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Syllabus information is only available for a single course. Enter a specific course number or select a specific course ID from the drop down list, to view syllabus information.
       
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.
Oasis Title:MAT DECISION MAKING
Semester Course
Offered:
Offered fall, spring and summer semester every year.
Grading System:A-F (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 real-world data and phenomena. The investigation and analysis of applied problems and questions, and of effective communication of quantitative concepts and results.
Oasis Title:INTRO MATH MODELING
Semester Course
Offered:
Offered fall, spring and summer semester every year.
Grading System:A-F (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.
Oasis 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:A-F (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.
Oasis 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:A-F (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.
Oasis Title:ARITH ELEM TEACHERS
Duplicate Credit:Not open to students with credit in MATH 5001/7001 or MATH 5003/7003
Prerequisite:MATH 2001 and MATH 2002
Semester Course
Offered:
Offered fall, spring and summer semester every year.
Grading System:A-F (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.
Oasis Title:CALC FOR ECONOMICS
Duplicate Credit:Not open to students with credit in MATH 2110
Nontraditional Format:Delivery mode is synchronous. There are no face-to-face meetings. E-mail regularly, as questions arise. Written feedback to students on assignments, quizzes, and exams.
Prerequisite:MATH 2200 or MATH 2250
Semester Course
Offered:
Not offered on a regular basis.
Grading System:A-F (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.
Oasis Title:CALC FOR ECONOMICS
Duplicate Credit:Not open to students with credit in MATH 2210, MATH 2210L or MATH 2260 or MATH 2310H or MATH 2410H
Prerequisite:MATH 2200 or MATH 2250
Semester Course
Offered:
Offered fall and spring semester every year.
Grading System:A-F (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.
Oasis 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:A-F (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.
Oasis Title:CALC I SCI ENG
Duplicate Credit:Not open to students with credit in MATH 2200 or MATH 2250 or MATH 2400 or 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:A-F (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.
Oasis Title:CALC I SCI ENG
Duplicate Credit:Not open to students with credit in MATH 2200 or MATH 2300H or MATH 2400H or MATH 2400
Prerequisite:MATH 1113 or permission of department
Semester Course
Offered:
Offered fall, spring and summer semester every year.
Grading System:A-F (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 three-dimensional space, dot product, cross product, lines and planes.
Oasis Title:CALC II SCI ENG
Duplicate Credit:Not open to students with credit in MATH 2410H or MATH 2410
Prerequisite:MATH 2250 or MATH 2300H
Semester Course
Offered:
Offered fall, spring and summer semester every year.
Grading System:A-F (Traditional)
       
Course ID:MATH 2270. 4 hours.
Course Title:Calculus III for Science and Engineering
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.
Oasis Title:CALC III SCI ENG
Duplicate Credit:Not open to students with credit in MATH 2500 or MATH 3510 or MATH 3510H
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:A-F (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'Hôpital's rule. Introduction to the integral, area between curves, antidifferentiation, and the fundamental theorem of calculus.
Oasis 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:
Offered fall semester every year.
Grading System:A-F (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.
Oasis 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:
Offered fall and spring semester every year.
Grading System:A-F (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.
Oasis 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:
Offered fall semester every year.
Grading System:A-F (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.
Oasis 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:
Offered fall semester every year.
Grading System:A-F (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.
Oasis Title:INT CALC THRY
Duplicate Credit:Not open to students with credit in MATH 2110 or MATH 2260 or MATH 2310H or MATH 2410H
Prerequisite:MATH 2400
Semester Course
Offered:
Offered spring semester every year.
Grading System:A-F (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.
Oasis Title:INT CALC THRY HNRS
Duplicate Credit:Not open to students with credit in MATH 2110 or MATH 2210 or MATH 2260 or MATH 2310H, MATH 2410
Prerequisite:(MATH 2400 or MATH 2400H) and permission of Honors
Semester Course
Offered:
Offered spring semester every year.
Grading System:A-F (Traditional)
       
