UVa Course Catalog - Catalog of Courses for Mathematics (Unofficial, Lou's List)

UVa Course Catalog (Unofficial, Lou's List)

Catalog of Courses for Mathematics

These pages present data mined from the University of Virginia's new student information system (SIS). I hope that you will find them useful. — Lou Bloomfield, Department of Physics

Mathematics
MATH 1030	Precalculus (3.00)
	Studies computational skills, patterns of quantitative problem solving, and mathematical thought. Includes linear and quadratic equations, polynomials, inverse functions, logarithms, arithmetic and geometric sequences, trigonometric functions, and linear systems. (Does not satisfy the College natural science and mathematics requirement.) Prerequisite: High school algebra II and geometry.
MATH 1110	Probability/Finite Mathematics (3.00)
Offered Spring 2010	Studies finite probability theory including combinatorics, equiprobable models, conditional probability and Bayes' theorem, expectation and variance, and Markov chains.
MATH 1140	Financial Mathematics (3.00)
Offered Spring 2010	The study of the mathematics needed to understand and answer a variety of questions that arise in everyday financial dealings. The emphasis is on applications, including simple and compound interest, valuation of bonds, amortization, sinking funds, and rates of return on investments. A solid understanding of algebra is assumed.
MATH 1150	The Shape of Space (3.00)
	Provides an activity and project-based exploration of informal geometry in two and three dimensions. Emphasizes visualization skill, fundamental geometric concepts, and the analysis of shapes and patterns. Topics include concepts of measurement, geometric analysis, transformations, similarity, tessellations, flat and curved spaces, and topology.
MATH 1160	Algebra, Number Systems, and Number Theory (3.00)
Offered Spring 2010	Studies basic concepts, operations, and structures occurring in number systems, number theory, and algebra. Inquiry-based student investigations explore historical developments and conceptual transitions in the development of number and algebraic systems.
MATH 1210	Applied Calculus I (3.00)
Offered Spring 2010	Topics include limits and continuity; differentiation and integration of algebraic and elementary transcendental functions; and applications to maximum-minimum problems, curve sketching and exponential growth. Credit is not given for both MATH 121, 121A and 131.
MATH 1212	Applied Calculus I with Algebra (4.00)
Offered Spring 2010	Topics include College Algebra; limits and continuity; differentiation and integration of algebraic and elementary transcendental functions; and applications to maximum-minimum problems, curve sketching and exponential growth. Credit is not given for both Math 121, 121A and 131. Prerequisite: No previous exposure to Calculus.
MATH 1220	Applied Calculus II (3.00)
Offered Spring 2010	A second calculus course for business, biology, and social science students. Analyzes functions of several variables, their graphs, partial derivatives and optimization; multiple integrals. Reviews basic single variable calculus and introduces differential equations and infinite series. Credit is not given for both MATH 122 and 132. Prerequisite: MATH 121 or equivalent.
MATH 1310	Calculus I (4.00)
Offered Spring 2010	Introduces calculus with emphasis on techniques and applications. Recommended for natural science majors and students planning additional work in mathematics. The differential and integral calculus for functions of a single variable is developed through the fundamental theorem of calculus. Credit is not given for both MATH 121, 121A and 131. Prerequisite: Background in algebra, trigonometry, exponentials, logarithms, and analytic geometry.
MATH 1320	Calculus II (4.00)
Offered Spring 2010	Continuation of 131. Applications of the integral, techniques of integration, infinite series, vectors. Credit is not given for both MATH 122 and 132. Prerequisite: MATH 131 or equivalent, or instructor permission.
MATH 1330	Calculus Workshop I (2.00)
	Intensive calculus problem-solving workshop with topics drawn from MATH 131. Prerequisite: Instructor permission; corequisite: MATH 131.
MATH 1340	Calculus Workshop II (2.00)
	Intensive calculus problem-solving workshop with topics drawn from MATH 132. Prerequisite: Instructor permission; corequisite: MATH 132.
MATH 1559	New Course in Mathematics (1.00 - 4.00)
	This course provides the opportunity to offer a new topic in the subject of mathematics.
MATH 2310	Calculus III (4.00)
