MATH 457  Partial Differential Equations

Fourier series, Fourier Integrals, the heat equation, StaumLiouville problems, the wave equation, the potential equation, problems in several dimensions, Laplace transforms numerical methods. Prerequisite: MATH 355.
3 Credit Hours.
 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 244.
3 Credit Hours.
 MATH 465  Cryptography

Classical cryptographic systems, public key cryptography, symmetric block ciphers, implementation issues. Related and supporting mathematical concepts and structures. Prerequisite: MATH 143.
3 Credit Hours.
 MATH 493  Special Topics

3 Credit Hours.
 MATH 495  Senior Residency

Required for graduating seniors.
0 Credit Hours.
Senior Residency
 MATH 498  Advanced Independent Study

Prior permission of sponsoring professor and chair required.
0 to 6 Credit Hours.
Independent Study.
 MATH 4WU  Washington Univeristy InterU

0 to 3 Credit Hours.
InterUniversity College
Graduate Courses
 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 411.
3 Credit Hours. (Crosslisted as MATH 412)
 MATH 502  Metric Spaces

Set theory, real line, separation properties, compactness, metric spaces, metrization. Offered every other spring semester. Prerequisite: MATH 421.
3 Credit Hours.
(Crosslisted as MATH 422)
 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 411.
3 Credit Hours. (Crosslisted as MATH 415)
 MATH 504  Multivariable Analysis
 Sequences and Series of functions, Differentiability, Integrability, Inverse and Implicit function theorems, Fundamental Theorems of Multivariable Calculus (Green’s Theorem, Stokes Theorem, Divergence Theorem). Prerequisite: MATH 421.
3 Credit Hours. (Crosslisted as MATH 423)
 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, CauchyRiemann conditions, geometry of a complex plane, conformal mapping, and engineering applications. Only offered occasionally.
Prerequisite: Permission of Instructor. 3 Credit Hours.
 MATH 507  Math Methods Engineering II

Calculus of residues, contour integration, multivalued functions, series solutions of differential equations, SturmLiouville 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 511  Algebra

Simple properties of groups, groups of transformations,subgroups, homomorphisms and isomorphisms, theorems of Schreier and JordanHölder, mappings into a group, rings, integral domains, fields, polynomials, direct sums and modules. Fall semester.
3 Credit Hours.
 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 511. 3 Credit Hours.
 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 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 521 and MATH 531. 3 Credit Hours. Offered occasionally.
 MATH 523  Functional Analysis
 Banach and Hilbert spaces. Linear functionals and linear operators. Dual spaces, weak and weak* topologies. HahnBanach, Closed Graph and Open Mapping Theorems. Topological Vector spaces. Prerequisite: MATH 521 and MATH 531. 3 Credit Hours. Offered occasionally.
 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 521. 3.000 Credit Hours. Offered occasionally.
 MATH 531  Topology I

Topological spaces, convergence, nets, product spaces, metrization, compact spaces, connected spaces. Fall semester.
3 Credit Hours.
 MATH 532  Topology II

Compact surfaces, fundamental groups, force groups and free products, Seifertvan Kampen theorem, covering spaces. Offered every spring semester.
Prerequisite: MATH 531. 3 Credit Hours.
 MATH 593  Special Topics in Mathematics

1 to 3 Credit Hours.
Graduate.
 MATH 595  Special Study for Examinations

0 Credit Hours.
Graduate
Special Study Exams.
 MATH 598  Graduate Reading Course

Prior permission of instructor and chairperson required.
1 to 3 Credit Hours.
Graduate
Independent Study
 MATH 599  Thesis Research

0 to 6 Credit Hours.
Graduate
Research.
 MATH 5CR  Master’s Degree Study

0 Credit Hours.
Graduate
Research.
 MATH 5WU  Washington University InterUniverisity Course

0 to 3 Credit Hours.
Graduate.
 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 ArtinWedderburn, tensor algebras. Offered occasionally.
3 Credit Hours.
 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 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 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 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 631  Algebraic Topology

Homotopy theory, homology theory, exact sequences, MayerVictoris sequences, degrees of maps, cohomology, Kunneth formula, cup and cap products, applications to manifolds including PoincareLefshetz duality. Offered every other year.
3 Credit Hours.
 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 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 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 642  Differential Geometry II

Continuation of MATH 641. Offered every spring semester.
3 Credit Hours.
 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 695  Special Study for Examinations

0 Credit Hours.
Graduate
Special Study Exams.
 MATH 698  Graduate Reading Course

Prior permission of instructor and chairperson required.
1 to 3 Credit Hours.
Graduate
Independent Study.
 MATH 699  Dissertation Research

0 to 6 Credit Hours.
Graduate
Research.
 MATH 6CR  Doctor of Philosophy Degree St

0 Credit Hours.
Graduate.

