 Course ID:  MATH 1060. 3 hours.  Course Title:  Mathematics of Decision Making  Course Description:  Applications of modern mathematics to management and decision making including the solution of optimization problems using network theory, methods for optimal scheduling, voting methods, game theory, and related strategies. Applications include planning of postal delivery routes, placement of cable television lines, United States Congressional apportionment, and dispute resolution.  Athena Title:  MAT DECISION MAKING  Semester Course Offered:  Offered fall, spring and summer semester every year.  Grading System:  AF (Traditional) 
 Course ID:  MATH 1101. 3 hours.  Course Title:  Introduction to Mathematical Modeling  Course Description:  Mathematical modeling using graphical, numerical, symbolic, and verbal techniques to describe and explore realworld data and phenomena. The investigation and analysis of applied problems and questions, and of effective communication of quantitative concepts and results.  Athena Title:  INTRO MATH MODELING  Semester Course Offered:  Offered fall, spring and summer semester every year.  Grading System:  AF (Traditional) 
 Course ID:  MATH 2001. 3 hours.  Course Title:  Geometry for Elementary School Teachers  Course Description:  A deep examination of mathematical topics designed for future
elementary school teachers. Visualization. Properties of angles,
circles, spheres, triangles, and quadrilaterals. Measurement,
length, area, and volume. Transformations, congruence, and
similarity.  Athena Title:  GEOM ELEM TEACHERS  Duplicate Credit:  Not open to students with credit in MATH 5002/7002  Semester Course Offered:  Offered fall and spring semester every year.  Grading System:  AF (Traditional) 
 Course ID:  MATH 2002. 3 hours.  Course Title:  Numbers, Algebra, and Statistics for Elementary School Teachers  Course Description:  A deep examination of mathematical topics designed for future
elementary school teachers. Numbers, the decimal system, number
lines. Fractions. Number theory: factors, multiples, greatest
common factor, least common multiple, prime numbers. Algebra,
expressions and solving equations. Basic descriptive statistics.  Athena Title:  NUM ALG ELEM TEACH  Duplicate Credit:  Not open to students with credit in MATH 5001/7001 or MATH 5003/7003  Semester Course Offered:  Offered fall and spring semester every year.  Grading System:  AF (Traditional) 
 Course ID:  MATH 2003. 3 hours.  Course Title:  Arithmetic for Elementary School Teachers  Course Description:  A deep examination of mathematical topics designed for future
elementary school teachers. The meaning of addition,
multiplication, and division. Adding, multiplying and dividing
whole numbers, decimals, and fractions. Ratio and proportion.  Athena Title:  ARITH ELEM TEACHERS  Duplicate Credit:  Not open to students with credit in or MATH 5001, MATH 5003 or MATH 7001, MATH 7003  Prerequisite:  MATH 2002  Semester Course Offered:  Offered fall, spring and summer semester every year.  Grading System:  AF (Traditional) 
 Course ID:  MATH 2110E. 3 hours.  Course Title:  Calculus for Economics  Course Description:  Topics specifically chosen to meet the needs of the student of
economics: the definite integral, functions of several
variables, partial derivatives, Lagrange multipliers, and
matrices.  Athena Title:  Calculus for Economics  Duplicate Credit:  Not open to students with credit in MATH 2110, MATH 2260, MATH 2310H, MATH 2410H  Nontraditional Format:  This course will be taught 95% or more online.  Prerequisite:  MATH 2200 or MATH 2250  Semester Course Offered:  Not offered on a regular basis.  Grading System:  AF (Traditional) 
 Course ID:  MATH 2110. 3 hours.  Course Title:  Calculus for Economics  Course Description:  Topics specifically chosen to meet the needs of the student of economics: the definite integral, functions of several variables, partial derivatives, Lagrange multipliers, and matrices.  Athena Title:  Calculus for Economics  Duplicate Credit:  Not open to students with credit in MATH 2110E, MATH 2260, MATH 2310H, MATH 2410H  Prerequisite:  MATH 2200 or MATH 2250  Semester Course Offered:  Offered fall and spring semester every year.  Grading System:  AF (Traditional) 
 Course ID:  MATH 2200. 4 hours.  Course Title:  Analytic Geometry and Calculus  Course Description:  Introductory differential calculus and its applications. Topics
include limits, continuity, differentiability, derivatives of
trigonometric, exponential and logarithmic functions,
optimization, curve sketching, antiderivatives, differential
equations, and applications.  Athena Title:  ANALY GEO AND CALC  Duplicate Credit:  Not open to students with credit in MATH 2250 or MATH 2400 or MATH 2400H  Prerequisite:  MATH 1113  Semester Course Offered:  Offered fall, spring and summer semester every year.  Grading System:  AF (Traditional) 
 Course ID:  MATH 2250E. 4 hours.  Course Title:  Calculus I for Science and Engineering  Course Description:  Limits, derivatives, differentiation of algebraic and
transcendental functions; linear approximation, curve sketching,
optimization, indeterminate forms. The integral, Fundamental
Theorem of Calculus, areas. Emphasis on science and engineering
applications.  Athena Title:  Calculus I for Sci and Eng  Duplicate Credit:  Not open to students with credit in MATH 2200, MATH 2250, MATH 2300H, MATH 2400, MATH 2400H  Nontraditional Format:  This course will be taught 95% or more online.  Prerequisite:  MATH 1113 or permission of department  Semester Course Offered:  Offered summer semester every year.  Grading System:  AF (Traditional) 
 Course ID:  MATH 2250. 4 hours.  Course Title:  Calculus I for Science and Engineering  Course Description:  Limits, derivatives, differentiation of algebraic and
transcendental functions; linear approximation, curve sketching,
optimization, indeterminate forms. The integral, Fundamental
Theorem of Calculus, areas. Emphasis on science and engineering
applications.  Athena Title:  Calculus I for Sci and Eng  Duplicate Credit:  Not open to students with credit in MATH 2250E, MATH 2200, MATH 2300H, MATH 2400H, MATH 2400  Prerequisite:  MATH 1113 or permission of department  Semester Course Offered:  Offered fall, spring and summer semester every year.  Grading System:  AF (Traditional) 
 Course ID:  MATH 2260. 4 hours.  Course Title:  Calculus II for Science and Engineering  Course Description:  Volumes, arclength, work, separable differential equations.
Techniques of integration. Sequences and series, convergence
tests, power series and Taylor series. Vectors in
threedimensional space, dot product, cross product, lines and
planes.  Athena Title:  Calc II for Science and Engr  Duplicate Credit:  Not open to students with credit in MATH 2310H  Prerequisite:  MATH 2250 or MATH 2300H  Semester Course Offered:  Offered fall, spring and summer semester every year.  Grading System:  AF (Traditional) 
 Course ID:  MATH 2270. 4 hours.  Course Title:  Calculus III for Science and Mathematics  Course Description:  Calculus of functions of two and three variables: Parametric
curves and applications to planetary motion. Derivatives, the
gradient, Lagrange multipliers. Multiple integration, area,
volume, and physical applications, polar, cylindrical, and
spherical coordinates. Line and surface integrals, Green's,
Stokes's, and Divergence theorems, with applications to physics.  Athena Title:  Calc III Science and Math  Duplicate Credit:  Not open to students with credit in MATH 2500  Prerequisite:  MATH 2260 or MATH 2310H or MATH 2410 or MATH 2410H  Semester Course Offered:  Offered fall, spring and summer semester every year.  Grading System:  AF (Traditional) 
 Course ID:  MATH 2300H. 4 hours.  Course Title:  Differential Calculus (Honors)  Course Description:  Honors differential calculus and applications, including
optimization and related rate problems, L'HÃ´pital's rule.
Introduction to the integral, area between curves,
antidifferentiation, and the fundamental theorem of calculus.  Athena Title:  DIFF CALC HONORS  Duplicate Credit:  Not open to students with credit in MATH 2200  Prerequisite:  MATH 1113 and permission of Honors  Semester Course Offered:  Not offered on a regular basis.  Grading System:  AF (Traditional) 
 Course ID:  MATH 2310H. 4 hours.  Course Title:  Integral Calculus (Honors)  Course Description:  Integral calculus with techniques of integration, differential
equations, applications to volumes and physics. Improper
integrals, Taylor series, and applications. Introduction to
vectors and applications.  Athena Title:  INT CALC (HONORS)  Duplicate Credit:  Not open to students with credit in MATH 2110 or MATH 2210 or MATH 2260 or MATH 2410, MATH 2410H  Prerequisite:  (MATH 2250 or MATH 2300H or MATH 2400 or MATH 2400H) and permission of Honors  Semester Course Offered:  Not offered on a regular basis.  Grading System:  AF (Traditional) 
 Course ID:  MATH 2400H. 4 hours.  Course Title:  Differential Calculus with Theory (Honors)  Course Description:  A more rigorous and extensive treatment of differential calculus. Topics include the real numbers, the least upper bound property, limits, continuity, differentiability, and applications. Students with a strong background and interest in mathematics are encouraged to take this course; prior experience with calculus is not required.  Athena Title:  DIF CALC THRY HNRS  Duplicate Credit:  Not open to students with credit in MATH 2110 or MATH 2210 or MATH 2260 or MATH 2310H, MATH 2400  Prerequisite:  Permission of Honors  Semester Course Offered:  Not offered on a regular basis.  Grading System:  AF (Traditional) 
 Course ID:  MATH 2400. 4 hours.  Course Title:  Differential Calculus with Theory  Course Description:  A rigorous and extensive treatment of differential calculus.