Offered Spring 2010	Studies functions of several variables including lines and planes in space, differentiation of functions of several variables, maxima and minima, multiple integration, line integrals, and volume. Prerequisite: MATH 132 or its equivalent.
MATH 2315	Honors Calculus III (4.00)
	Covers the material from Math 2310 (multivariable calculus) plus topics from complex numbers, set theory and linear algebra. Prepares students for taking advanced mathematics classes at an early stage. Prerequisite: MATH 1320 or its equivalent.
MATH 2700	Euclidean and Noneuclidean Geometry ** available as of 01/01/2010 (3.00)
	Examines assumptions and methods in the original text of Euclid's Elements. Covers selected geometric topics such as symmetries, spherical geometry, curvature, the dissection theory of area, constructible numbers, and the discovery of non-Euclidean geometry. Prerequisites: Some familiarily with calculus
MATH 3000	Transition to Higher Mathematics ** available as of 01/01/2010 (4.00)
Offered Spring 2010	Covers basic concepts with an emphasis on writing mathematical proofs. Topics include logic, sets, functions and relations, equivalence relations and partitions, induction, and cardinality. Prerequisite: Math 1320
MATH 3100	Introduction to Probability (3.00)
	Includes sample spaces, combinatorial analysis, discrete and continuous random variables, classical distributions, expectation, Chebyshev theorem, independence, central limit theorem, conditional probability, and generating functions. Prerequisite: MATH 132. A knowledge of double integrals is recommended.
MATH 3120	Introduction to Mathematical Statistics (3.00)
	Includes sampling theory, point estimation, interval estimation, testing hypotheses (including the Neyman-Pearson lemma and likelihood ratio tests), and regression and correlation. Prerequisite: MATH 310.
MATH 3250	Ordinary Differential Equations (4.00)
Offered Spring 2010	Introduces the methods, theory, and applications of differential equations. Includes first-order, second and higher-order linear equations, series solutions, linear systems of first-order differential equations, and the associated matrix theory. May include numerical methods, non-linear systems, boundary value problems, and additional applications. Prerequisite: MATH 132 or its equivalent.
MATH 3255	Ordinary Differential Equations (4.00)
Offered Spring 2010	Usually offered in the spring, this course covers the same material as MATH 325 with some additional topics, including an introduction to Sturm-Liouville theory, Fourier series and boundary value problems, and their connection with partial differential equations. Physics majors should enroll in MATH 325P, although no knowledge of physics is assumed. Prerequisite: MATH 132 or its equivalent.
MATH 3310	Basic Real Analysis (3.00)
Offered Spring 2010	Concentrates on proving the basic theorems of calculus, with due attention to the beginner with little or no experience in the techniques of proof. Includes limits, continuity, differentiability, the Bolzano-Weierstrass theorem, Taylor's theorem, integrability of continuous functions, and uniform convergence. Prerequisite: MATH 132.
MATH 3340	Complex Variables with Applications (3.00)
Offered Spring 2010	Topics include analytic functions, Cauchy formulas, power series, residue theorem, conformal mapping, and Laplace transforms. Prerequisite: MATH 231.
MATH 3351	Elementary Linear Algebra (3.00)
Offered Spring 2010	Includes matrices, elementary row operations, inverses, vector spaces and bases, inner products and Gram-Schmidt orthogonalization, orthogonal matrices, linear transformations and change of basis, eigenvalues, eigenvectors, and symmetric matrices. Prerequisite: MATH 132.
MATH 3354	Survey of Algebra (3.00)
Offered Spring 2010	Surveys major topics of modern algebra: groups, rings, and fields. Presents applications to areas such as geometry and number theory; explores rational, real, and complex number systems, and the algebra of polynomials. Prerequisite: MATH 132 or equivalent.
MATH 3559	New Course in Mathematics (1.00 - 4.00)
	This course provides the opportunity to offer a new topic in the subject of mathematics.
MATH 4040	Discrete Mathematics (3.00)
	Includes combinatorial principles, the binomial and multinomial theorems, partitions, discrete probability, algebraic structures, trees, graphs, symmetry groups, Polya's enumeration formula, linear recursions, generating functions and introduction to cryptography, time permitting. Prerequisite: MATH 354 or instructor permission.
MATH 4080	Operations Research (3.00)