Course ID:MATH 2500. 3 hours.
Course Title:Multivariable Calculus
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.
Oasis Title:MULTIVARIABLE CALC
Duplicate Credit:Not open to students with credit in MATH 2270 or MATH 3510 or MATH 3510H
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:A-F (Traditional)
       
Course ID:CSCI(MATH) 2610. 4 hours.
Course Title:Discrete Mathematics for Computer Science
Course
Description:
The fundamental mathematical tools used in computer science: sets, relations, and functions; propositional logic, predicate logic, and inductive proofs; summations, recurrences, and elementary asymptotics; counting and discrete probability; undirected and directed graphs; introductory linear algebra, with applications in computer science.
Oasis Title:DISCRETE MATH
Duplicate Credit:Not open to students with credit in CSCI 2611
Prerequisite:MATH 1113
Semester Course
Offered:
Offered fall and spring semester every year.
Grading System:A-F (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.
Oasis 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:A-F (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.
Oasis Title:INTRO TO LINEAR ALG
Duplicate Credit:Not open to students with credit in MATH 3300 or MATH 3500 or MATH 3500 H
Prerequisite:MATH 3200 or permission of department
Semester Course
Offered:
Offered fall, spring and summer semester every year.
Grading System:A-F (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.
Oasis Title:SEQUENCES & SERIES
Prerequisite:MATH 3200 or permission of department
Semester Course
Offered:
Offered fall and spring semester every year.
Grading System:A-F (Traditional)
       
