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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These course descriptions are unofficial and may be out of date.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 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 094 - 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 095 - 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. Prerequisite: Math-Index ≥ 700.  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: Math-Index ≥ 800, or a 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: Math-Index ≥ 750 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: Math-Index ≥ 750 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:
Math-Index ≥ 750 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: Math-Index ≥ 750 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, t-test; correlation and regression; crosstabulations and chi-square.  Students learn to use a statistical package such as SPSS.  Prerequisite: Math-Index ≥ 900 or 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.  Math-Index ≥ 900 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 - 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 ≥ 950 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: Math-Index ≥ 1020 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: Score ≥ 4 on the Calculus AP Test (AB), Math-Index ≥ 1050, or 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, finite-precision arithmetic and round-off, condition number, iterative methods, vector and matrix norms, eigenvalues and eigenvectors, CAS package.  3 Credit Hours. 
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 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: 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 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, non-Euclidean 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 two-dimensional Euclidean geometry from a selected set of postulates.  Offered occasionally.  Prerequisite: MATH 142.  3 Credit Hours.  
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 142.  3 Credit Hours. 
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 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 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 355.  3 Credit Hours. 
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 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 Inter-U
0 to 3 Credit Hours.  Inter-University 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.  (Cross-listed 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.  (Cross-listed 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.  (Cross-listed as MATH 415)
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 421.  3 Credit Hours.  (Cross-listed 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, Cauchy-Riemann 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, 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 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 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.  Hahn-Banach, 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, Seifert-van 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 Inter-Univerisity 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 Artin-Wedderburn, 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, 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 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.
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