	Development of mathematical models and their solutions, including linear programming, the simplex algorithm, dual programming, parametric programming, integer programming, transportation models, assignment models, and network analysis. Prerequisite: MATH 132 and 351.
MATH 4300	Elementary Numerical Analysis (3.00)
	Includes Taylor's theorem, solution of nonlinear equations, interpolation and approximation by polynomials, numerical quadrature. May also cover numerical solutions of ordinary differential equations, Fourier series, or least-square approximation. Prerequisite: MATH 325 and computer proficiency.
MATH 4452	Algebraic Coding Theory (3.00)
	Introduces algebraic techniques for communicating information in the presence of noise. Includes linear codes, bounds for codes, BCH codes and their decoding algorithms. May also include quadratic residue codes, Reed-Muller codes, algebraic geometry codes, and connections with groups, designs, and lattices. Prerequisite: MATH 351 and 354, or instructor permission.
MATH 4559	New Course in Mathematics (1.00 - 4.00)
	This course provides the opportunity to offer a new topic in the subject of mathematics.
MATH 4595	Undergraduate Research Seminar (3.00)
	Emphasizes direct contact with advanced mathematical ideas, communication of these ideas, the discovery of new results and connections among them, and the experience of mathematics as a collaborative venture among researchers at all levels. Students work collaboratively and individually on research projects, and present their results to the class. Prerequisite: Instructor permission.
MATH 4750	Introduction to Knot Theory (3.00)
	Examines the knotting and linking of curves in space. Studies equivalence of knots via knot diagrams and Reidemeister moves in order to define certain invariants for distinguishing among knots. Also considers knots as boundaries of surfaces and via algebraic structures arising from knots. Prerequisite: MATH 354 or instructor permission.
MATH 4993	Independent Study (3.00)
Offered Spring 2010	Reading and study programs in areas of interest to individual students. For third- and fourth-years interested in topics not covered in regular courses. Students must obtain a faculty advisor to approve and direct the program.
MATH 5010	The History of the Calculus (3.00)
	Studies the evolution of the various mathematical ideas leading up to the development of calculus in the 17th century, and how those ideas were perfected and extended by succeeding generations of mathematicians. Emphasizes primary source materials. Prerequisite: MATH 231 and 351, or instructor permission.
MATH 5030	The History of Mathematics (3.00)
	Studies the development of mathematics from classical antiquity to the end of the 19th century, focusing on critical periods in the evolution of geometry, number theory, algebra, probability, and set theory. Emphasizes primary source materials. Prerequisite: MATH 231 and 351, or instructor permission.
MATH 5090	Mathematical Probability (3.00)
	Mathematical Probability
MATH 5100	Probability (3.00)
	Studies the development and analysis of probability models through the basic concepts of sample spaces, random variables, probability distributions, expectations, and conditional probability. Additional topics include distributions of transformed variables, moment generating functions, and the central limit theorem. Prerequisite: MATH 132 or equivalent, and graduate standing. Credit cannot be received for both MATH 310 and 510.
MATH 5110	Introduction to Stochastic Processes (3.00)
	Topics in probability selected from Random walks, Markov processes, Brownian motion, Poisson processes, branching processes, stationary time series, linear filtering and prediction, queuing processes, and renewal theory. Prerequisite: MATH 310 and a knowledge of matrix algebra, or instructor permission.
MATH 5140	Mathematics of Derivative Securities (3.00)
	Topics include arbitrage arguments, valuation of futures, forwards and swaps, hedging, option-pricing theory, and sensitivity analysis. Prerequisite: MATH 231 or 122 or its equivalent, and a knowledge of probability and statistics; MATH 310 or its equivalent is recommended.
MATH 5210	Advanced Calculus with Applied Mathematics (3.00)
	Includes vector analysis, Green's, Stokes', divergence theorems, conservation of energy, and potential energy functions. Emphasizes physical interpretation, Sturm-Liouville problems and Fourier series, special functions, orthogonal polynomials, and Green's functions. Prerequisite: MATH 231, 325; 351 recommended.
MATH 5220	Partial Differential Equations and Applied Mathematics (3.00)