Course ID:MATH 3200. 3 hours.
Course Title:Introduction to Higher Mathematics
Course
Description:
Preparation in mathematical reasoning and proof-writing 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).
Oasis Title:INTRO HIGHER MATH
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:A-F (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. Methods will be demonstrated through examples and exercises. (Will not count towards the mathematics degree.)
Oasis Title:ADV PROB SOLV
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.
Oasis Title:APPLIED LINEAR ALG
Duplicate Credit:Not open to students with credit in MATH 3000 or MATH 3500 or MATH 3500H
Prerequisite:MATH 2260
Semester Course
Offered:
Offered fall and spring semester every year.
Grading System:A-F (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 proof-oriented treatment of the material in Multivariable Calculus and Introduction to Linear Algebra.
Oasis Title:MULTI MATH I HONORS
Duplicate Credit:Not open to students with credit in MATH 3000 or MATH 3300
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:A-F (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 proof-oriented treatment of the material in Multivariable Calculus and Introduction to Linear Algebra.
Oasis Title:MULTIVAR MATH I
Duplicate Credit:Not open to students with credit in MATH 3000 or MATH 3300 or MATH 3500 H
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:A-F (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.
Oasis Title:MULTIVAR MATH II
Duplicate Credit:Not open to students with credit in MATH 2270 or MATH 2500 or MATH 3510H
Prerequisite:MATH 3500 or MATH 3500H
Semester Course
Offered:
Offered spring semester every year.
Grading System:A-F (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.
Oasis Title:MULT MATH II HONORS
Duplicate Credit:Not open to students with credit in MATH 2270 or MATH 2500 or MATH 3510
Prerequisite:(MATH 3500 or MATH 3500H) and permission of Honors
Semester Course
Offered:
Offered spring semester every year.
Grading System:A-F (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.
Oasis Title:MOD ALG & GEOM I
Prerequisite:(MATH 3000 or MATH 3500 or MATH 3500H) and (MATH 3200 or MATH 3610)
Semester Course
Offered:
Offered fall, spring and summer semester every year.
Grading System:A-F (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.
Oasis Title:MOD ALG & GEOM II
Prerequisite:MATH 4000/6000
Semester Course
Offered:
Offered spring semester every year.
Grading System:A-F (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.
Oasis Title:ADV LIN ALG
Prerequisite:MATH 4000/6000
Semester Course
Offered:
Not offered on a regular basis.
Grading System:A-F (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 finite-dimensional spectral theorem, group actions, classification of finitely generated modules over principal ideal domains, and canonical forms of linear operators.
Oasis Title:ADVANCED ALGEBRA
Prerequisite:MATH 4010/6010 or permission of department
Semester Course
Offered:
Not offered on a regular basis.
Grading System:A-F (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.
Oasis Title:REAL ANALYSIS
Prerequisite:MATH 3100 and (MATH 3200 or MATH 3610)
Semester Course
Offered:
Offered fall semester every year.
Grading System:A-F (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.
Oasis Title:LEBESGUE INTEGRAL
Prerequisite:MATH 4100/6100 or MATH 4200/6200 or permission of department
Semester Course
Offered:
Offered spring semester every even-numbered year.
Grading System:A-F (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.
Oasis Title:MULTIVAR ANALYSIS
Prerequisite:MATH 3510 or MATH 3510H or MATH 4100/6100 or MATH 4200/6200
Semester Course
Offered:
Offered spring semester every odd-numbered year.
Grading System:A-F (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.
Oasis 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:A-F (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.
Oasis Title:POINT SET TOPOLOGY
Prerequisite:MATH 3100 and (MATH 3200 or MATH 3610)
Semester Course
Offered:
Offered every year.
Grading System:A-F (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.
Oasis 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 odd-numbered year.
Grading System:A-F (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; Gauss-Bonnet Theorem; discussion of non-Euclidean geometries.
Oasis Title:DIFF GEOMETRY
Prerequisite:(MATH 2270 and MATH 3000) or (MATH 2500 and MATH 3000) or MATH 3510 or MATH 3510H
Semester Course
Offered:
Offered every year.
Grading System:A-F (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.
Oasis Title:INTRO TO ALG CURVES
Prerequisite:MATH 4000/6000 or permission of department
Semester Course
Offered:
Not offered on a regular basis.
Grading System:A-F (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.
Oasis Title:NUMBER THEORY
Prerequisite:MATH 4000/6000
Semester Course
Offered:
Not offered on a regular basis.
Grading System:A-F (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.
Oasis Title:COMP NUMBER THY
Prerequisite:MATH 4000/6000
Semester Course
Offered:
Offered every year.
Grading System:A-F (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.
Oasis Title:NUMER ANALYSIS I
Prerequisite:MATH 3000 or MATH 3500 or MATH 3500H
Pre or Corequisite:MATH 3100
Semester Course
Offered:
Offered fall semester every year.
Grading System:A-F (Traditional)
       
Course ID:MATH 4510/6510. 3 hours.
Course Title:Numerical Analysis II
Course
Description:
Numerical solutions of ordinary and partial differential equations, higher-dimensional Newton's method, and splines.
Oasis 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:A-F (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.
Oasis 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:A-F (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.
Oasis Title:COMBINATORICS
Prerequisite:(MATH 3000 or MATH 3500 or MATH 3500H) and (CSCI(MATH) 2610 or MATH 3200)
Semester Course
Offered:
Offered fall semester every even-numbered year.
Grading System:A-F (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.
Oasis Title:GRAPH THEORY
Prerequisite:(MATH 3000 or MATH 3500 or MATH 3500H) and (CSCI(MATH) 2610 or MATH 3200)
Semester Course
Offered:
Offered spring semester every even-numbered year.
Grading System:A-F (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.
Oasis Title:QUAL ORD DIFF EQNS
Prerequisite:MATH 2700 and (MATH 3000 or MATH 3500 or MATH 3500H)
Semester Course
Offered:
Offered fall semester every year.
Grading System:A-F (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.
Oasis 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 even-numbered year.
Grading System:A-F (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.
Oasis Title:TRANSFORMS
Prerequisite:(MATH 3000 or MATH 3510 or MATH 3510H) and MATH 3100
Grading System:A-F (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.
Oasis 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:A-F (Traditional)
       