Topics include the real numbers, the least upper bound property,
limits, continuity, differentiability, and applications.  Athena Title:  DIFF CALC THRY  Duplicate Credit:  Not open to students with credit in MATH 2260 or MATH 2110 or MATH 2210 or MATH 2310H, MATH 2400H  Nontraditional Format:  Students with a strong background and interest in mathematics are
encouraged to take this course; prior experience with calculus is
not required.  Prerequisite:  MATH 1113  Semester Course Offered:  Not offered on a regular basis.  Grading System:  AF (Traditional) 
 Course ID:  MATH 2410. 4 hours.  Course Title:  Integral Calculus with Theory  Course Description:  A rigorous and extensive treatment of integral calculus. Topics
include the Fundamental Theorem of calculus, applications of
integration, logarithms and exponentials, Taylor polynomials,
`sequences, series, and uniform convergence.  Athena Title:  Integral Calculus with Theory  Duplicate Credit:  Not open to students with credit in MATH 2410H  Prerequisite:  MATH 2400  Semester Course Offered:  Not offered on a regular basis.  Grading System:  AF (Traditional) 
 Course ID:  MATH 2410H. 4 hours.  Course Title:  Integral Calculus with Theory (Honors)  Course Description:  A more rigorous and extensive treatment of integral calculus. Topics include the Fundamental Theorem of calculus, applications of integration, logarithms and exponentials, Taylor polynomials, sequences, series, and uniform convergence.  Athena Title:  Integral Calc with Theory Hon  Duplicate Credit:  Not open to students with credit in MATH 2410  Prerequisite:  (MATH 2400 or MATH 2400H) and permission of Honors  Grading System:  AF (Traditional) 
 Course ID:  MATH 2500. 3 hours.  Course Title:  Accelerated Calculus III for Engineering Students  Course Description:  Calculus of functions of two and three variables: Parametric
curves, derivatives, gradient, Lagrange multipliers. Multiple
integration, area, volume, polar, cylindrical, and spherical
coordinates. Line integrals and Green's Theorem. Introduction to
surface integrals and Stokes's and Divergence Theorems. This is
an accelerated version of Calculus III for Science and
Engineering that covers fewer topics and applications.  Athena Title:  Calculus III for Engineering  Duplicate Credit:  Not open to students with credit in MATH 2270  Prerequisite:  MATH 2210 or MATH 2260 or MATH 2310H or MATH 2410 or MATH 2410H  Semester Course Offered:  Offered fall, spring and summer semester every year.  Grading System:  AF (Traditional) 
 Course ID:  MATH 2700. 3 hours.  Course Title:  Elementary Differential Equations  Course Description:  First and second order ordinary differential equations, including physical and biological applications, numerical solutions, and mathematical modeling.  Athena Title:  ELEM DIFF EQNS  Prerequisite:  MATH 2210 or MATH 2260 or MATH 2310H or MATH 2410 or MATH 2410H  Semester Course Offered:  Offered fall, spring and summer semester every year.  Grading System:  AF (Traditional) 
 Course ID:  MATH 3000. 3 hours.  Course Title:  Introduction to Linear Algebra  Course Description:  Theory and applications of systems of linear equations, vector spaces, and linear transformations. Fundamental concepts include: linear independence, basis, and dimension; orthogonality, projections, and least squares solutions of inconsistent systems; eigenvalues, eigenvectors, and applications to Markov chains, difference equations, and quadratic forms.  Athena Title:  Introduction to Linear Algebra  Duplicate Credit:  Not open to students with credit in MATH 3300  Prerequisite:  MATH 3200 or permission of department  Semester Course Offered:  Offered fall semester every year.  Grading System:  AF (Traditional) 
 Course ID:  MATH 3100. 3 hours.  Course Title:  Sequences and Series  Course Description:  Precise definitions of limit and convergence concepts; practical tests for convergence of infinite series; power series representations and numerical error estimates; applications to calculus and explicit summation formulae; trigonometric series.  Athena Title:  SEQUENCES & SERIES  Prerequisite:  MATH 3200 or permission of department  Semester Course Offered:  Offered fall and spring semester every year.  Grading System:  AF (Traditional) 
 Course ID:  MATH 3100H. 3 hours.  Course Title:  Sequences and Series (Honors)  Course Description:  Induction, functions, limits, and convergence of sequences and
series. Discussions of proof techniques. Definitions of
continuity, Intermediate and Maximum Value Theorems. Taylor's
Theorem and applications.  Athena Title:  Sequences and Series Honors  Duplicate Credit:  Not open to students with credit in MATH 3100  Prerequisite:  (MATH 2260 or MATH 2310H) and permission of Honors  Semester Course Offered:  Offered spring semester every year.  Grading System:  AF (Traditional) 
 Course ID:  MATH 3200. 3 hours.  Course Title:  Introduction to Higher Mathematics  Course Description:  Preparation in mathematical reasoning and proofwriting necessary for upper division course work in mathematics. Topics include logic, integers and induction, sets and relations, equivalence relations and partitions, and functions (including injectivity and surjectivity).  Athena Title:  Intro to Higher Mathematics  Prerequisite:  MATH 2260 or MATH 2310H or MATH 2410 or MATH 2410H or MATH 2270 or MATH 2500  Semester Course Offered:  Offered fall, spring and summer semester every year.  Grading System:  AF (Traditional) 
 Course ID:  MATH 3220. 1 hour. Repeatable for maximum 4 hours credit.  Course Title:  Advanced Problem Solving  Course Description:  Strategies and tactics for solving advanced problems in
undergraduate mathematics, designed to prepare students for a
challenging external exam (Putnam Exam/Mathematics Subject
GRE/Actuarial Exam) which is ordinarily a required part of the
course.  Athena Title:  Advanced Problem Solving  Nontraditional Format:  Will not count towards the mathematics degree.  Pre or Corequisite:  MATH 3000 or MATH 3100 or MATH 3200 or MATH 3500 or MATH 3500H  Semester Course Offered:  Offered fall and spring semester every year.  Grading System:  S/U (Satisfactory/Unsatisfactory) 
 Course ID:  MATH 3300. 3 hours.  Course Title:  Applied Linear Algebra  Course Description:  Linear algebra from an applied and computational viewpoint.