Offered Spring 2010	Introduces partial differential equations, Fourier transforms. Includes separation of variables, boundary value problems, classification of partial differential equations in two variables, Laplace and Poisson equations, and heat and wave equations. Prerequisite: MATH 521; 351 recommended.
MATH 5250	Advanced Ordinary Differential Equations (3.00)
	Studies the qualitative geometrical theory of ordinary differential equations. Includes basic well posedness; linear systems and periodic systems; stability theory; perturbation of linear systems; center manifold theorem; periodic solutions and Poincar-Bendixson theory; Hopf bifurcation; introduction to chaotic dynamics; control theoretic questions; differential geometric methods. Prerequisite: MATH 231, 325, 351 or instructor permission.
MATH 5310	Introduction to Real Analysis (3.00)
	The basic topology of Euclidean spaces; continuity, and differentiation of functions of a single variable; Riemann-Stieltjes integration; and convergence of sequences and series. Prerequisite: MATH 331 or permission of instructor.
MATH 5330	Advanced Multivariate Calculus (3.00)
Offered Spring 2010	Differential and Integral Calculus in Euclidean spaces; implicit and inverse function theorems, differential forms and Stokes' Theorem. Prerequisite: MATH 531.
MATH 5340	Complex Variables with Applications (3.00)
Offered Spring 2010	Analytic functions, Cauchy formulas, power series, residue theorem, conformal mapping, and Laplace transforms. Prerequisite: graduate standing.
MATH 5559	New Course in Mathematics (1.00 - 4.00)
	This course provides the opportunity to offer a new topic in the subject of mathematics.
MATH 5651	Advanced Linear Algebra (3.00)
	Introduction to algebraic systems, including groups, rings, fields, vector spaces, and their general properties, including subsystems, quotient systems, and homomorphisms. Study of basic examples such as permutation groups, polynomial rings, groups, and rings of matrices. Additional topics may include applications to linear algebra and number theory. Prerequisite: MATH 351 or instructor permission.
MATH 5652	Introduction to Abstract Algebra (3.00)
Offered Spring 2010	Structural properties of basic algebraic systems such as groups, rings and fields. A special emphasis is made on polynomials in one and several variables, including irreducible polynomials, unique factorization and symmetric polynomials. Time permitting, such topics as group representations or algebras over a field may be included. Prerequisite: MATH 351 or 551, or instructor permission.
MATH 5653	Number Theory (3.00)
Offered Spring 2010	Includes congruences, quadratic reciprocity, Diophantine equations, and number-theoretic functions, among others. Prerequisite: MATH 354 or instructor permission.
MATH 5654	Survey of Algebra (3.00)
Offered Spring 2010	Surveys groups, rings, and fields, and presents applications to other areas of mathematics, such as geometry and number theory. Explores the rational, real, and complex number systems, and the algebra of polynomials. Prerequisite: MATH 132 or equivalent and graduate standing.
MATH 5655	Automata Theory (3.00)
	Studies finite and infinite automata, Turing machines; discusses relations between automata and groups, respectively, other algebraic structures.
MATH 5700	Introduction to Geometry (3.00)
Offered Spring 2010	Topics selected from analytic, affine, projective, hyperbolic, and non-Euclidean geometry. Prerequisite: MATH 231, 351, or instructor permission.
MATH 5720	Introduction to Differential Geometry (3.00)
Offered Spring 2010	Topics selected from the theory of curves and surfaces in Euclidean space and the theory of manifolds. Prerequisite: MATH 231 and 351, or instructor permission.
MATH 5770	General Topology (3.00)
	Topological spaces and continuous functions, connectedness, compactness, countability and separation axioms, and function spaces. Time permitting, more advanced examples of topological spaces, such as projectives spaces, as well as an introduction to the fundamental group will be covered. Prerequisite: MATH 231 and 351, with 331 recommended.
MATH 5830	Seminar (3.00)
Offered Spring 2010	Presentation of selected topics in mathematics. Prerequisite: MATH 531; corequisite: MATH 552 or instructor permission.
MATH 5896	Supervised Study in Mathematics (3.00)
Offered Spring 2010	A rigorous program of supervised study designed to expose the student to a particular area of mathematics. Prerequisite: Instructor permission and graduate standing.
MATH 6040	Discrete Mathematics: Concepts, Algorithms, and Applications for Teachers (3.00)

