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| 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) |
| 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 Fall 2013 | 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. Course was offered Spring 2013, Fall 2012, Summer 2012, Spring 2012, Fall 2011, Summer 2011, Spring 2011, Fall 2010, Summer 2010, Spring 2010, Fall 2009 |
| MATH 1150 | The Shape of Space (3.00) |
| Offered Fall 2013 | 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) |
| 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 1190 | Applied Calculus I with Algebra (4.00) |
| Offered Fall 2013 | 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 1210, 1190, and 1310. Prerequisite: No previous exposure to Calculus. |
| MATH 1210 | Applied Calculus I (3.00) |
| Offered Fall 2013 | 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 1210, 1212, and 1310. Course was offered Spring 2013, Fall 2012, Summer 2012, Spring 2012, Fall 2011, Summer 2011, Spring 2011, Fall 2010, Summer 2010, Spring 2010, Fall 2009 |
| MATH 1220 | Applied Calculus II (3.00) |
| Offered Fall 2013 | 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 1220 and 1320. Prerequisite: MATH 1210 or equivalent. Course was offered Spring 2013, Fall 2012, Summer 2012, Spring 2012, Fall 2011, Summer 2011, Spring 2011, Fall 2010, Summer 2010, Spring 2010, Fall 2009 |
| MATH 1310 | Calculus I (4.00) |
| Offered Fall 2013 | 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 1210, 1212, and 1310. Prerequisite: Background in algebra, trigonometry, exponentials, logarithms, and analytic geometry. Course was offered Spring 2013, Fall 2012, Summer 2012, Spring 2012, Fall 2011, Summer 2011, Spring 2011, Fall 2010, Summer 2010, Spring 2010, Fall 2009 |
| MATH 1320 | Calculus II (4.00) |
| Offered Fall 2013 | Continuation of 1310. Applications of the integral, techniques of integration, infinite series, vectors. Credit is not given for both MATH 1220 and 1320. Prerequisite: MATH 1310 or equivalent, or instructor permission. Course was offered Spring 2013, Fall 2012, Summer 2012, Spring 2012, Fall 2011, Summer 2011, Spring 2011, Fall 2010, Summer 2010, Spring 2010, Fall 2009 |
| MATH 1330 | Calculus Workshop I (2.00) |
| Intensive calculus problem-solving workshop with topics drawn from MATH 1310. Prerequisite: Instructor permission; corequisite: MATH 1310. | |
| MATH 1340 | Calculus Workshop II (2.00) |
| Intensive calculus problem-solving workshop with topics drawn from MATH 1320. Prerequisite: Instructor permission; corequisite: MATH 1320. | |
| 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 Fall 2013 | 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 1320 or its equivalent. Course was offered Spring 2013, Fall 2012, Summer 2012, Spring 2012, Fall 2011, Summer 2011, Spring 2011, Fall 2010, Summer 2010, Spring 2010, Fall 2009 |
| 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 2559 | New Course in Mathematics (1.00 - 4.00) |
| This course provides the opportunity to offer a new topic in the subject of mathematics. | |
| MATH 2700 | Euclidean and Noneuclidean Geometry (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, constructable numbers, and the discovery of non-Euclidean geometry. Prerequisites: Some familiarity with calculus. | |
| MATH 3000 | Transition to Higher Mathematics (4.00) |
| 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; and students with a grade of B or better in Math 3310, 3354, or any 5000-level Math course are not eligible to enroll in Math 3000. | |
| MATH 3100 | Introduction to Probability (3.00) |
| Offered Fall 2013 | 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 1320. A knowledge of double integrals is recommended. Course was offered Spring 2013, Fall 2012, Summer 2012, Fall 2011, Summer 2011, Fall 2010, Summer 2010, Fall 2009 |
| 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 3100. Course was offered Summer 2010 | |
| MATH 3250 | Ordinary Differential Equations (4.00) |
| Offered Fall 2013 | 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 1320 or its equivalent. Course was offered Spring 2013, Fall 2012, Spring 2012, Fall 2011, Spring 2011, Fall 2010, Spring 2010, Fall 2009 |
| MATH 3255 | Ordinary Differential Equations (4.00) |
| Usually offered in the spring, this course covers the same material as MATH 3250 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 3255, although no knowledge of physics is assumed. Prerequisite: MATH 1320 or its equivalent. | |
| MATH 3310 | Basic Real Analysis (3.00) |