Linear equations, vector spaces, linear transformations; linear
independence, basis, dimension; orthogonality, projections, and
least squares solutions; eigenvalues, eigenvectors, singular
value decomposition. Applications to science and engineering.  Athena Title:  Applied Linear Algebra  Duplicate Credit:  Not open to students with credit in MATH 3000  Prerequisite:  MATH 2260 or MATH 2410 or MATH 2410H  Semester Course Offered:  Offered fall, spring and summer semester every year.  Grading System:  AF (Traditional) 
 Course ID:  MATH 3500H. 4 hours.  Course Title:  Multivariable Mathematics I (Honors)  Course Description:  Vector algebra and geometry, fundamental concepts of linear
algebra, linear transformations, differential calculus of
functions of several variables, solutions of linear systems and
linear independence, extremum problems and projections. This
course and its sequel give an integrated and more prooforiented
treatment of the material in Multivariable Calculus and
Introduction to Linear Algebra.  Athena Title:  Multivariable Mathematic I Hon  Duplicate Credit:  Not open to students with credit in MATH 3500  Prerequisite:  (MATH 2210 or MATH 2260 or MATH 2310H or MATH 2410 or MATH 2410H) and permission of Honors  Semester Course Offered:  Offered fall semester every year.  Grading System:  AF (Traditional) 
 Course ID:  MATH 3500. 4 hours.  Course Title:  Multivariable Mathematics I  Course Description:  Vector algebra and geometry, fundamental concepts of linear
algebra, linear transformations, differential calculus of
functions of several variables, solutions of linear systems and
linear independence, extremum problems and projections. This
course and its sequel give an integrated and more prooforiented
treatment of the material in Multivariable Calculus and
Introduction to Linear Algebra.  Athena Title:  Multivariable Mathematics I  Duplicate Credit:  Not open to students with credit in MATH 3500H  Prerequisite:  MATH 2210 or MATH 2260 or MATH 2310H or MATH 2410 or MATH 2410H  Semester Course Offered:  Offered fall semester every year.  Grading System:  AF (Traditional) 
 Course ID:  MATH 3510. 4 hours.  Course Title:  Multivariable Mathematics II  Course Description:  Inverse function theorem and manifolds, integration in several
variables, the change of variables theorem. Differential forms,
line integrals, surface integrals, and Stokes's Theorem;
applications to physics. Eigenvalues, eigenvectors, spectral
theorem, and applications.  Athena Title:  Multivariable Mathematics II  Duplicate Credit:  Not open to students with credit in MATH 3510H  Prerequisite:  MATH 3500 or MATH 3500H  Semester Course Offered:  Offered spring semester every year.  Grading System:  AF (Traditional) 
 Course ID:  MATH 3510H. 4 hours.  Course Title:  Multivariable Mathematics II (Honors)  Course Description:  Inverse function theorem and manifolds, integration in several
variables, the change of variables theorem. Differential forms,
line integrals, surface integrals, and Stokes's Theorem;
applications to physics. Eigenvalues, eigenvectors, spectral
theorem, and applications.  Athena Title:  Multivariable Mathematics II H  Duplicate Credit:  Not open to students with credit in MATH 3510  Prerequisite:  (MATH 3500 or MATH 3500H) and permission of Honors  Semester Course Offered:  Offered spring semester every year.  Grading System:  AF (Traditional) 
 Course ID:  MATH 4000/6000. 3 hours.  Course Title:  Modern Algebra and Geometry I  Course Description:  Abstract algebra, emphasizing geometric motivation and applications. Beginning with a careful study of integers, modular arithmetic, and the Euclidean algorithm, the course moves on to fields, isometries of the complex plane, polynomials, splitting fields, rings, homomorphisms, field extensions, and compass and straightedge constructions.  Athena Title:  Modern Algebra and Geometry I  Prerequisite:  (MATH 3000 or MATH 3300 or MATH 3500 or MATH 3500H) and (MATH 3200 or CSCI(MATH) 2610 )  Semester Course Offered:  Offered fall, spring and summer semester every year.  Grading System:  AF (Traditional) 
 Course ID:  MATH 4010/6010. 3 hours.  Course Title:  Modern Algebra and Geometry II  Course Description:  More advanced abstract algebraic structures and concepts, such as groups, symmetry, group actions, counting principles, symmetry groups of the regular polyhedra, Burnside's Theorem, isometries of R^3, Galois Theory, and affine and projective geometry.  Athena Title:  MOD ALG & GEOM II  Prerequisite:  MATH 4000/6000  Semester Course Offered:  Offered spring semester every year.  Grading System:  AF (Traditional) 
 Course ID:  MATH 4050/6050. 3 hours.  Course Title:  Advanced Linear Algebra  Course Description:  Orthogonal and unitary groups, spectral theorem; infinite dimensional vector spaces; Jordan and rational canonical forms and applications.  Athena Title:  ADV LIN ALG  Prerequisite:  MATH 4000/6000  Semester Course Offered:  Not offered on a regular basis.  Grading System:  AF (Traditional) 
 Course ID:  MATH 4080/6080. 3 hours.  Course Title:  Advanced Algebra  Course Description:  Linear algebra, groups, rings, and modules, intermediate in level between Modern Algebra and Geometry II and Algebra. Topics include the finitedimensional spectral theorem, group actions, classification of finitely generated modules over principal ideal domains, and canonical forms of linear operators.  Athena Title:  ADVANCED ALGEBRA  Prerequisite:  MATH 4010/6010 or permission of department  Semester Course Offered:  Not offered on a regular basis.  Grading System:  AF (Traditional) 
 Course ID:  MATH 4100/6100. 3 hours.  Course Title:  Real Analysis  Course Description:  Metric spaces and continuity; differentiable and integrable functions of one variable; sequences and series of functions.  Athena Title:  REAL ANALYSIS  Prerequisite:  MATH 3100 and (MATH 3200 or MATH 3610)  Semester Course Offered:  Offered fall semester every year.  Grading System:  AF (Traditional) 
 Course ID:  MATH 4110/6110. 3 hours.  Course Title:  The Lebesgue Integral and Applications  Course Description:  The Lebesgue integral with applications to Fourier analysis and probability.  Athena Title:  LEBESGUE INTEGRAL  Prerequisite:  MATH 4100/6100 or MATH 4200/6200 or permission of department  Semester Course Offered:  Offered spring semester every evennumbered year.  Grading System:  AF (Traditional) 
 Course ID:  MATH 4120/6120. 3 hours.  Course Title:  Multivariable Analysis  Course Description:  The derivative as a linear map, inverse and implicit function theorems, change of variables in multiple integrals; manifolds, differential forms, and the generalized Stokes' Theorem.  Athena Title:  MULTIVAR ANALYSIS  Prerequisite:  MATH 3510 or MATH 3510H or MATH 4100/6100 or MATH 4200/6200  Semester Course Offered:  Not offered on a regular basis.  Grading System:  AF (Traditional) 
 Course ID:  MATH 4150/6150. 3 hours.  Course Title:  Complex Variables  Course Description:  Differential and integral calculus of functions of a complex variable, with applications. Topics include the Cauchy integral formula, power series and Laurent series, and the residue theorem.  Athena Title:  COMPLEX VARIABLES  Prerequisite:  (MATH 2270 and MATH 3100) or (MATH 2500 and MATH 3100) or MATH 3510 or MATH 3510H  Semester Course Offered:  Offered every year.  Grading System:  AF (Traditional) 
 Course ID:  MATH 4200/6200. 3 hours.  Course Title:  Point Set Topology  Course Description:  Topological spaces, continuity; connectedness, compactness; separation axioms and Tietze extension theorem; function spaces.  Athena Title:  POINT SET TOPOLOGY  Prerequisite:  MATH 3100 and (MATH 3200 or MATH 3610)  Semester Course Offered:  Offered every year.  Grading System:  AF (Traditional) 
 Course ID:  MATH 4220/6220. 3 hours.  Course Title:  Differential Topology  Course Description:  Manifolds in Euclidean space: fundamental ideas of transversality, homotopy, and intersection theory; differential forms, Stokes' Theorem, deRham cohomology, and degree theory.  Athena Title:  DIFF TOPOLOGY  Prerequisite:  (MATH 3510 or MATH 3510H or MATH 4120/6120) and (MATH 4100/6100 or MATH 4200/6200)  Semester Course Offered:  Offered fall semester every oddnumbered year.  Grading System:  AF (Traditional) 
 Course ID:  MATH 4250/6250. 3 hours.  Course Title:  Differential Geometry  Course Description:  The geometry of curves and surfaces in Euclidean space: Frenet formulas for curves, notions of curvature for surfaces; GaussBonnet Theorem; discussion of nonEuclidean geometries.  Athena Title:  Differential Geometry  Prerequisite:  (MATH 2270 and MATH 3000) or (MATH 2270 and MATH 3200 and MATH 3300) or (MATH 2500 and MATH 3000) or (MATH 2500 and MATH 3200 and MATH 3300) or MATH 3510 or MATH 3510H  Semester Course Offered:  Offered every year.  Grading System:  AF (Traditional) 
 Course ID:  MATH 4300/6300. 3 hours.  Course Title:  Introduction to Algebraic Curves  Course Description:  Polynomials and resultants, projective spaces. The focus is on plane algebraic curves: intersection, Bezout's theorem, linear systems, rational curves, singularities, blowing up.  Athena Title:  INTRO TO ALG CURVES  Prerequisite:  MATH 4000/6000 or permission of department  Semester Course Offered:  Not offered on a regular basis.  Grading System:  AF (Traditional) 
 Course ID:  MATH 4400/6400. 3 hours.  Course Title:  Number Theory  Course Description:  Euler's theorem, public key cryptology, pseudoprimes, multiplicative functions, primitive roots, quadratic reciprocity, continued fractions, sums of two squares and Gaussian integers.  Athena Title:  NUMBER THEORY  Prerequisite:  MATH 4000/6000  Semester Course Offered:  Not offered on a regular basis.  Grading System:  AF (Traditional) 
 Course ID:  MATH 4450/6450. 3 hours.  Course Title:  Cryptology and Computational Number Theory  Course Description:  Recognizing prime numbers, factoring composite numbers, finite fields, elliptic curves, discrete logarithms, private key cryptology, key exchange systems, signature authentication, public key cryptology.  Athena Title:  COMP NUMBER THY  Prerequisite:  MATH 4000/6000  Semester Course Offered:  Offered every year.  Grading System:  AF (Traditional) 
 Course ID:  MATH 4500/6500. 3 hours.  Course Title:  Numerical Analysis I  Course Description:  Methods for finding approximate numerical solutions to a variety of mathematical problems, featuring careful error analysis. A mathematical software package will be used to implement iterative techniques for nonlinear equations, polynomial interpolation, integration, and problems in linear algebra such as matrix inversion, eigenvalues and eigenvectors.