MATH 6110	Probability/Finite Mathematics (1.00)

MATH 6120	Measurement and Data Analysis (3.00)

MATH 6210	Calculus Excursions (3.00)

MATH 6401	Algebraic Thinking for K-8 Teachers (3.00)

MATH 6402	Algebra, Number Systems, and Number Theory for Teachers (3.00)

MATH 6451	Linear Algebra (3.00)

MATH 6452	Functions and Algebra (3.00)

MATH 6453	Number Systems and Number Theory for K-8 Mathematics Specialists (3.00)

MATH 6454	Rational Numbers and Proportional Reasoning (3.00)

MATH 6455	HQT Numbers and Operations (3.00)

MATH 6456	HQT Algebra and Functions (3.00)

MATH 6457	HQT Measurement and Geometry (3.00)

MATH 6458	HQT Data Analysis Probability and Statistics (3.00)

MATH 6459	HQT Fractions, Decimals, Perce (3.00)

MATH 6559	New Course in Mathematics (1.00 - 4.00)
	This course provides the opportunity to offer a new topic in the subject of mathematics.
MATH 6600	Algebra for Middle School Specialists (3.00)

MATH 6620	AAO Elem Algebra and Functions (3.00)

MATH 6630	AAO Introductory College Algebra and Trigonometry (3.00)

MATH 6640	AAO Linear Algebra (3.00)

MATH 6650	AAO Calculus With Applications (3.00)

MATH 6660	Euclidean Geometry (3.00)

MATH 6670	AAO Probability and Statistics (3.00)
	Explores introductory descriptive statistics, probability, and statistical inference. Develops conceptual understanding and procedural fluency in problem settings based on real data which investigate the use of visual methods from summarizing quantitative information, basic experimental design, sampling methods, and interpretation of statistical analysis.
MATH 6700	Geometry and Measurement for K-8 Math Specialists (3.00)

MATH 6710	Geometry for Teachers Leadership Institute (3.00)

MATH 6720	MM Number Systems for Middle School Teachers (3.00)

MATH 6730	MM Fractions, Decimals, and Percents for Middle School Teachers (3.00)

MATH 6740	MM Patterns, Relations, and Algebraic Concepts for Middle School Teachers (3.00)

MATH 6750	MM Geometric Concepts and Measurement for Middle School Teachers (3.00)

MATH 6760	MM Data Analysis, Probability, and Statistics for Middle School Teachers (3.00)
	Focuses on the representation of data for decision making and predictability based on data analysis as it relates to middle school mathematics and defined in the NCTM Professional Standards for School Mathematics and Virginia SOLS in Mathematics. Teachers deepen their understanding and use of the fundamental ideas in mathematics that underlie the probability and statistics strand.
MATH 6770	Mathematical Applications Through Problem Solving and Lesson Study for Middle School Teachers (3.00)

MATH 6800	Teaching Mathematics to Diverse Populations (3.00)