Course ID:MATH 4780/6780. 3 hours.
Course Title:Mathematical Biology
Course
Description:
Mathematical models in the biological sciences, systems, phase-plane 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.
Oasis Title:MAT 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 odd-numbered year.
Grading System:A-F (Traditional)
       
Course ID:MATH 4790. 3 hours.
Course Title:The Mathematics of Option Pricing
Course
Description:
Bonds, stock markets, derivatives, arbitrage, and binomial tree models for stocks and options, Black-Scholes formula for options pricing, hedging. Computational methods will be incorporated.
Oasis Title:MATH OPTION PRICING
Prerequisite:[(MATH 2270 or MATH 2500) and MATH 3000] or MATH 3510 or MATH 3510H or permission of department
Grading System:A-F (Traditional)
       
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.
Oasis Title:HISTORY OF MATH
Prerequisite:Senior standing
Semester Course
Offered:
Not offered on a regular basis.
Grading System:A-F (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.
Oasis Title:TOPICS IN MATH
Prerequisite:Senior standing
Semester Course
Offered:
Not offered on a regular basis.
Grading System:A-F (Traditional)
       
Course ID:MATH 4950. 1-3 hours. Repeatable for maximum 6 hours credit. 2-6 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.
Oasis 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 4960H. 3 hours.
Course Title:Directed Readings and/or Undergraduate Research (Honors)
Course
Description:
Individual study, reading, projects, or research under the direction of a project director.
Oasis Title:DIRECTED READINGS
Nontraditional Format:Directed study.
Prerequisite:Senior standing and permission of Honors
Semester Course
Offered:
Not offered on a regular basis.
Grading System:A-F (Traditional)
       
Course ID:MATH 4970H. 3 hours.
Course Title:Directed Readings and/or Undergraduate Research (Honors)
Course
Description:
Individual study, reading, projects, or research under the direction of a project director.
Oasis Title:DIRECTED READINGS
Nontraditional Format:Directed study.
Prerequisite:Senior standing and permission of Honors
Semester Course
Offered:
Not offered on a regular basis.
Grading System:A-F (Traditional)
       
Course ID:MATH 4990H. 3 hours.
Course Title:Honors Thesis
Course
Description:
Individual research in the major or in a closely related field.
Oasis Title:HONORS THESIS
Nontraditional Format:Thesis course.
Prerequisite:Permission of Honors
Semester Course
Offered:
Offered fall, spring and summer semester every year.
Grading System:A-F (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.
Oasis Title:ARITH & PROB SOLV
Duplicate Credit:Not open to students with credit in MATH 1700 or MATH 5020/7020
Semester Course
Offered:
Offered fall and spring semester every year.
Grading System:A-F (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.
Oasis Title:GEOM & PROB SOLV
Duplicate Credit:Not open to students with credit in MATH 5030/7030
Prerequisite:MATH 5001/7001
Semester Course
Offered:
Offered fall and spring semester every year.
Grading System:A-F (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.
Oasis 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:A-F (Traditional)
       
Course ID:MATH 5020/7020. 3 hours.
Course Title:Arithmetic for Middle School Teachers
Course
Description:
Operations of arithmetic for middle school teachers; number systems; set theory to study mappings, functions, and equivalence relations.
Oasis Title:IDEAS OF ARITHMETIC
Duplicate Credit:Not open to students with credit in MATH 5001/7001
Prerequisite:MATH 2200 or MATH 2250
Semester Course
Offered:
Offered fall semester every year.
Grading System:A-F (Traditional)
       
Course ID:MATH 5030/7030. 3 hours.
Course Title:Geometry and Measurement for Middle School Teachers
Course
Description:
Principles of geometry and measurement for middle school teachers.
Oasis Title:GEOM AND MEAS
Duplicate Credit:Not open to students with credit in MATH 5002/7002
Prerequisite:MATH 2200 or MATH 2250
Semester Course
Offered:
Offered spring semester every year.
Grading System:A-F (Traditional)
       