 Athena Title:  Numerical Analysis I  Prerequisite:  [(MATH 3000 or MATH 3300 or MATH 3500 or MATH 3500H) and (MATH 3100 or MATH 3100H) and CSCI 13011301L] or permission of department  Semester Course Offered:  Offered fall and spring semester every year.  Grading System:  AF (Traditional) 
 Course ID:  MATH 4510/6510. 3 hours.  Course Title:  Numerical Analysis II  Course Description:  Numerical solutions of ordinary and partial differential equations, higherdimensional Newton's method, and splines.  Athena Title:  NUMER ANALYSIS II  Prerequisite:  (MATH 2270 or MATH 2500 or MATH 3510 or MATH 3510H) and MATH 2700 and MATH 4500/6500  Semester Course Offered:  Offered spring semester every year.  Grading System:  AF (Traditional) 
 Course ID:  MATH 4600/6600. 3 hours.  Course Title:  Probability  Course Description:  Discrete and continuous random variables, expectation, independence and conditional probability; binomial, Bernoulli, normal, and Poisson distributions; law of large numbers and central limit theorem.  Athena Title:  PROBABILITY  Prerequisite:  [(MATH 2270 or MATH 2500) and (MATH 2260 or MATH 3100)] or MATH 3510 or MATH 3510H  Semester Course Offered:  Offered every year.  Grading System:  AF (Traditional) 
 Course ID:  MATH(CSCI) 4670/6670. 3 hours.  Course Title:  Combinatorics  Course Description:  Basic counting principles: permutations, combinations, probability, occupancy problems, and binomial coefficients. More sophisticated methods include generating functions, recurrence relations, inclusion/exclusion principle, and the pigeonhole principle. Additional topics include asymptotic enumeration, Polya counting theory, combinatorial designs, coding theory, and combinatorial optimization.  Athena Title:  Combinatorics  Prerequisite:  MATH 3000 or MATH 3300 or MATH 3500 or MATH 3500H or CSCI(MATH) 2610 or MATH 3200  Semester Course Offered:  Offered fall semester every evennumbered year.  Grading System:  AF (Traditional) 
 Course ID:  MATH(CSCI) 4690/6690. 3 hours.  Course Title:  Graph Theory  Course Description:  Elementary theory of graphs and digraphs. Topics include connectivity, reconstruction, trees, Euler's problem, hamiltonicity, network flows, planarity, node and edge colorings, tournaments, matchings, and extremal graphs. A number of algorithms and applications are included.  Athena Title:  Graph Theory  Prerequisite:  CSCI(MATH) 2610 or MATH 3200  Semester Course Offered:  Offered spring semester every evennumbered year.  Grading System:  AF (Traditional) 
 Course ID:  MATH 4700/6700. 3 hours.  Course Title:  Qualitative Ordinary Differential Equations  Course Description:  Transform methods, linear and nonlinear systems of ordinary differential equations, stability, and chaos.  Athena Title:  Qual Ordinary Differ Equations  Prerequisite:  MATH 2700 and [MATH 3000 or (MATH 3200 and MATH 3300) or MATH 3500 or MATH 3500H]  Semester Course Offered:  Offered fall semester every year.  Grading System:  AF (Traditional) 
 Course ID:  MATH 4720/6720. 3 hours.  Course Title:  Introduction to Partial Differential Equations  Course Description:  The basic partial differential equations of mathematical physics: Laplace's equation, the wave equation, and the heat equation. Separation of variables and Fourier series techniques are featured.  Athena Title:  Intro to PDEs  Prerequisite:  MATH 2700 and (MATH 2270 or MATH 2500 or MATH 3510 or MATH 3510H) and MATH 3100  Semester Course Offered:  Offered spring semester every evennumbered year.  Grading System:  AF (Traditional) 
 Course ID:  MATH(MARS) 4730/6730. 3 hours.  Course Title:  Mathematics of Climate  Course Description:  Basic mathematical models describing the physical, chemical, and
biological interactions that affect climate. Mathematical and
computational tools for analyzing these models.  Athena Title:  Mathematics of Climate  Prerequisite:  MATH 2700  Semester Course Offered:  Offered fall semester every evennumbered year.  Grading System:  AF (Traditional) 
 Course ID:  MATH 4750/6750. 3 hours.  Course Title:  Matrix and Integral Transforms with Applications  Course Description:  Foundations in the most commonly used transforms in mathematics,
science, and engineering. Eigenvector decompositions, Fourier
transforms, singular value decompositions, and the Radon
transform, with emphasis on mathematical structure and
applications.  Athena Title:  Matrix and Integral Transforms  Prerequisite:  [MATH 3000 or (MATH 3200 and MATH 3300) or MATH 3510 or MATH 3510H] and (MATH 3100 or MATH 3100H)  Grading System:  AF (Traditional) 
 Course ID:  MATH 4760/6760. 3 hours.  Course Title:  Mathematics and Music  Course Description:  This course is intended for undergraduates (math majors, music majors, and others) interested in the mathematical aspects of music. At least some familiarity with musical notation is a prerequisite. Topics to be discussed include the structure of sound, the construction of scales, and synthesis. There is a serious writing component.  Athena Title:  MATH AND MUSIC  Prerequisite:  (MATH 2260 or MATH 2310H or MATH 2410H) and (MATH 2270 or MATH 2500 or MATH 2700)  Semester Course Offered:  Not offered on a regular basis.  Grading System:  AF (Traditional) 
 Course ID:  MATH(BINF) 4780/6780. 3 hours.  Course Title:  Mathematical Biology  Course Description:  Mathematical models in the biological sciences, systems,
phaseplane analysis, diffusion, convective transport,
bifurcation analysis. Possible applications will include
population models, infectious disease and epidemic models,
acquired immunity and drug distribution, tumor growth, and
analysis of arterial flow dynamics.  Athena Title:  Mathematical Biology  Undergraduate Prerequisite:  (MATH 2270 or MATH 2500 or MATH 3510 or MATH 3510H) and [(MATH 4700/6700 or MATH 2700) and permission of department)]  Graduate Prerequisite:  Permission of department  Semester Course Offered:  Offered spring semester every oddnumbered year.  Grading System:  AF (Traditional) 
 Course ID:  MATH 4790/6790. 3 hours.  Course Title:  The Mathematics of Option Pricing  Course Description:  Bonds, stock markets, derivatives, arbitrage, and binomial tree
models for stocks and options, BlackScholes formula for options
pricing, hedging. Computational methods will be incorporated.  Athena Title:  Mathematics of Option Pricing  Prerequisite:  [(MATH 2270 or MATH 2500) and MATH 3000] or [(MATH 2270 or MATH 2500) and MATH 3200 and MATH 3300] or MATH 3510 or MATH 3510H or permission of department  Grading System:  AF (Traditional) 
 Course ID:  MATH 4801. 36 hours. Repeatable for maximum 6 hours credit.  Course Title:  Mathematics Internship  Course Description:  Students are permitted to enter an organization to obtain
practical and applied experience. A paper describing and
analyzing this experience is required.  Athena Title:  Mathematics Internship  Nontraditional Format:  This course is designed for undergraduate internship and does
not meet formally. The hours of credit will be determined by the
faculty supervisor and will reflect the time involved at the
internship site. Typically students would earn three hours of
academic credit for 240 hours of work during the semester. A
final paper (report) reflecting on the internship experience
is required.  Prerequisite:  Permission of department  Semester Course Offered:  Offered fall, spring and summer semester every year.  Grading System:  S/U (Satisfactory/Unsatisfactory) 
 Course ID:  MATH 4850/6850. 3 hours.  Course Title:  History of Mathematics  Course Description:  The development of mathematical thought from ancient times to the present, paying particular attention to the context of today's mathematics curriculum.  Athena Title:  HISTORY OF MATH  Prerequisite:  Senior standing  Semester Course Offered:  Not offered on a regular basis.  Grading System:  AF (Traditional) 
 Course ID:  MATH 4900/6900. 3 hours. Repeatable for maximum 6 hours credit.  Course Title:  Topics in Mathematics  Course Description:  A special topic not otherwise offered in the mathematics curriculum.  Athena Title:  TOPICS IN MATH  Prerequisite:  Senior standing  Semester Course Offered:  Not offered on a regular basis.  Grading System:  AF (Traditional) 
 Course ID:  MATH 4950. 13 hours. Repeatable for maximum 6 hours credit. 26 hours lab per week.  Course Title:  Research in Mathematics  Course Description:  Research in mathematics directed by a faculty member in the department of mathematics. A final report is required.  Athena Title:  RESEARCH MATH  Nontraditional Format:  Students will meet with faculty members on a regular basis.  Semester Course Offered:  Offered every year.  Grading System:  S/U (Satisfactory/Unsatisfactory) 
 Course ID:  MATH 4960R. 16 hours. Repeatable for maximum 16 hours credit.  Course Title:  FacultyMentored Undergraduate Research I  Course Description:  Facultysupervised independent or collaborative inquiry into
fundamental and applied problems within a discipline that requires
students to gather, analyze, and synthesize and interpret data and
to present results in writing and other relevant communication
formats.  Athena Title:  Undergraduate Research I  Nontraditional Format:  This course belongs to a progressive research course sequence to
promote a student's increasing skill development and depth of
inquiry, as well as growing independent research capability.
This course requires the close supervision of a faculty member
as the student undertakes a systematic and indepth inquiry into
unknown, fundamental, and applied problems. In some cases, the
student will work collaboratively as part of a research team.
