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Course Catalog 2009-2010
Mathematics |
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MATH 101 - SINGLE VARIABLE CALCULUS I
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Credits: 3 |
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Differentiation, extrema, Newton's method, integration, fundamental theorem of calculus, area, volume, natural logarithm, exponential, arc length, surface area, Simpson's rule, L'Hopital's rule. May substitute MATH 111-112 or take MATH 101 after completing MATH 111. |
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College: School of Natural Sciences |
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Department: Mathematics |
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MATH 102 - SINGLE VARIABLE CALCULUS II
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Credits: 3 |
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Continuation of MATH 101. Includes further techniques of integration, as well as infinite sequences and series, tests for convergence, power series, radius of convergence, polar coordinates, parametric equations, and arc length. |
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College: School of Natural Sciences |
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Department: Mathematics |
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MATH 111 - FUNDAMENTAL THEOREM OF CALCULUS
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Credits: 3 |
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Study of calculus, forming with MATH 112 a slower-paced version of MATH 101/102. Contains less detail in the coverage of infinite series. Students may take MATH 111/112 followed by MATH 102, or MATH 111 followed by MATH 101/102. |
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College: School of Natural Sciences |
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Department: Mathematics |
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MATH 112 - CALCULUS AND ITS APPLICATIONS
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Credits: 3 |
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Continuation of the study of calculus from MATH 111. |
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College: School of Natural Sciences |
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Department: Mathematics |
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MATH 211 - ORDINARY DIFFERENTIAL EQUATIONS AND LINEAR ALGEBRA
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Credits: 3 |
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Study of ordinary differential equations (e.g., solutions to separable and linear first-order equations and to higher-order linear equations with constant coefficients, the properties of solutions to differential equations, and numerical solution methods) and linear algebra (e.g., vector spaces and solutions to algebraic linear equations, dimension, eigenvalues, and eigenvectors of a matrix), as well as the application of linear algebra to first-order systems of differential equations and the qualitative theory of nonlinear systems and phase portraits. Use of the computers in Owlnet as part of each homework assignment required. Credit may not be received for both MATH 211 and MATH 213. |
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College: School of Natural Sciences |
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Department: Mathematics |
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MATH 212 - MULTIVARIABLE CALCULUS
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Credits: 3 |
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Study of gradient, divergence, and curl, Lagrange multipliers, multiple integrals, as well as line integrals, conservative vector fields, Green's theorem, Stokes's theorem, and Gauss's theorem. May substitute Math 221 and 222. Equivalency: MATH 222. |
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College: School of Natural Sciences |
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Department: Mathematics |
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MATH 213 - BASIC MATHEMATICAL BIOLOGY
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Credits: 3 |
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Study of systems of differential and difference equations, with special attention to modeling of basic biological processes. Phase plane analysis of ordinary differential systems. Qualitative understanding of solutions of differential equations. Credit may not be received for this course and MATH 211. |
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College: School of Natural Sciences |
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Department: Mathematics |
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Pre-requisites: MATH 102 |
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MATH 221 - HONORS CALCULUS III
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Credits: 3 |
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This course and MATH 222 include the material of MATH 212 and much more. Topology of Rn, calculus for functions of several variables, linear and multilinear algebra, theory of determinants, inner product spaces, integration on manifolds. |
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College: School of Natural Sciences |
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Department: Mathematics |
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MATH 222 - HONORS CALCULUS IV
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Credits: 3 |
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See MATH 221. A student may not receive credit for both MATH 222 and MATH 212. Equivalency: MATH 212. |
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College: School of Natural Sciences |
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Department: Mathematics |
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MATH 300 - TOPICS IN UNDERGRADUATE MATH
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Credits: 3 |
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Treatment of topics in undergraduate mathematics with an emphasis on writing of clear, cogent compete mathematical proofs. Topics vary by year. May be repeated for credit with permission of department. Pre-requisite: MATH 102 |
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College: School of Natural Sciences |
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Department: Mathematics |
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Pre-requisites: MATH 102 |
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MATH 310 - MATHEMATICS OF MUSIC |
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Credits: 2 |
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This course will survey the many places in which mathematics plays a role in music. The topics and mathematical tools used are diverse: simple number theory in musical scales and tunings, differential equations in the physics of musical instruments, and symmetry in music explained in terms of mathematical group theory. Throughout the course we will use Csound, a compiler language for creating sound, to give concrete examples. |
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College: School of Music |
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Department: Mathematics |
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Pre-requisites: MATH 211 OR MATH 213 |
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MATH 321 - INTRODUCTION TO ANALYSIS I
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Credits: 3 |
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A thorough treatment of basic methods of analysis such as metric spaces, compactness, sequences and series of functions. Also further topics in analysis, such as Hilbert spaces, Fourier series, Sturm- Liouville theory. |
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College: School of Natural Sciences |
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Department: Mathematics |
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Pre-requisites: MATH 221
or permission of department |
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MATH 322 - INTRODUCTION TO ANALYSIS II
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Credits: 3 |
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See MATH 321. Includes proofs of the basic results for multivariable calculus (MATH 321 provides proofs for single-variable calculus). |
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College: School of Natural Sciences |
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Department: Mathematics |
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Pre-requisites: MATH 321
or permission of instructor |
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MATH 354 - HONORS LINEAR ALGEBRA
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Credits: 3 |
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Course URL: http://math.rice.edu/~cochran |
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Systems of linear equations, matrices, vector spaces, linear transformations, eigenvalues, canonical forms, inner product spaces, bilinear and quadratic forms. Content is similar to that of MATH 355, but with more emphasis on theory. The course will include instruction on how to construct mathematical proofs. This course is appropriate for potential Mathematics majors and others interested in learning how to construct rigorous mathematical arguments. Credit may not be received for both MATH 354 and MATH 355. Equivalency: MATH 355.