MATH 7000	Seminar on College Teaching (1.00 - 3.00)
	Discussion of issues related to the practice of teaching, pedagogical concerns in college level mathematics, and aspects of the responsibilities of a professional mathematician. Credits may not be used towards a Master's degree. Prerequisite: Graduate standing in mathematics.
MATH 7010	Seminar on Research in Mathematics (1.00 - 3.00)
Offered Spring 2010	This seminar discusses the issues related to research in Mathematics. There are speakers from the different areas of mathematics represented at the University of Virginia. Credit may not be used towards a Master's degree. Prerequisite: Graduate standing in mathematics.
MATH 7250	Ordinary Differential Equations and Dynamical Systems (3.00)
	Topics include well-posedness and stability of dynamical flows, attractors, invariant manifolds and their properties, and dissipative and Hamiltonian systems. Prerequisite: MATH 531 and linear algebra, or the equivalent.
MATH 7310	Real Analysis and Linear Spaces I (3.00)
	Introduces measure and integration theory. Prerequisite: MATH 531 or equivalent.
MATH 7320	Real Analysis and Linear Spaces II (3.00)
	Additional topics in measure theory. Banach and Hilbert spaces, and Fourier analysis. Prerequisite: MATH 731, 734, or equivalent.
MATH 7340	Complex Analysis I (4.00)
Offered Spring 2010	Studies the fundamental theorems of analytic function theory.
MATH 7350	Complex Analysis II (3.00)
	Studies the Riemann mapping theorem, meromorphic and entire functions, topics in analytic function theory. Prerequisite: MATH 734 or equivalent.
MATH 7360	Probability Theory I (3.00)
	Rigorous introduction to probability, using techniques of measure theory. Includes limit theorems, martingales, and stochastic processes. Prerequisite: 7310 or equivalent.
MATH 7370	Probability Theory II ** available as of 01/01/2010 (3.00)
Offered Spring 2010	Continuation of Probability Theory I. Elements of stochastic processes, including Brownian motion, continuous time martingales, and Markov processes.
MATH 7410	Functional Analysis I (3.00)
	Studies the basic principles of linear analysis, including spectral theory of compact and selfadjoint operators. Prerequisite: MATH 734 and 731, or equivalent.
MATH 7420	Functional Analysis II (3.00)
Offered Spring 2010	Studies the spectral theory of unbounded operators, semigroups, and distribution theory. Prerequisite: MATH 741 or equivalent.
MATH 7450	Introduction to Mathematical Physics (3.00)
	An introduction to classical mechanics, with topics in statistical and quantum mechanics, as time permits. Prerequisite: MATH 531.
MATH 7559	New Course in Mathematics (1.00 - 4.00)
	This course provides the opportunity to offer a new topic in the subject of mathematics.
MATH 7600	Homological Algebra (3.00)
	Examines categories, functors, abelian catqegories, limits and colimits, chain complexes, homology and cohomology, homological dimension, derived functors, Tor and Ext, group homology, Lie algebra homology, spectral sequences, and calculations. Prerequisite: MATH 577.
MATH 7751	Algebra I (3.00)
	Studies groups, rings, fields, modules, tensor products, and multilinear functions. Prerequisite: MATH 551, 552, or equivalent.
MATH 7752	Algebra II (4.00)
Offered Spring 2010	Studies groups, rings, fields, modules, tensor products, and multilinear functions. Prerequisite: MATH 551, 552, or equivalent.
MATH 7753	Algebra III (3.00)
	Studies the Wedderburn theory, commutative algebra, and topics in advanced algebra. Prerequisite: MATH 751, 752, or equivalent.
MATH 7754	Algebra IV (3.00)
Offered Spring 2010	Further topics in algebra.
MATH 7800	Algebraic Topology I (3.00)
Offered Spring 2010	Topics include the fundamental group, covering spaces, covering transformations, the universal covering spaces, graphs and subgroups of free groups, and the fundamental groups of surfaces. Additional topics will be from homology, including chain complexes, simplicial and singular homology, exact sequences and excision, cellular homology, and classical applications. Prerequisite: MATH 552, 577, or equivalent.