| Offered Fall 2013 | 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 1320. Course was offered Spring 2013, Fall 2012, Summer 2012, Spring 2012, Fall 2011, Summer 2011, Spring 2011, Fall 2010, Summer 2010, Spring 2010, Fall 2009 |
| MATH 3340 | Complex Variables with Applications (3.00) |
| Topics include analytic functions, Cauchy formulas, power series, residue theorem, conformal mapping, and Laplace transforms. Prerequisite: MATH 2310. | |
| MATH 3351 | Elementary Linear Algebra (3.00) |
| Offered Fall 2013 | 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 1320. Course was offered Spring 2013, Fall 2012, Spring 2012, Fall 2011, Spring 2011, Fall 2010, Spring 2010, Fall 2009 |
| MATH 3354 | Survey of Algebra (3.00) |
| Offered Fall 2013 | 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 1320 or equivalent. Course was offered Spring 2013, Fall 2012, Spring 2012, Fall 2011, Spring 2011, Fall 2010, Spring 2010, Fall 2009 |
| 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) |
| Offered Fall 2013 | 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 3354 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 1320 and 3351. | |
| 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 3250 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 3351 and 3354, 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 3354 or instructor permission. | |
| MATH 4993 | Independent Study (1.00 - 3.00) |
| Offered Fall 2013 | 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. Course was offered Spring 2013, Fall 2012, Summer 2012, Spring 2012, Fall 2011, Summer 2011, Spring 2011, Fall 2010, Summer 2010, Spring 2010, Fall 2009 |
| 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 2310 and 3351, 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 2310 and 3351, or instructor permission. Course was offered Spring 2013, Spring 2011 | |
| MATH 5100 | Probability (3.00) |
| Offered Fall 2013 | 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 1320 or equivalent, and graduate standing. Credit cannot be received for both MATH 3100 and 5100. Course was offered Spring 2013, Fall 2012, Summer 2012, Fall 2011, Summer 2011, Fall 2010, Summer 2010, Fall 2009 |
| MATH 5110 | Introduction to Stochastic Processes (3.00) |
| Offered Fall 2013 | 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 3100 and a knowledge of matrix algebra, or instructor permission. Course was offered Spring 2013, Fall 2012, Spring 2012, Fall 2011, Spring 2011, Fall 2010, Fall 2009 |
| MATH 5140 | Mathematics of Derivative Securities (3.00) |
| Offered Fall 2013 | Topics include arbitrage arguments, valuation of futures, forwards and swaps, hedging, option-pricing theory, decision theory, and sensitivity analysis. Prerequisite: MATH 3100; MATH 5110 is recommended |
| MATH 5210 | Advanced Calculus with Applied Mathematics (3.00) |
| Offered Fall 2013 | 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 2310, 3250; 3351 recommended. |
| MATH 5220 | Partial Differential Equations and Applied Mathematics (3.00) |
| 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 5210; 3351 recommended. | |
| MATH 5305 | Proofs in Analysis (3.00) |
| This course reviews the proofs of the main theorems in analysis in preparation for the advanced graduate analysis courses. This course is offered in the summer and restricted to Mathematics and Graduate Arts and Science students. | |
| MATH 5310 | Introduction to Real Analysis (3.00) |
| Offered Fall 2013 | 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 3310 or permission of instructor. |
| MATH 5330 | Advanced Multivariate Calculus (3.00) |
| Differential and Integral Calculus in Euclidean spaces; implicit and inverse function theorems, differential forms and Stokes' Theorem. Prerequisite: MATH 5310. Course was offered Spring 2010 | |
| MATH 5340 | Complex Variables with Applications (3.00) |
| 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) |
| Offered Fall 2013 | This course provides the opportunity to offer a new topic in the subject of mathematics. |
| MATH 5651 | Advanced Linear Algebra (3.00) |
| Offered Fall 2013 | 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 3351 or instructor permission. |
| MATH 5652 | Introduction to Abstract Algebra (3.00) |
| 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 3351 or 5651, or instructor permission. | |
| MATH 5653 | Number Theory (3.00) |
| Includes congruences, quadratic reciprocity, Diophantine equations, and number-theoretic functions, among others. Prerequisite: MATH 3354 or instructor permission. | |
| MATH 5654 | Survey of Algebra (3.00) |