Course ID:MATH 5035/7035. 3 hours.
Course Title:Algebra for Middle School Teachers
Course
Description:
Algebra for middle school teachers. Relationships between quantities and the interpretation of such relationships numerically, graphically, algebraically, and functionally. Emphasis on problem solving and applications, connections with geometry, arithmetic and data analysis, and math competitions such as Mathcounts.
Oasis Title:ALG MID SCH TEACH
Prerequisite:(MATH 2200 or MATH 2250) and MATH 5020/7020 and MATH 5030/7030
Semester Course
Offered:
Offered fall semester every year.
Grading System:A-F (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 non-Euclidean geometries.
Oasis 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:A-F (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 non-Euclidean geometry; transformation geometry.
Oasis Title:FNDNS GEOMETRY II
Prerequisite:MATH 5200/7200
Semester Course
Offered:
Offered spring semester every year.
Grading System:A-F (Traditional)
       
Course ID:MATH 6800. 1-6 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.
Oasis Title:DIR READ AND/OR PRO
Nontraditional Format:Directed study.
Semester Course
Offered:
Offered every year.
Grading System:A-F (Traditional)
       
Course ID:MATH 7000. 1-6 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.
Oasis 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.
Oasis Title:GRAD STUDENT SEM
Nontraditional Format:Seminar.
Semester Course
Offered:
Offered fall, spring and summer semester every year.
Grading System:S/U (Satisfactory/Unsatisfactory)
       
Course ID:MATH 7040. 3 hours.
Course Title:Basic Ideas of Calculus I
Course
Description:
Survey of one-variable calculus in preparation for teaching calculus at the secondary level: combines review of basic techniques with careful study of underlying concepts.
Oasis Title:CALCULUS IDEAS I
Prerequisite:MATH 2210 or MATH 2310H or MATH 2410H
Semester Course
Offered:
Not offered on a regular basis.
Grading System:A-F (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.
Oasis Title:CALCULUS IDEAS II
Prerequisite:MATH 2210 or MATH 2310H or MATH 2410H
Semester Course
Offered:
Not offered on a regular basis.
Grading System:A-F (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.
Oasis 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:A-F (Traditional)
       
Course ID:MATH 7300. 1-9 hours. Repeatable for maximum 18 hours credit.
Course Title:Master's Thesis
Course
Description:
Thesis writing under the direction of the major professor.
Oasis 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 Bolzano-Weierstrass theorem, and the diagonalization theorem.
Oasis 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:A-F (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, Jordan-Holder 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.
Oasis Title:ALGEBRA I
Prerequisite:MATH 4010/6010 or permission of department
Semester Course
Offered:
Offered fall semester every year.
Grading System:A-F (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.
Oasis 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.
Oasis Title:ALGEBRA II
Prerequisite:MATH 8000
Semester Course
Offered:
Offered spring semester every year.
Grading System:A-F (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 Cohen-Macaulay rings, regular local rings.
Oasis Title:COMMUTATIVE ALGEBRA
Prerequisite:MATH 8000
Semester Course
Offered:
Offered every year.
Grading System:A-F (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.
Oasis Title:TOPICS IN ALGEBRA
Prerequisite:MATH 8000 or permission of department
Semester Course
Offered:
Offered every year.
Grading System:A-F (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 p-complement theorem.
Oasis Title:REPS OF FIN GROUPS
Prerequisite:MATH 8010
Semester Course
Offered:
Not offered on a regular basis.
Grading System:A-F (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, finite-dimensional representations.
Oasis Title:LIE ALGEBRAS
Prerequisite:MATH 8000
Semester Course
Offered:
Offered every year.
Grading System:A-F (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, Radon-Nikodym Theorem and Fubini's Theorem.
Oasis Title:REAL ANALYSIS I
Prerequisite:MATH 4100/6100 or permission of department
Semester Course
Offered:
Offered every year.
Grading System:A-F (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.
Oasis 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, Hahn-Banach theorem for Hilbert spaces, Banach spaces and Fourier theory (series, transform, Gelfand-Fourier homomorphism).
Oasis Title:REAL ANALYSIS II
Prerequisite:MATH 8100
Semester Course
Offered:
Offered every year.
Grading System:A-F (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.
Oasis Title:TOPICS IN ANALYSIS
Prerequisite:MATH 8100 or MATH 8150
Semester Course
Offered:
Not offered on a regular basis.
Grading System:A-F (Traditional)
       