The student will have to apply understanding of the discipline
to identify or shape research questions and apply skills and
techniques learned to the research project. Students will gather
data, synthesize relevant literature, analyze, and interpret
data. The student will present results in writing or through
participation in researchgroup or program meetings and meetings
with their faculty mentor. The student will receive feedback
from the faculty mentor on their research progress and written
or oral presentation of results. A minimum of 45 hours of work
per credit hour per semester is required.  Prerequisite:  Permission of department  Semester Course Offered:  Offered fall, spring and summer semester every year.  Grading System:  AF (Traditional) 
 Course ID:  MATH 4970R. 16 hours. Repeatable for maximum 8 hours credit.  Course Title:  FacultyMentored Undergraduate Research II  Course Description:  Facultysupervised independent or collaborative inquiry into
fundamental and applied problems within a discipline that requires
students to gather, analyze, and synthesize and interpret data and
to present results in writing and other relevant communication
formats.  Athena Title:  Undergraduate Research II  Nontraditional Format:  These courses belong to a progressive research course sequence
to promote a student's increasing skill development and depth of
inquiry, as well as growing independent research capability. The
courses require the close supervision of a faculty member as the
student undertakes a systematic and indepth inquiry into
unknown, fundamental, and applied problems. In some cases, the
student will work collaboratively as part of a research team.
The student will have to apply understanding of the discipline
to identify or shape research questions and apply skills and
techniques learned to the research project. Students will gather
data, synthesize relevant literature, analyze, and interpret
data. The student will present results in writing or through
participation in researchgroup or program meetings and meetings
with their faculty mentor. The student will receive feedback
from the faculty mentor on their research progress and written
or oral presentation of results. A minimum of 45 hours of work
per credit hour per semester is required.  Prerequisite:  Permission of department  Semester Course Offered:  Offered fall, spring and summer semester every year.  Grading System:  AF (Traditional) 
 Course ID:  MATH 4990R. 16 hours. Repeatable for maximum 8 hours credit.  Course Title:  Undergraduate Research Thesis (or Final Project)  Course Description:  Facultysupervised independent or collaborative inquiry into
fundamental and applied problems within a discipline that requires
students to gather, analyze, and synthesize and interpret data.
Students will write or produce a thesis or other professional
capstone product, such as a report or portfolio that describes
their systematic and indepth inquiry.  Athena Title:  Undergraduate Thesis  Nontraditional Format:  This is a capstone course under the direct supervision of a
faculty member. This course may be the culmination of the 4960R
4980R sequence. Students will write a thesis or other
professional capstone product, such as a report or portfolio,
that describes their systematic and indepth inquiry into an
unknown, fundamental, or applied problem. The thesis or capstone
product is written in close collaboration with the faculty
member and must be approved by that faculty member and/or the
department. The student will apply understanding of the
discipline to identify or shape the research question and apply
skills and techniques learned to complete the research project.
The student will have gathered data, synthesized relevant
literature and materials, analyzed, and interpreted data. The
student will demonstrate in writing the contribution of their
work to the discovery and interpretation of knowledge
significant to their field of study. The student will have
presented results in the form of a properly formatted,
professionally rigorous thesis document or other appropriate
professional capstone product and through the formal
presentation of the thesis or product to faculty and peers
during an approved event. The student will receive feedback from
the faculty member on the overall execution of their thesis
project, the written thesis, and their presentation.  Prerequisite:  Permission of department  Semester Course Offered:  Offered fall, spring and summer semester every year.  Grading System:  AF (Traditional) 
 Course ID:  MATH 5001/7001. 3 hours.  Course Title:  Arithmetic and Problem Solving  Course Description:  Topics in mathematics designed for future elementary school teachers. Problem solving. Number systems: whole numbers, integers, rational numbers (fractions) and real numbers (decimals), and the relationships between these systems. Understanding multiplication and division, including why standard computational algorithms work. Properties of arithmetic. Applications of elementary mathematics.  Athena Title:  Arithmetic and Problem Solving  Semester Course Offered:  Offered fall and spring semester every year.  Grading System:  AF (Traditional) 
 Course ID:  MATH 5002/7002. 3 hours.  Course Title:  Geometry and Problem Solving  Course Description:  A deep examination of mathematical topics designed for future
elementary school teachers. Length, area, and volume. Geometric
shapes and their properties. Probability. Elementary number theory. Applications of elementary mathematics.  Athena Title:  Geometry and Problem Solving  Prerequisite:  MATH 5001/7001  Semester Course Offered:  Offered fall and spring semester every year.  Grading System:  AF (Traditional) 
 Course ID:  MATH 5003/7003. 3 hours.  Course Title:  Algebra and Problem Solving  Course Description:  A deep examination of topics in mathematics that are relevant for elementary school teaching. Probability, number theory, algebra and functions, including ratio and proportion. Posing and modifying problems.  Athena Title:  ALG & PROB SOLV  Undergraduate Prerequisite:  MATH 5002/7002  Graduate Prerequisite:  MATH 5002/7002  Semester Course Offered:  Offered fall and spring semester every year.  Grading System:  AF (Traditional) 
 Course ID:  MATH 5020/7020. 3 hours.  Course Title:  Arithmetic for Middle Grades Teachers  Course Description:  A deep examination of topics in mathematics that are relevant for
middle grades teachers. Reasoning about addition, subtraction,
multiplication, and division within the baseten system and with
fractions. Deriving and explaining procedures and algorithms in
arithmetic.  Athena Title:  Arithmetic for MG Teachers  Prerequisite:  MATH 2200 or MATH 2250  Semester Course Offered:  Offered fall semester every year.  Grading System:  AF (Traditional) 
 Course ID:  MATH 5030/7030. 3 hours.  Course Title:  Geometry and Measurement for Middle Grades Teachers  Course Description:  Principles of geometry and measurement for middle school teachers.  Athena Title:  Geom Measure Mid Grades Teach  Prerequisite:  MATH 2200 or MATH 2250  Semester Course Offered:  Not offered on a regular basis.  Grading System:  AF (Traditional) 
 Course ID:  MATH 5035/7035. 3 hours.  Course Title:  Algebra for Middle Grades Teachers  Course Description:  A deep examination of topics in mathematics that are relevant for
middle grades teachers. Reasoning about fraction division, ratio,
proportional relationships, inversely proportional relationships,
descriptive statistics, probability, factors, multiples, and
prime numbers. Deriving and explaining equations and solution
methods.  Athena Title:  Algebra for MG Teachers  Prerequisite:  (MATH 2200 or MATH 2250 or MATH 2250E) and MATH 5020/7020  Semester Course Offered:  Offered spring semester every year.  Grading System:  AF (Traditional) 
 Course ID:  MATH 5200/7200. 3 hours.  Course Title:  Foundations of Geometry I  Course Description:  Advanced elementary geometry for prospective teachers of secondary school mathematics: axiom systems and models; the parallel postulate; neutral, Euclidean, and nonEuclidean geometries.  Athena Title:  FNDNS GEOMETRY I  Prerequisite:  (MATH 3000 or MATH 3500) and (MATH 3200 or MATH 3610)  Semester Course Offered:  Offered fall and spring semester every year.  Grading System:  AF (Traditional) 
 Course ID:  MATH 5210/7210. 3 hours.  Course Title:  Foundations of Geometry II  Course Description:  Further development of the axioms and models for Euclidean and nonEuclidean geometry; transformation geometry.  Athena Title:  FNDNS GEOMETRY II  Prerequisite:  MATH 5200/7200  Semester Course Offered:  Offered spring semester every year.  Grading System:  AF (Traditional) 
 Course ID:  MATH 6800. 16 hours. Repeatable for maximum 30 hours credit.  Course Title:  Directed Reading and/or Projects  Course Description:  Directed reading and/or project at the master's level.  Athena Title:  DIR READ AND/OR PRO  Nontraditional Format:  Directed study.  Semester Course Offered:  Offered every year.  Grading System:  AF (Traditional) 
 Course ID:  MATH 7000. 16 hours. Repeatable for maximum 30 hours credit.  Course Title:  Master's Research  Course Description:  Research while enrolled for a master's degree under the direction of faculty members.  Athena Title:  MASTER'S RESEARCH  Nontraditional Format:  Independent research under the direction of a faculty member.  Prerequisite:  Permission of department  Semester Course Offered:  Offered fall, spring and summer semester every year.  Grading System:  S/U (Satisfactory/Unsatisfactory) 
 Course ID:  MATH 7005. 3 hours. Repeatable for maximum 45 hours credit.  Course Title:  Graduate Student Seminar  Course Description:  Advanced supervised experience in an applied setting. This
course may not be used to satisfy a student's approved program of
study.  Athena Title:  Graduate Student Seminar  Nontraditional Format:  Seminar.  Semester Course Offered:  Offered fall, spring and summer semester every year.  Grading System:  AF (Traditional) 
 Course ID:  MATH 7040. 3 hours.  Course Title:  Basic Ideas of Calculus I  Course Description:  Survey of onevariable calculus in preparation for teaching calculus at the secondary level: combines review of basic techniques with careful study of underlying concepts.  Athena Title:  CALCULUS IDEAS I  Prerequisite:  MATH 2210 or MATH 2310H or MATH 2410H  Semester Course Offered:  Not offered on a regular basis.  Grading System:  AF (Traditional) 
 Course ID:  MATH 7050. 3 hours.  Course Title:  Basic Ideas of Calculus II  Course Description:  A continuation of Basic Ideas of Calculus I focusing on functions of several variables.  Athena Title:  CALCULUS IDEAS II  Prerequisite:  MATH 2210 or MATH 2310H or MATH 2410H  Semester Course Offered:  Not offered on a regular basis.  Grading System:  AF (Traditional) 
 Course ID:  MATH 7100. 3 hours.  Course Title:  Technical Report  Course Description:  For use with the Master's degree in Applied Mathematical Science  Mathematics option.  Athena Title:  TECHNICAL REPORT  Nontraditional Format:  Independent research under the direction of a faculty member.  Semester Course Offered:  Offered fall, spring and summer semester every year.  Grading System:  AF (Traditional) 