| Offered Fall 2013 | 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 1320 or equivalent and graduate standing. Course was offered Spring 2013, Fall 2012, Spring 2012, Fall 2011, Spring 2011, Fall 2010, Spring 2010, Fall 2009 |
| MATH 5655 | Automata Theory (3.00) |
| Studies finite and infinite automata, Turing machines; discusses relations between automata and groups, respectively, other algebraic structures. Course was offered Fall 2009 | |
| MATH 5700 | Introduction to Geometry (3.00) |
| Topics selected from analytic, affine, projective, hyperbolic, and non-Euclidean geometry. Prerequisite: MATH 2310, 3351, or instructor permission. | |
| MATH 5720 | Introduction to Differential Geometry (3.00) |
| Offered Fall 2013 | Topics selected from the theory of curves and surfaces in Euclidean space and the theory of manifolds. Prerequisite: MATH 2310 and 3351, or instructor permission. |
| MATH 5770 | General Topology (3.00) |
| Offered Fall 2013 | 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 2310 and 3351, with 3310 recommended. |
| MATH 5830 | Seminar (3.00) |
| Presentation of selected topics in mathematics. Prerequisite: MATH 5310; corequisite: MATH 5652 or instructor permission. | |
| MATH 5855 | Proofs in Algebra (3.00) |
| This course reviews the proofs of the main theorems in algebra in preparation for the advanced graduate algebra courses.This course is offered in the summer and restricted to Mathematics and Graduate Arts and Science students. | |
| MATH 5896 | Supervised Study in Mathematics (3.00) |
| Offered Fall 2013 | A rigorous program of supervised study designed to expose the student to a particular area of mathematics. Prerequisite: Instructor permission and graduate standing. |
| MATH 6060 | AFDA: Mathematical Modeling with Probability and Statistics (3.00) |
| Examines experimental design and probability and statistics through exploring, analyzing, and interpreting data sets. Explores the graphing calculator as a tool to display and analyze data obtained from sampling, observations, measurement, experiments, and internet sources. Course was offered Spring 2010 | |
| MATH 6120 | Measurement and Data Analysis (3.00) |
| Measurement and Data Analysis Course was offered Spring 2010 | |
| MATH 6452 | Functions and Algebra (3.00) |
| Functions and Algebra | |
| MATH 6453 | Number Systems and Number Theory for K-8 Mathematics Specialists (3.00) |
| Number Systems and Number Theory for K-8 Mathematics Specialists Course was offered Spring 2010 | |
| MATH 6454 | Rational Numbers and Proportional Reasoning (3.00) |
| Rational Numbers and Proportional Reasoning | |
| 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) |
| Algebra for Middle School Specialists | |
| MATH 6620 | AAO Elem Algebra and Functions (3.00) |
| AAO Elem Algebra and Functions | |
| MATH 6630 | AAO Introductory College Algebra and Trigonometry (3.00) |
| AAO Introductory College Algebra and Trigonometry Course was offered Spring 2010 | |
| MATH 6640 | AAO Linear Algebra (3.00) |
| AAO Linear Algebra | |
| MATH 6650 | AAO Calculus with Applications (3.00) |
| AAO Calculus with Applications | |
| MATH 6660 | Euclidean Geometry (3.00) |
| Euclidean Geometry Course was offered Spring 2012 | |
| 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) |
| Geometry and Measurement for K-8 Math Specialists | |
| MATH 6750 | MM Geometric Concepts and Measurement for Middle School Teachers (3.00) |
| MM Geometric Concepts and Measurement for Middle School Teachers | |
| 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) |
| Mathematical Applications Through Problem Solving and Lesson Study for Middle School Teachers | |
| MATH 6800 | Teaching Mathematics to Diverse Populations (3.00) |
| Teaching Mathematics to Diverse Populations | |
| MATH 7000 | Seminar on College Teaching (1.00 - 3.00) |
| Offered Fall 2013 | 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) |
| 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 5310 and linear algebra, or the equivalent. | |
| MATH 7305 | Problems in Analysis (3.00) |
| Applications of the theory presented in MATH 7310, 7320, and 7340 to specific examples in real and complex analysis. The course emphasizes problem-solving and preparation for the General Examination in Analysis. Problems are based on those from past General Exams. This course is offered in the summer and restricted to Mathematics and Graduate Arts and Science students. | |
| MATH 7310 | Real Analysis and Linear Spaces I (3.00) |
| Introduces measure and integration theory. Prerequisite: MATH 5310 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 7310, 7340, or equivalent. Course was offered Spring 2011 | |