Course ID:MATH 8150. 3 hours.
Course Title:Complex Variables I
Course
Description:
The Cauchy-Riemann 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.
Oasis Title:COMPLEX VARIABLES I
Semester Course
Offered:
Offered every year.
Grading System:A-F (Traditional)
       
Course ID:MATH 8160. 3 hours.
Course Title:Complex Variables II
Course
Description:
Topics including Riemann Mapping Theorem, elliptic functions, Mittag-Leffler and Weierstrass Theorems, analytic continuation and Riemann surfaces.
Oasis Title:COMPLEX VAR II
Prerequisite:MATH 8150
Semester Course
Offered:
Offered every year.
Grading System:A-F (Traditional)
       
Course ID:MATH 8170. 3 hours.
Course Title:Functional Analysis I
Course
Description:
Hilbert spaces and Banach spaces, spectral theory, topological vector spaces, comvexity and its consequences, including the Krein-Milman theorem.
Oasis Title:FUNC ANALYSIS I
Prerequisite:MATH 8100
Semester Course
Offered:
Offered every year.
Grading System:A-F (Traditional)
       
Course ID:MATH 8190. 3 hours.
Course Title:Lie Groups
Course
Description:
Classical groups, exponential map, Poincare-Birkhoff-Witt Theorem, homogeneous spaces, adjoint representation, covering groups, compact groups, Peter-Weyl Theorem, Weyl character formula.
Oasis Title:LIE GROUPS
Prerequisite:MATH 8000 and MATH 8250
Semester Course
Offered:
Offered every year.
Grading System:A-F (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.
Oasis Title:ALGEBRAIC TOPOLOGY
Prerequisite:MATH 4200/6200
Semester Course
Offered:
Offered every year. Offered every even-numbered year. Offered every odd-numbered year.
Grading System:A-F (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.
Oasis 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.
Oasis Title:TOP OF MANIFOLDS
Prerequisite:MATH 8200
Semester Course
Offered:
Offered every year.
Grading System:A-F (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.
Oasis Title:TOPICS IN TOP & GEO
Prerequisite:MATH 8200 or permission of department
Semester Course
Offered:
Offered every year.
Grading System:A-F (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.
Oasis Title:DIFF GEOMETRY I
Prerequisite:MATH 4200/6200
Semester Course
Offered:
Offered every year.
Grading System:A-F (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. Gauss-Bonnet theorem. Additional topics, such as characteristic classes, complex manifolds, integral geometry.
Oasis Title:DIFF GEOMETRY II
Prerequisite:MATH 8250
Semester Course
Offered:
Offered every year.
Grading System:A-F (Traditional)
       