 Course ID:  MATH 7300. 19 hours. Repeatable for maximum 18 hours credit.  Course Title:  Master's Thesis  Course Description:  Thesis writing under the direction of the major professor.  Athena Title:  MASTER'S THESIS  Nontraditional Format:  Independent research and thesis preparation.  Prerequisite:  Permission of department  Semester Course Offered:  Offered every year.  Grading System:  S/U (Satisfactory/Unsatisfactory) 
 Course ID:  MATH 7900. 3 hours. Repeatable for maximum 6 hours credit.  Course Title:  Foundations for Graduate Mathematics  Course Description:  An intensive review of techniques and material essential for graduate study in mathematics, including background in calculus and linear algebra. Emphasis is on small group study and presentations. Topics include proofs, induction, the metric structure of the reals, the BolzanoWeierstrass theorem, and the diagonalization theorem.  Athena Title:  FOUND GRAD MATH  Nontraditional Format:  The intention is to limit lectures by the instructor to a
minimum essential for progress of the course. The traditional lecture format will be replaced by whole group discussions and planning, directed study in small groups, and student presentations. Class enrollment for this course will normally be limited to ten students.  Prerequisite:  Permission of department  Semester Course Offered:  Offered fall semester every year.  Grading System:  AF (Traditional) 
 Course ID:  MATH 8000. 3 hours.  Course Title:  Algebra I  Course Description:  Groups and rings, including Sylow theorems, classifying small groups, finitely generated abelian groups, JordanHolder theorem, solvable groups, simplicity of the alternating group, euclidean domains, principal ideal domains, unique factorization domains, noetherian rings, Hilbert basis theorem, Zorn's lemma, and existence of maximal ideals and vector space bases.  Athena Title:  Algebra I  Prerequisite:  MATH 4010/6010 or permission of department  Corequisite:  MATH 8005  Semester Course Offered:  Offered fall semester every year.  Grading System:  AF (Traditional) 
 Course ID:  MATH 8005. 2 hours.  Course Title:  Problem Session in Algebra  Course Description:  Techniques and approaches to problems in algebra as an aid to
mastery of the basic theory.  Athena Title:  PROBLEMS IN ALGEBRA  Nontraditional Format:  Significant outside preparation will be expected.  Corequisite:  MATH 8000  Semester Course Offered:  Offered every year.  Grading System:  S/U (Satisfactory/Unsatisfactory) 
 Course ID:  MATH 8010. 3 hours.  Course Title:  Algebra II  Course Description:  Modules and fields, including noetherian modules, finitely generated modules over principal ideal domains, canonical forms of matrices, spectral theorems, tensor products, algebraic and transcendental field extensions, galois theory, solvability of polynomials, symmetric functions, cyclotomic extensions, finite fields, solution formulas for polynomials of low degree.  Athena Title:  ALGEBRA II  Prerequisite:  MATH 8000  Semester Course Offered:  Offered spring semester every year.  Grading System:  AF (Traditional) 
 Course ID:  MATH 8020. 3 hours.  Course Title:  Commutative Algebra  Course Description:  Localization and completion, Nakayama's lemma, Dedekind domains, Hilbert's basis theorem, Hilbert's Nullstellensatz, Krull dimension, depth and CohenMacaulay rings, regular local rings.  Athena Title:  COMMUTATIVE ALGEBRA  Prerequisite:  MATH 8000  Semester Course Offered:  Offered every year.  Grading System:  AF (Traditional) 
 Course ID:  MATH 8030. 3 hours. Repeatable for maximum 18 hours credit.  Course Title:  Topics in Algebra  Course Description:  Topics in abstract algebra at the level of current research.  Athena Title:  TOPICS IN ALGEBRA  Prerequisite:  MATH 8000 or permission of department  Semester Course Offered:  Offered every year.  Grading System:  AF (Traditional) 
 Course ID:  MATH 8040. 3 hours.  Course Title:  Representation Theory of Finite Groups  Course Description:  Irreducible and indecomposable representations, Schur's lemma, Maschke's theorem, the Wedderburn structure theorem, characters and orthogonality relations, induced representations and Frobenius reciprocity, central characters and central idempotents, Burnside's p^a q^b theorem, Frobenius normal pcomplement theorem.  Athena Title:  REPS OF FIN GROUPS  Prerequisite:  MATH 8010  Semester Course Offered:  Not offered on a regular basis.  Grading System:  AF (Traditional) 
 Course ID:  MATH 8080. 3 hours.  Course Title:  Lie Algebras  Course Description:  Nilpotent and solvable Lie algebras, structure and classification of semisimple Lie algebras, roots, weights, finitedimensional representations.  Athena Title:  LIE ALGEBRAS  Prerequisite:  MATH 8000  Semester Course Offered:  Offered every year.  Grading System:  AF (Traditional) 
 Course ID:  MATH 8100. 3 hours.  Course Title:  Real Analysis I  Course Description:  Measure and integration theory with relevant examples from Lebesgue integration, Hilbert spaces (only with regard to L^2), L^p spaces and the related Riesz representation theorem. Hahn, Jordan and Lebesgue decomposition theorems, RadonNikodym Theorem and Fubini's Theorem.  Athena Title:  Real Analysis I  Prerequisite:  MATH 4100/6100 or permission of department  Corequisite:  MATH 8105  Semester Course Offered:  Offered every year.  Grading System:  AF (Traditional) 
 Course ID:  MATH 8105. 2 hours.  Course Title:  Problem Session in Real Analysis  Course Description:  Techniques and approaches to problems in real analysis as an aid
to mastery of basic theory.  Athena Title:  PROBLEMS IN REAL  Nontraditional Format:  Significant outside preparation will be expected.  Corequisite:  MATH 8100  Semester Course Offered:  Offered every year.  Grading System:  S/U (Satisfactory/Unsatisfactory) 
 Course ID:  MATH 8110. 3 hours.  Course Title:  Real Analysis II  Course Description:  Topics including: Haar Integral, change of variable formula, HahnBanach theorem for Hilbert spaces, Banach spaces and Fourier theory (series, transform, GelfandFourier homomorphism).  Athena Title:  REAL ANALYSIS II  Prerequisite:  MATH 8100  Semester Course Offered:  Offered every year.  Grading System:  AF (Traditional) 
 Course ID:  MATH 8130. 3 hours. Repeatable for maximum 18 hours credit.  Course Title:  Topics in Analysis  Course Description:  Topics in analysis at the level of current research.  Athena Title:  TOPICS IN ANALYSIS  Prerequisite:  MATH 8100 or MATH 8150  Semester Course Offered:  Not offered on a regular basis.  Grading System:  AF (Traditional) 
 Course ID:  MATH 8150. 3 hours.  Course Title:  Complex Variables I  Course Description:  The CauchyRiemann Equations, linear fractional transformations and elementary conformal mappings, Cauchy's theorems and its consequences, including Morera's theorem, Taylor and Laurent expansions, maximum principle, residue theorem, argument principle, Rouche's theorem and Liouville's theorem.  Athena Title:  COMPLEX VARIABLES I  Semester Course Offered:  Offered every year.  Grading System:  AF (Traditional) 
 Course ID:  MATH 8160. 3 hours.  Course Title:  Complex Variables II  Course Description:  Topics including Riemann Mapping Theorem, elliptic functions, MittagLeffler and Weierstrass Theorems, analytic continuation and Riemann surfaces.  Athena Title:  COMPLEX VAR II  Prerequisite:  MATH 8150  Semester Course Offered:  Offered every year.  Grading System:  AF (Traditional) 
 Course ID:  MATH 8170. 3 hours.  Course Title:  Functional Analysis I  Course Description:  Hilbert spaces and Banach spaces, spectral theory, topological
vector spaces, convexity and its consequences, including the
KreinMilman theorem.  Athena Title:  Functional Analysis I  Prerequisite:  MATH 8100  Semester Course Offered:  Offered every year.  Grading System:  AF (Traditional) 
 Course ID:  MATH 8190. 3 hours.  Course Title:  Lie Groups  Course Description:  Classical groups, exponential map, PoincareBirkhoffWitt Theorem, homogeneous spaces, adjoint representation, covering groups, compact groups, PeterWeyl Theorem, Weyl character formula.  Athena Title:  LIE GROUPS  Prerequisite:  MATH 8000 and MATH 8250  Semester Course Offered:  Offered every year.  Grading System:  AF (Traditional) 
 Course ID:  MATH 8200. 3 hours.  Course Title:  Algebraic Topology  Course Description:  The fundamental group, van Kampen's theorem, and covering spaces. Introduction to homology: simplicial, singular, and cellular. Applications.  Athena Title:  Algebraic Topology  Prerequisite:  MATH 4200/6200  Corequisite:  MATH 8205  Semester Course Offered:  Offered every year. Offered every evennumbered year. Offered every oddnumbered year.  Grading System:  AF (Traditional) 
 Course ID:  MATH 8205. 2 hours.  Course Title:  Problem Session in Topology  Course Description:  Techniques and approaches to problems in topology as an aid to
mastery of the basic theory.  Athena Title:  PROBLEMS IN TOPOLOG  Nontraditional Format:  Significant outside preparation will be expected.  Corequisite:  MATH 8200  Semester Course Offered:  Offered every year.  Grading System:  S/U (Satisfactory/Unsatisfactory) 
 Course ID:  MATH 8210. 3 hours.  Course Title:  Topology of Manifolds  Course Description:  Poincare duality, deRham's theorem, topics from differential topology.  Athena Title:  TOP OF MANIFOLDS  Prerequisite:  MATH 8200  Semester Course Offered:  Offered every year.  Grading System:  AF (Traditional) 
 Course ID:  MATH 8230. 3 hours. Repeatable for maximum 18 hours credit.  Course Title:  Topics in Topology and Geometry  Course Description:  Advanced topics in topology and/or differential geometry leading to and including research level material.  Athena Title:  TOPICS IN TOP & GEO  Prerequisite:  MATH 8200 or permission of department  Semester Course Offered:  Offered every year.  Grading System:  AF (Traditional) 
 Course ID:  MATH 8250. 3 hours.  Course Title:  Differential Geometry I  Course Description:  Differentiable manifolds, vector bundles, tensors, flows, and Frobenius' theorem. Introduction to Riemannian geometry.  Athena Title:  DIFF GEOMETRY I  Prerequisite:  MATH 4200/6200  Semester Course Offered:  Offered every year.  Grading System:  AF (Traditional) 
 Course ID:  MATH 8260. 3 hours.  Course Title:  Differential Geometry II  Course Description:  Riemannian geometry: connections, curvature, first and second variation; geometry of submanifolds. GaussBonnet theorem. Additional topics, such as characteristic classes, complex manifolds, integral geometry.  Athena Title:  DIFF GEOMETRY II  Prerequisite:  MATH 8250  Semester Course Offered:  Offered every year.  Grading System:  AF (Traditional) 
 Course ID:  MATH 8300. 3 hours.  Course Title:  Introduction to Algebraic Geometry  Course Description:  An invitation to algebraic geometry through a study of examples.