| MATH 7340 | Complex Analysis I (3.00) |
| Offered Fall 2013 | Studies the fundamental theorems of analytic function theory. |
| MATH 7360 | Probability Theory I (3.00) |
| Offered Fall 2013 | 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 (3.00) |
| 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) |
| Offered Fall 2013 | Studies the basic principles of linear analysis, including spectral theory of compact and selfadjoint operators. Prerequisite: MATH 7340 and 7310, or equivalent. |
| MATH 7420 | Functional Analysis II (3.00) |
| Studies the spectral theory of unbounded operators, semigroups, and distribution theory. Prerequisite: MATH 7410 or equivalent. Course was offered Spring 2013, Spring 2010 | |
| 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 5310. Course was offered Spring 2011 | |
| 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 5770. Course was offered Spring 2011 | |
| MATH 7705 | Problems In Topology (3.00) |
| A continuation of the theory presented in MATH 5770 and 7800 intensively training students to apply the theory to proving theorems and solving problems in topology, especially in preparation for the General Examination in Topology. Problems are based on those from past General Exams. This course is offered in the summer and restricted to Mathematics and Graduate Arts and Science students. Course was offered Summer 2012, Summer 2011 | |
| MATH 7751 | Algebra I (3.00) |
| Offered Fall 2013 | Studies groups, rings, fields, modules, tensor products, and multilinear functions. Prerequisite: MATH 5651, 5652, or equivalent. |
| MATH 7752 | Algebra II (3.00) |
| Studies groups, rings, fields, modules, tensor products, and multilinear functions. Prerequisite: MATH 5651, 5652, or equivalent. | |
| MATH 7753 | Algebra III (3.00) |
| Offered Fall 2013 | Studies the Wedderburn theory, commutative algebra, and topics in advanced algebra. Prerequisite: MATH 7751, 7752, or equivalent. |
| MATH 7754 | Algebra IV (3.00) |
| Further topics in algebra. | |
| MATH 7755 | Problems in Algebra (3.00) |
| A continuation of the theory presented in MATH 7751 and 7752 intensively training students to apply the theory to proving theorems in algebra, especially in preparation for the General Examination in Algebra. Problems are based on those from past General Exams. This course is offered in the summer and restricted to Mathematics and Graduate Arts and Science students. | |
| MATH 7800 | Algebraic Topology I (3.00) |
| 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 5352, 5770, or equivalent. | |
| MATH 7810 | Algebraic Topology II (3.00) |
| Offered Fall 2013 | 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 7800. |
| MATH 7820 | Differential Topology (3.00) |
| Offered Fall 2013 | 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 5310, 5770, or equivalent. |
| MATH 7830 | Fiber Bundles (3.00) |
| Examines fiber bundles; induced bundles, principal bundles, classifying spaces, vector bundles, and characteristic classes, and introduces K-theory and Bott periodicity. Prerequisite: MATH 7800. | |
| MATH 7840 | Homotopy Theory (3.00) |
| Offered Fall 2013 | 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 7800. |
| MATH 8250 | Partial Differential Equations (3.00) |
| 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 7410 and 7250. Course was offered Spring 2013, Fall 2012, Spring 2012, Fall 2011, Fall 2010, Spring 2010, Fall 2009 | |
| MATH 8310 | Operator Theory I, II (3.00) |
| Topics in the theory of operators on a Hilbert space and related areas of function theory. Course was offered Spring 2012, Spring 2010 | |
| MATH 8320 | Operator Theory I, II (3.00) |
| Topics in the theory of operators on a Hilbert space and related areas of function theory. Course was offered Spring 2013 | |
| MATH 8360 | Stochastic Calculus and Differential Equations (3.00) |
| Offered Fall 2013 | 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 7360 and 7370, or instructor permission. Course was offered Fall 2010 |
| MATH 8370 | Topics in Probability Theory (3.00) |
| Selected topics in probability. Prerequisite: MATH 7360 or instructor permission. | |
| 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. Course was offered Spring 2012 | |
| MATH 8620 | Algebraic Geometry (3.00) |
| Studies the foundations of algebraic geometry. | |
| MATH 8700 | Lie Groups (3.00) |
| Offered Fall 2013 | 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. Course was offered Fall 2010 | |
| MATH 8720 | Differential Geometry (3.00) |
| Studies differential geometry in the large; connections; Riemannian geometry; Gauss-Bonnet formula; and differential forms. | |