Course ID:MATH 8300. 3 hours.
Course Title:Introduction to Algebraic Geometry
Course
Description:
An invitation to algebraic 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.
Oasis Title:INTRO ALG GEOMETRY
Prerequisite:MATH 8000
Semester Course
Offered:
Offered every year.
Grading System:A-F (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, quasi-coherent sheaves of ideals, and the functor of points.
Oasis Title:GEOMETRY OF SCHEMES
Prerequisite:MATH 8020 and MATH 8300
Semester Course
Offered:
Offered every year.
Grading System:A-F (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.
Oasis Title:ALGEBRAIC CURVES
Prerequisite:MATH 8300
Semester Course
Offered:
Offered every year.
Grading System:A-F (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.
Oasis Title:TOPICS ALG GEOMETRY
Prerequisite:MATH 8300
Semester Course
Offered:
Offered every year.
Grading System:A-F (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; p-adic fields, Hensel's lemma, adeles and ideles, the strong approximation theorem.
Oasis Title:ALG/AN NUMBER TH I
Prerequisite:MATH 4080/6080 or permission of department
Semester Course
Offered:
Offered every year.
Grading System:A-F (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 Bombieri-Vinogradov theorem, the Chebotarev density theorem.
Oasis Title:ALG/AN NUMBER TH II
Prerequisite:MATH 8400 or permission of department
Semester Course
Offered:
Offered every year.
Grading System:A-F (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, L-functions, representation theory.
Oasis Title:ARITHMETIC GEOMETRY
Prerequisite:Permission of department
Semester Course
Offered:
Offered every year.
Grading System:A-F (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.
Oasis Title:COMB/ANLY NUMBER TH
Prerequisite:Permission of department
Semester Course
Offered:
Offered every year.
Grading System:A-F (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.
Oasis Title:ADV NUM ANALY I
Prerequisite:MATH 4510/6510
Pre or Corequisite:MATH 4100/6100
Semester Course
Offered:
Offered every year.
Grading System:A-F (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.
Oasis 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.
Oasis Title:ADV NUM ANALY II
Prerequisite:MATH 8500
Semester Course
Offered:
Not offered on a regular basis.
Grading System:A-F (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.
Oasis Title:TOPICS IN NUM ANALY
Prerequisite:MATH 8500
Semester Course
Offered:
Offered every year.
Grading System:A-F (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.
Oasis Title:PROBABILITY
Prerequisite:MATH 8100
Semester Course
Offered:
Offered every year.
Grading System:A-F (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.
Oasis 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 8620. 3 hours.
Course Title:Stochastic Processes
Course
Description:
Conditional expectation, Markov processes, martingales and convergence theorems, stationary processes, introduction to stochastic integration.
Oasis Title:STOCH PROCESSES
Prerequisite:MATH 8100
Semester Course
Offered:
Offered every year.
Grading System:A-F (Traditional)
       
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.
Oasis Title:STOCHASTIC ANALYSIS
Prerequisite:MATH 8100
Semester Course
Offered:
Offered every year.
Grading System:A-F (Traditional)
       
Course ID:MATH 8700. 3 hours. Repeatable for maximum 15 hours credit.
Course Title:Applied Mathematics: Applications in Industry
Course
Description:
Mathematical modeling of some real-world industrial problems. Topics will be selected from a list which includes air quality modeling, crystal precipitation, electron beam lithography, image processing, photographic film development, production planning in manufacturing, and optimal control of chemical reactions.
Oasis Title:AP MATH IN INDUSTRY
Prerequisite:MATH 4720/6720
Semester Course
Offered:
Offered every year.
Grading System:A-F (Traditional)
       
Course ID:MATH 8710. 3 hours.
Course Title:Applied Mathematics: Variational Methods/Perturbation Theory
Course
Description:
Calculus of variations, Euler-Lagrange 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.
Oasis Title:AP MATH VAR/PERTURB
Prerequisite:MATH 4100/6100
Semester Course
Offered:
Offered every year.
Grading System:A-F (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, self-adjoint eigenvalue problems, Floquet Theory.
Oasis Title:ORDINARY DIFF EQNS
Prerequisite:MATH 4100/6100
Semester Course
Offered:
Offered every year.
Grading System:A-F (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 two-dimensional autonomous systems of ODE's, Poincare-Bendixson Theorem, discrete dynamical systems, infinite dimensional spaces, semi-dynamical systems, functional differential equations.
Oasis Title:DYNAMICAL SYSTEMS
Prerequisite:MATH 8740
Semester Course
Offered:
Offered every year.
Grading System:A-F (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.
Oasis Title:PARTIAL DIFF EQNS
Prerequisite:MATH 4100/6100
Semester Course
Offered:
Offered every year.
Grading System:A-F (Traditional)
       