Affine and projective varieties, regular and rational maps,
Nullstellensatz. Veronese and Segre varieties, Grassmannians,
algebraic groups, quadrics. Smoothness and tangent spaces,
singularities and tangent cones.  Athena Title:  Intro to Algebraic Geometry  Prerequisite:  MATH 8000  Semester Course Offered:  Offered every year.  Grading System:  AF (Traditional) 
 Course ID:  MATH 8310. 3 hours.  Course Title:  Geometry of Schemes  Course Description:  The language of Grothendieck's theory of schemes. Topics include the spectrum of a ring, "gluing" spectra to form schemes, products, quasicoherent sheaves of ideals, and the functor of points.  Athena Title:  GEOMETRY OF SCHEMES  Prerequisite:  MATH 8020 and MATH 8300  Semester Course Offered:  Offered every year.  Grading System:  AF (Traditional) 
 Course ID:  MATH 8320. 3 hours. Repeatable for maximum 9 hours credit.  Course Title:  Algebraic Curves  Course Description:  The theory of curves, including linear series and the Riemann Roch theorem. Either the algebraic (variety), arithmetic (function field), or analytic (Riemann surface) aspect of the subject may be emphasized in different years.  Athena Title:  ALGEBRAIC CURVES  Prerequisite:  MATH 8300  Semester Course Offered:  Offered every year.  Grading System:  AF (Traditional) 
 Course ID:  MATH 8330. 3 hours. Repeatable for maximum 18 hours credit.  Course Title:  Topics in Algebraic Geometry  Course Description:  Advanced topics such as algebraic surfaces, or cohomology and sheaves.  Athena Title:  TOPICS ALG GEOMETRY  Prerequisite:  MATH 8300  Semester Course Offered:  Offered every year.  Grading System:  AF (Traditional) 
 Course ID:  MATH 8400. 3 hours.  Course Title:  Algebraic/Analytic Number Theory I  Course Description:  The core material of algebraic number theory: number fields, rings of integers, discriminants, ideal class groups, Dirichlet's unit theorem, splitting of primes; padic fields, Hensel's lemma, adeles and ideles, the strong approximation theorem.  Athena Title:  ALG/AN NUMBER TH I  Prerequisite:  MATH 4080/6080 or permission of department  Semester Course Offered:  Offered every year.  Grading System:  AF (Traditional) 
 Course ID:  MATH 8410. 3 hours.  Course Title:  Algebraic/Analytic Number Theory II  Course Description:  A continuation of Algebraic and Analytic Number Theory I, introducing analytic methods: the Riemann Zeta function, its analytic continuation and functional equation, the Prime number theorem; sieves, the BombieriVinogradov theorem, the Chebotarev density theorem.  Athena Title:  ALG/AN NUMBER TH II  Prerequisite:  MATH 8400 or permission of department  Semester Course Offered:  Offered every year.  Grading System:  AF (Traditional) 
 Course ID:  MATH 8430. 3 hours. Repeatable for maximum 18 hours credit.  Course Title:  Topics in Arithmetic Geometry  Course Description:  Topics in Algebraic number theory and Arithmetic geometry, such as class field theory, Iwasawa theory, elliptic curves, complex multiplication, cohomology theories, Arakelov theory, diophantine geometry, automorphic forms, Lfunctions, representation theory.  Athena Title:  ARITHMETIC GEOMETRY  Prerequisite:  Permission of department  Semester Course Offered:  Offered every year.  Grading System:  AF (Traditional) 
 Course ID:  MATH 8440. 3 hours. Repeatable for maximum 18 hours credit.  Course Title:  Topics in Combinatorial/Analytic Number Theory  Course Description:  Topics in combinatorial and analytic number theory, such as sieve methods, probabilistic models of prime numbers, the distribution of arithmetic functions, the circle method, additive number theory, transcendence methods.  Athena Title:  COMB/ANLY NUMBER TH  Prerequisite:  Permission of department  Semester Course Offered:  Offered every year.  Grading System:  AF (Traditional) 
 Course ID:  MATH 8500. 3 hours.  Course Title:  Advanced Numerical Analysis I  Course Description:  Numerical solution of nonlinear equations in one and several variables, numerical methods for constrained and unconstrained optimization, numerical solution of linear systems, numerical methods for computing eigenvalues and eigenvectors, numerical solution of linear least squares problems, computer applications for applied problems.  Athena Title:  Advanced Numerical Analysis I  Prerequisite:  MATH 4510/6510  Pre or Corequisite:  MATH 4100/6100  Corequisite:  MATH 8505  Semester Course Offered:  Offered every year.  Grading System:  AF (Traditional) 
 Course ID:  MATH 8505. 2 hours.  Course Title:  Problem Session in Numerical Analysis  Course Description:  Techniques and approaches to problems in numerical analysis as an
aid to mastery of the basic theory.  Athena Title:  PROBLEMS IN NUMERIC  Corequisite:  MATH 8500  Semester Course Offered:  Offered every year.  Grading System:  S/U (Satisfactory/Unsatisfactory) 
 Course ID:  MATH 8510. 3 hours.  Course Title:  Advanced Numerical Analysis II  Course Description:  Polynomial and spline interpolation and approximation theory, numerical integration methods, numerical solution of ordinary differential equations, computer applications for applied problems.  Athena Title:  ADV NUM ANALY II  Prerequisite:  MATH 8500  Semester Course Offered:  Not offered on a regular basis.  Grading System:  AF (Traditional) 
 Course ID:  MATH 8550. 3 hours. Repeatable for maximum 18 hours credit.  Course Title:  Special Topics in Numerical Analysis  Course Description:  Special topics in numerical analysis, including iterative methods for large linear systems, computer aided geometric design, multivariate splines, numerical solutions for pde's, numerical quadrature and cubature, numerical optimization, wavelet analysis for numerical imaging. In any semester, one of the above topics will be covered.  Athena Title:  TOPICS IN NUM ANALY  Prerequisite:  MATH 8500  Semester Course Offered:  Offered every year.  Grading System:  AF (Traditional) 
 Course ID:  MATH 8600. 3 hours.  Course Title:  Probability  Course Description:  Probability spaces, random variables, distributions, expectation and higher moments, conditional probability and expectation, convergence of sequences and series of random variables, strong and weak laws of large numbers, characteristic functions, infinitely divisible distributions, weak convergence of measures, central limit theorems.  Athena Title:  Probability  Prerequisite:  MATH 8100  Corequisite:  MATH 8605  Semester Course Offered:  Offered every year.  Grading System:  AF (Traditional) 
 Course ID:  MATH 8605. 2 hours.  Course Title:  Problem Session in Probability  Course Description:  Techniques and approaches to problems in probability as an aid to
mastery of the basic theory.  Athena Title:  PROBLEMS IN PROB  Nontraditional Format:  Significant outside preparation will be expected.  Corequisite:  MATH 8600  Semester Course Offered:  Offered every year.  Grading System:  S/U (Satisfactory/Unsatisfactory) 
 Course ID:  MATH 8630. 3 hours.  Course Title:  Stochastic Analysis  Course Description:  Conditional expectation, Brownian motion, semimartingales, stochastic calculus, stochastic differential equations, stochastic control, stochastic filtering.  Athena Title:  STOCHASTIC ANALYSIS  Prerequisite:  MATH 8100  Semester Course Offered:  Offered every year.  Grading System:  AF (Traditional) 
 Course ID:  MATH 8710. 3 hours.  Course Title:  Applied Mathematics: Variational Methods/Perturbation Theory  Course Description:  Calculus of variations, EulerLagrange equations, Hamilton's principle, approximate methods, eigenvalue problems, asymptotic expansions, method of steepest descent, method of stationary phase, perturbation of eigenvalues, nonlinear eigenvalue problems, oscillations and periodic solutions, Hopf bifurcation, singular perturbation theory, applications.  Athena Title:  AP MATH VAR/PERTURB  Prerequisite:  MATH 4100/6100  Semester Course Offered:  Offered every year.  Grading System:  AF (Traditional) 