MATH 7810	Algebraic Topology II (3.00)
	Devoted to chomology theory: cohomology groups, the universal coefficient theorem, the Kunneth formula, cup products, the cohomology ring of manifolds, Poincare duality, and other topics if time permits. Prerequisite: MATH 780.
MATH 7820	Differential Topology (3.00)
	Topics include smooth manifolds and functions, tangent bundles and vector fields, embeddings, immersions, transversality, regular values, critical points, degree of maps, differential forms, de Rham cohomology, and connections. Prerequisite: MATH 531, 577, or equivalent.
MATH 7830	Fiber Bundles (3.00)
Offered Spring 2010	Examines fiber bundles; induced bundles, principal bundles, classifying spaces, vector bundles, and characteristic classes, and introduces K-theory and Bott periodicity. Prerequisite: MATH 780.
MATH 7840	Homotopy Theory (3.00)
	Definition of homotopy groups, homotopy theory of CW complexes, Huriewich theorem and Whitehead's theorem, Eilenberg-Maclane spaces, fibration and cofibration sequences, Postnikov towers, and obstruction theory. Prerequisite: MATH 780.
MATH 8250	Partial Differential Equations (3.00)
Offered Spring 2010	Theory of distributions. Sobolev spaces and their properties (trace and embedding theorems). Theory of elliptic equations. Time-dependent partial differential equations: parabolic and hyperbolic equations. Topics in nonlinear partial differential equations. Prerequisites: MATH 741 and 725.
MATH 8300	Topics in Function Theory (3.00)
	Topics in real and complex function theory.
MATH 8310	Operator Theory I, II (3.00)
Offered Spring 2010	Topics in the theory of operators on a Hilbert space and related areas of function theory.
MATH 8320	Operator Theory I, II (3.00)
	Topics in the theory of operators on a Hilbert space and related areas of function theory.
MATH 8360	Stochastic Calculus and Differential Equations (3.00)
	This course presents the basic theory of stochastic differential equations and provides examples of its applications. It is an essential topic for students preparing to do research in probability. Topics covered include a review of the relevant stochastic process and martingale theory; stochastic calculus including Ito's formula; existence and uniqueness for stochastic differential equations, strong Markov property; and applications. Prerequisite: MATH 736 and 737, or instructor permission.
MATH 8370	Topics in Probability Theory (3.00)
	Selected topics in probability. Prerequisite: MATH 736 or instructor permission.
MATH 8400	Harmonic Analysis (3.00)
	Studies Banach and C* algebras, topological vector spaces, locally compact groups, Fourier analysis.
MATH 8450	Topics in Mathematical Physics (3.00)
	Applies functional analysis to physical problems; scattering theory, statistical mechanics, and quantum field theory.
MATH 8559	New Course in Mathematics (1.00 - 4.00)
	This course provides the opportunity to offer a new topic in the subject of mathematics.
MATH 8600	Commutative Algebra (3.00)
	The foundations of commutative algebra, algebraic number theory, or algebraic geometry.
MATH 8620	Algebraic Geometry (3.00)
	Studies the foundations of algebraic geometry.
MATH 8650	Algebraic K-Theory (3.00)
	Includes projective class groups and Whitehead groups; Milnor's K2 and symbols; higher K-theory and finite fields.
MATH 8700	Lie Groups (3.00)
	Studies basic results concerning Lie groups, Lie algebras, and the correspondence between them.
MATH 8710	Lie Algebras (3.00)
	Studies basic structure theory of Lie algebras.
MATH 8720	Differential Geometry (3.00)
Offered Spring 2010	Studies differential geometry in the large; connections; Riemannian geometry; Gauss-Bonnet formula; and differential forms.