Course ID:MATH 8800. 1-6 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.
Oasis Title:DIR READ AND/OR PRO
Nontraditional Format:Directed study.
Semester Course
Offered:
Not offered on a regular basis.
Grading System:A-F (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 literature-search skills. Required for all first year graduate students.
Oasis 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. 1-3 hours. Repeatable for maximum 30 hours credit.
Course Title:Seminar in Algebra
Course
Description:
A study of some phase of current research in algebra.
Oasis Title:SEMINAR IN ALGEBRA
Prerequisite:Permission of department
Semester Course
Offered:
Offered every year.
Grading System:A-F (Traditional)
       
Course ID:MATH 8910. 1-3 hours. Repeatable for maximum 30 hours credit.
Course Title:Seminar in Analysis
Course
Description:
A study of some phase of current research in analysis.
Oasis Title:SEMINAR IN ANALYSIS
Prerequisite:Permission of department
Semester Course
Offered:
Offered every year.
Grading System:A-F (Traditional)
       
Course ID:MATH 8920. 1-3 hours. Repeatable for maximum 30 hours credit.
Course Title:Seminar in Topology
Course
Description:
A study of some phase of current research in topology.
Oasis Title:SEMINAR IN TOPOLOGY
Prerequisite:Permission of department
Semester Course
Offered:
Offered every year.
Grading System:A-F (Traditional)
       
Course ID:MATH 8930. 1-3 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.
Oasis Title:SEMINAR IN ALG GEOM
Prerequisite:Permission of department
Semester Course
Offered:
Offered every year.
Grading System:A-F (Traditional)
       
Course ID:MATH 8940. 1-3 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.
Oasis Title:SEMINAR IN NUM TH
Prerequisite:Permission of department
Semester Course
Offered:
Offered every year.
Grading System:A-F (Traditional)
       
Course ID:MATH 8950. 1-3 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.
Oasis Title:SEMINAR IN NUM ANLY
Prerequisite:Permission of department
Semester Course
Offered:
Offered every year.
Grading System:A-F (Traditional)
       
Course ID:MATH 8960. 1-3 hours. Repeatable for maximum 30 hours credit.
Course Title:Seminar in Probability
Course
Description:
A study of some phase of current research in probability.
Oasis Title:SEMINAR IN PROB
Prerequisite:Permission of department
Semester Course
Offered:
Offered every year.
Grading System:A-F (Traditional)
       
Course ID:MATH 8970. 1-3 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.
Oasis Title:SEMINAR IN AP MATH
Prerequisite:Permission of department
Semester Course
Offered:
Offered every year.
Grading System:A-F (Traditional)
       
Course ID:MATH 8980. 1-3 hours. Repeatable for maximum 30 hours credit.
Course Title:Seminar in Geometry
Course
Description:
A study of some phase of current research in geometry.
Oasis Title:SEMINAR IN GEOMETRY
Prerequisite:Permission of department
Semester Course
Offered:
Offered every year.
Grading System:A-F (Traditional)
       
Course ID:MATH 9000. 1-9 hours. Repeatable for maximum 36 hours credit.
Course Title:Doctoral Research
Course
Description:
Research while enrolled for a doctoral degree under the direction of faculty members.
Oasis 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.
Oasis Title:DOC GRAD STU SEM
Nontraditional Format:Seminar.
Semester Course
Offered:
Offered fall, spring and summer semester every year.
Grading System:S/U (Satisfactory/Unsatisfactory)
       
Course ID:MATH 9300. 1-9 hours. Repeatable for maximum 40 hours credit.
Course Title:Doctoral Dissertation
Course
Description:
Dissertation writing under the direction of the major professor.
Oasis Title:DOCT 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)
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