 Course ID:  MATH 8740. 3 hours.  Course Title:  Ordinary Differential Equations  Course Description:  Solutions of initial value problems: existence, uniqueness, and dependence on parameters, differential inequalities, maximal and minimal solutions, continuation of solutions, linear systems, selfadjoint eigenvalue problems, Floquet Theory.  Athena Title:  ORDINARY DIFF EQNS  Prerequisite:  MATH 4100/6100  Semester Course Offered:  Offered every year.  Grading System:  AF (Traditional) 
 Course ID:  MATH 8750. 3 hours.  Course Title:  Introduction to Dynamical Systems  Course Description:  Continuous dynamical systems, trajectories, periodic orbits, invariant sets, structure of alpha and omega limit sets, applications to twodimensional autonomous systems of ODE's, PoincareBendixson Theorem, discrete dynamical systems, infinite dimensional spaces, semidynamical systems, functional differential equations.  Athena Title:  DYNAMICAL SYSTEMS  Prerequisite:  MATH 8740  Semester Course Offered:  Offered every year.  Grading System:  AF (Traditional) 
 Course ID:  MATH 8770. 3 hours.  Course Title:  Partial Differential Equations  Course Description:  Classification of second order linear partial differential equations, modern treatment of characteristics, function spaces, Sobolev spaces, Fourier transform of generalized functions, generalized and classical solutions, initial and boundary value problems, eigenvalue problems.  Athena Title:  PARTIAL DIFF EQNS  Prerequisite:  MATH 4100/6100  Semester Course Offered:  Offered every year.  Grading System:  AF (Traditional) 
 Course ID:  MATH 8800. 16 hours. Repeatable for maximum 30 hours credit.  Course Title:  Directed Reading and/or Projects  Course Description:  Directed reading and/or project at the doctoral level.  Athena Title:  DIR READ AND/OR PRO  Nontraditional Format:  Directed study.  Semester Course Offered:  Not offered on a regular basis.  Grading System:  AF (Traditional) 
 Course ID:  MATH 8850. 3 hours. Repeatable for maximum 18 hours credit.  Course Title:  Directed Collaborative Research  Course Description:  Research in a group setting on a topic of current interest in
mathematics, under the direction of one or more faculty members.
Emphasis will be given to problems that may be accessible to
elementary methods. An introduction to basic research methods in
mathematics, as well as expository and literaturesearch skills.
Required for all first year graduate students.  Athena Title:  COLLAB RESEARCH  Nontraditional Format:  The course is a 3 credit hour seminar since it includes both a
weekly meeting of separate research groups and a joint weekly
meeting of all the groups. The course is repeatable for 18
credit hours since the groups are required both semesters for
first year students and are also appropriate for continuing
students. By design the research experience will be different
each semester as the group, topic, or investigation changes. The
interaction among students and faculty is considered an important
aspect of the seminar. The research group format is the main
feature of recent reforms in the mathematics curriculum.  Semester Course Offered:  Offered fall, spring and summer semester every year.  Grading System:  S/U (Satisfactory/Unsatisfactory) 
 Course ID:  MATH 8900. 13 hours. Repeatable for maximum 30 hours credit.  Course Title:  Seminar in Algebra  Course Description:  A study of some phase of current research in algebra.  Athena Title:  SEMINAR IN ALGEBRA  Prerequisite:  Permission of department  Semester Course Offered:  Offered every year.  Grading System:  AF (Traditional) 
 Course ID:  MATH 8910. 13 hours. Repeatable for maximum 30 hours credit.  Course Title:  Seminar in Analysis  Course Description:  A study of some phase of current research in analysis.  Athena Title:  SEMINAR IN ANALYSIS  Prerequisite:  Permission of department  Semester Course Offered:  Offered every year.  Grading System:  AF (Traditional) 
 Course ID:  MATH 8920. 13 hours. Repeatable for maximum 30 hours credit.  Course Title:  Seminar in Topology  Course Description:  A study of some phase of current research in topology.  Athena Title:  SEMINAR IN TOPOLOGY  Prerequisite:  Permission of department  Semester Course Offered:  Offered every year.  Grading System:  AF (Traditional) 
 Course ID:  MATH 8930. 13 hours. Repeatable for maximum 30 hours credit.  Course Title:  Seminar in Algebraic Geometry  Course Description:  A study of some phase of current research in algebraic geometry.  Athena Title:  SEMINAR IN ALG GEOM  Prerequisite:  Permission of department  Semester Course Offered:  Offered every year.  Grading System:  AF (Traditional) 
 Course ID:  MATH 8940. 13 hours. Repeatable for maximum 30 hours credit.  Course Title:  Seminar in Number Theory  Course Description:  A study of some phase of current research in number theory.  Athena Title:  SEMINAR IN NUM TH  Prerequisite:  Permission of department  Semester Course Offered:  Offered every year.  Grading System:  AF (Traditional) 
 Course ID:  MATH 8950. 13 hours. Repeatable for maximum 30 hours credit.  Course Title:  Seminar in Numerical Analysis  Course Description:  A study of some phase of current research in numerical analysis.  Athena Title:  SEMINAR IN NUM ANLY  Prerequisite:  Permission of department  Semester Course Offered:  Offered every year.  Grading System:  AF (Traditional) 
 Course ID:  MATH 8960. 13 hours. Repeatable for maximum 30 hours credit.  Course Title:  Seminar in Probability  Course Description:  A study of some phase of current research in probability.  Athena Title:  SEMINAR IN PROB  Prerequisite:  Permission of department  Semester Course Offered:  Offered every year.  Grading System:  AF (Traditional) 
 Course ID:  MATH 8970. 13 hours. Repeatable for maximum 30 hours credit.  Course Title:  Seminar in Applied Mathematics  Course Description:  A study of some phase of current research in applied mathematics.  Athena Title:  SEMINAR IN AP MATH  Prerequisite:  Permission of department  Semester Course Offered:  Offered every year.  Grading System:  AF (Traditional) 
 Course ID:  MATH 8980. 13 hours. Repeatable for maximum 30 hours credit.  Course Title:  Seminar in Geometry  Course Description:  A study of some phase of current research in geometry.  Athena Title:  SEMINAR IN GEOMETRY  Prerequisite:  Permission of department  Semester Course Offered:  Offered every year.  Grading System:  AF (Traditional) 
 Course ID:  MATH 9000. 19 hours. Repeatable for maximum 90 hours credit.  Course Title:  Doctoral Research  Course Description:  Research while enrolled for a doctoral degree under the direction of faculty members.  Athena Title:  Doctoral Research  Nontraditional Format:  Independent research under the direction of a faculty member.  Prerequisite:  Permission of department  Semester Course Offered:  Offered fall, spring and summer semester every year.  Grading System:  S/U (Satisfactory/Unsatisfactory) 
 Course ID:  MATH 9005. 3 hours. Repeatable for maximum 45 hours credit.  Course Title:  Doctoral Graduate Student Seminar  Course Description:  Advanced supervised experience in an applied setting. This
course may not be used to satisfy a student's approved program of
study.  Athena Title:  Doctoral Graduate Student Sem  Nontraditional Format:  Seminar.  Semester Course Offered:  Offered fall, spring and summer semester every year.  Grading System:  AF (Traditional) 
 Course ID:  MATH 9300. 19 hours. Repeatable for maximum 90 hours credit.  Course Title:  Doctoral Dissertation  Course Description:  Dissertation writing under the direction of the major professor.  Athena Title:  Doctoral Dissertation  Nontraditional Format:  Independent research and preparation of the doctoral dissertation.  Prerequisite:  Permission of department  Semester Course Offered:  Offered fall, spring and summer semester every year.  Grading System:  S/U (Satisfactory/Unsatisfactory) 