MATH 8750	Topology of Manifolds (3.00)
	Studies regular and critical values, gradient flow, handle decompositions, Morse theory, h-cobordism theorem, Dehn's lemma in dimension 3, and disk theorem in dimension 4. Prerequisite: Math 577.
MATH 8800	Generalized Cohomology Theory (3.00)
	Topics include the axiomatic generalized cohomology theory; representability and spectra; spectra and ring spectra; orientability of bundles in generalized cohomology theory; Adams spectral sequence, and stable homotopy.
MATH 8830	Cobordism and K-Theory (3.00)
	Studies classical cobordism theories; Pontryagin-Thom construction; bordism and cobordism of spaces; K-theory and Bott periodicity; formal groups, and cobordism.
MATH 8850	Topics in Algebraic Topology (3.00)
	Selected advanced topics in algebraic topology.
MATH 8851	Group Theory (3.00)
Offered Spring 2010	Studies the basic structure theory of groups, especially finite groups.
MATH 8852	Representation Theory (3.00)
Offered Spring 2010	Studies the foundations of representation and character theory of finite groups.
MATH 8853	Algebraic Combinatorics (3.00)
	Studies geometries, generating functions, partitions, and error-correcting codes and graphs using algebraic methods involving group theory, number theory, and linear algebra.
MATH 8854	Arithmetic Groups (3.00)
	General methods of analyzing groups viewed as discrete subgroups of real algebraic subgroups. Additional topics include the congruence subgroup problem. Prerequisite: MATH 752.
MATH 8855	Theory of Algebras (3.00)
Offered Spring 2010	Studies the basic structure theory of associative or nonassociative algebras.
MATH 8880	Transformation Groups (3.00)
	Studies groups of transformations operating on a space; properties of fixed-point sets, orbit spaces; and local and global invariants.
MATH 8995	Thesis (3.00 - 12.00)
Offered Spring 2010
MATH 8998	Non-Topical Research, Preparation for Research (3.00 - 12.00)
Offered Spring 2010	For master's research, taken before a thesis director has been selected.
MATH 8999	Non-Topical Research (3.00 - 12.00)
Offered Spring 2010	For master's thesis, taken under the supervision of a thesis director.
MATH 9000	Mathematics Colloquium (0.00)
Offered Spring 2010	Forum for invited speakers giving mathematical colloquium) talks
MATH 9010	History of Mathematics Seminar (1.00 - 3.00)
	Discusses subjects from the history of mathematics.
MATH 9020	Graduate Seminar (0.00)
Offered Spring 2010	This is a meeting place for junior faculty members and graduate students to discuss mathematics and give talks reflecting the mathematical interests of the participants.
MATH 9250	Differential Equations and Dynamical Systems Seminar (3.00)
Offered Spring 2010
MATH 9310	Operator Theory Seminar (3.00)
Offered Spring 2010
MATH 9360	Probability Seminar (3.00)
Offered Spring 2010
MATH 9410	Analysis Seminar (3.00)
Offered Spring 2010
MATH 9450	Mathematical Physics Seminar (3.00)
Offered Spring 2010
MATH 9559	New Course in Mathematics (1.00 - 4.00)
	This course provides the opportunity to offer a new topic in the subject of mathematics.
MATH 9800	Topology Seminar (3.00)
Offered Spring 2010
MATH 9820	Geometry Seminar (1.00 - 3.00)
Offered Spring 2010	Discusses subjects from geometry.
MATH 9950	Algebra Seminar (3.00)
Offered Spring 2010
MATH 9952	Coding Theory Seminar (3.00)

MATH 9995	Independent Research (3.00 - 9.00)
Offered Spring 2010
MATH 9998	Non-Topical Research, Preparation for Doctoral Research (3.00 - 12.00)
Offered Spring 2010	For doctoral research, taken before a dissertation director has been selected.
MATH 9999	Non-Topical Research (3.00 - 12.00)
Offered Spring 2010	The Mathematics Colloquium is held weekly, the sessions being devoted to research activities of students and faculty members, and to reports by visiting mathematicians on current work of interest. For doctoral dissertation, taken under the supervision of a dissertation director.