| MATH 8750 | Topology of Manifolds (3.00) |
| Offered Fall 2013 | 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 5770. Course was offered Spring 2012, Fall 2009 |
| 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) |
| Studies the basic structure theory of groups, especially finite groups. Course was offered Spring 2013, Fall 2012, Fall 2011, Spring 2011, Fall 2010, Spring 2010, Fall 2009 | |
| MATH 8852 | Representation Theory (3.00) |
| Offered Fall 2013 | Studies the foundations of representation and character theory of finite groups. |
| MATH 8855 | Theory of Algebras (3.00) |
| 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 Fall 2013 | Thesis Course was offered Spring 2013, Fall 2012, Spring 2012, Fall 2011, Spring 2011, Fall 2010, Spring 2010, Fall 2009 |
| MATH 8998 | Non-Topical Research, Preparation for Research (1.00 - 12.00) |
| Offered Fall 2013 | For master's research, taken before a thesis director has been selected. Course was offered Spring 2013, Fall 2012, Spring 2012, Fall 2011, Spring 2011, Fall 2010, Spring 2010, Fall 2009 |
| MATH 8999 | Non-Topical Research (1.00 - 12.00) |
| Offered Fall 2013 | For master's thesis, taken under the supervision of a thesis director. Course was offered Spring 2013, Fall 2012, Spring 2012, Fall 2011, Spring 2011, Fall 2010, Spring 2010, Fall 2009 |
| MATH 9000 | Mathematics Colloquium (0.00) |
| Offered Fall 2013 | Forum for invited speakers giving mathematical colloquium talks. Course was offered Spring 2013, Fall 2012, Spring 2012, Fall 2011, Spring 2011, Fall 2010, Spring 2010, Fall 2009 |
| MATH 9010 | History of Mathematics Seminar (1.00 - 3.00) |
| Discusses subjects from the history of mathematics. | |
| MATH 9020 | Graduate Seminar (0.00) |
| Offered Fall 2013 | 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. Course was offered Spring 2013, Fall 2012, Spring 2012, Fall 2011, Spring 2011, Fall 2010, Spring 2010, Fall 2009 |
| MATH 9250 | Differential Equations and Dynamical Systems Seminar (3.00) |
| Offered Fall 2013 | Differential Equations and Dynamical Systems Seminar Course was offered Spring 2013, Fall 2012, Spring 2012, Fall 2011, Spring 2011, Fall 2010, Spring 2010, Fall 2009 |
| MATH 9310 | Operator Theory Seminar (3.00) |
| Offered Fall 2013 | Operator Theory Seminar Course was offered Spring 2013, Fall 2012, Spring 2012, Fall 2011, Spring 2011, Fall 2010, Spring 2010, Fall 2009 |
| MATH 9360 | Probability Seminar (3.00) |
| Offered Fall 2013 | Probability Seminar Course was offered Spring 2013, Fall 2012, Spring 2012, Fall 2011, Spring 2011, Fall 2010, Spring 2010, Fall 2009 |
| MATH 9410 | Analysis Seminar (3.00) |
| Analysis Seminar Course was offered Fall 2012, Spring 2012, Fall 2011, Spring 2011, Fall 2010, Spring 2010, Fall 2009 | |
| MATH 9450 | Mathematical Physics Seminar (3.00) |
| Offered Fall 2013 | Mathematical Physics Seminar Course was offered Spring 2013, Fall 2012, Spring 2012, Fall 2011, Spring 2011, Fall 2010, Spring 2010, Fall 2009 |
| MATH 9559 | New Course in Mathematics (1.00 - 4.00) |
| Offered Fall 2013 | This course provides the opportunity to offer a new topic in the subject of mathematics. |
| MATH 9800 | Topology Seminar (3.00) |
| Offered Fall 2013 | Topology Seminar Course was offered Spring 2013, Fall 2012, Spring 2012, Fall 2011, Spring 2011, Fall 2010, Spring 2010, Fall 2009 |
| MATH 9820 | Geometry Seminar (1.00 - 3.00) |
| Offered Fall 2013 | Discusses subjects from geometry. Course was offered Spring 2013, Fall 2012, Spring 2012, Fall 2011, Spring 2011, Fall 2010, Spring 2010, Fall 2009 |
| MATH 9950 | Algebra Seminar (3.00) |
| Offered Fall 2013 | Algebra Seminar Course was offered Spring 2013, Fall 2012, Spring 2012, Fall 2011, Spring 2011, Fall 2010, Spring 2010, Fall 2009 |
| MATH 9995 | Independent Research (3.00 - 9.00) |
| Offered Fall 2013 | Independent Research Course was offered Spring 2013, Fall 2012, Spring 2012, Fall 2011, Spring 2011, Fall 2010, Spring 2010, Fall 2009 |
| MATH 9998 | Non-Topical Research, Preparation for Doctoral Research (1.00 - 12.00) |
| Offered Fall 2013 | For doctoral research, taken before a dissertation director has been selected. Course was offered Spring 2013, Fall 2012, Summer 2012, Spring 2012, Fall 2011, Summer 2011, Spring 2011, Fall 2010, Spring 2010, Fall 2009 |
| MATH 9999 | Non-Topical Research (1.00 - 12.00) |
| Offered Fall 2013 | 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. Course was offered Spring 2013, Fall 2012, Summer 2012, Spring 2012, Fall 2011, Summer 2011, Spring 2011, Fall 2010, Summer 2010, Spring 2010, Fall 2009 |