Recommend a 200-level math class. |
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College: School of Natural Sciences |
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Department: Mathematics |
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MATH 355 - LINEAR ALGEBRA
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Credits: 3 |
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Linear transformations and matrices, solution of linear equations, eigenvalues and eigenvectors, quadratic forms, Jordan canonical form. Credit may not be received for both MATH 354 and MATH 355. Equivalency: MATH 354. |
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College: School of Natural Sciences |
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Department: Mathematics |
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MATH 356 - ABSTRACT ALGEBRA I
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Credits: 3 |
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Group theory: normal subgroups, factor groups, Abelian groups, permutations, matrix groups, and group action. |
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College: School of Natural Sciences |
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Department: Mathematics |
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MATH 365 - NUMBER THEORY
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Credits: 3 |
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Properties of numbers depending mainly on the notion of divisibility. Continued fractions. Offered alternate years. |
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College: School of Natural Sciences |
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Department: Mathematics |
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MATH 366 - GEOMETRY
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Credits: 3 |
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Topics chosen from Euclidean, spherical, hyperbolic, and projective geometry, with emphasis on the similarities and differences found in various geometries. Isometries and other transformations are studied and used throughout. The history of the development of geometric ideas is discussed. This course is strongly recommended for prospective high school teachers. |
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College: School of Natural Sciences |
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Department: Mathematics |
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MATH 368 - TOPICS IN COMBINATORICS
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Credits: 3 |
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Study of combinatorics and discrete mathematics. Topics that may be covered include graph theory, Ramsey theory, finite geometries, combinatorial enumeration, combinatorial games. |
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College: School of Natural Sciences |
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Department: Mathematics |
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MATH 381 - INTRODUCTION TO PARTIAL DIFFERENTIAL EQUATIONS
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Credits: 3 |
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Laplace transform: inverse transform, applications to constant coefficient differential equations. Boundary value problems: Fourier series, Bessel functions, Legendre polynomials. |
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College: School of Natural Sciences |
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Department: Mathematics |
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MATH 382 - COMPLEX ANALYSIS
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Credits: 3 |
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Study of the Cauchy integral theorem, Taylor series, residues, as well as the evaluation of integrals by means of residues, conformal mapping, and application to two-dimensional fluid flow. May not receive credit for this course and MATH 427. Equivalency: MATH 427. |
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College: School of Natural Sciences |
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Department: Mathematics |
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MATH 390 - UNDERGRADUATE COLLOQUIUM
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Credits: 1 |
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Lectures by undergraduate students on mathematical topics not usually covered in other courses. Presentation of one lecture and attendance at all sessions required. |
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College: School of Natural Sciences |
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Department: Mathematics |
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MATH 401 - DIFFERENTIAL GEOMETRY
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Credits: 3 |
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Study of the differential geometry of curves and surfaces in R3. Includes an introduction to the concept of curvature and thorough treatment of the Gauss-Bonnet theorem. |
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College: School of Natural Sciences |
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Department: Mathematics |
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MATH 402 - DIFFERENTIAL GEOMETRY
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Credits: 3 |
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Introduction to Riemannian geometry. Content varies from year to year. |
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College: School of Natural Sciences |
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Department: Mathematics |
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Pre-requisites: MATH 401 |
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MATH 410 - CALCULUS OF VARIATIONS
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Credits: 3 |
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Study of classical and modern theories about functions having some integral expression which is maximal, minimal, or critical. Geodesics, brachistochrone problem, minimal surfaces, and numerous applications to physics. Euler-Lagrange equations, 1st and 2nd variations, Hamilton's Principle. |
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College: School of Natural Sciences |
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Department: Mathematics |
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Pre-requisites: MATH 211
AND MATH 212 |
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MATH 423 - PARTIAL DIFFERENTIAL EQUATIONS
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Credits: 3 |
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Wave equation, Laplace's equation, heat equation. Fundamental solutions. Other topics include first order hyperbolic systems, Cauchy-Kowalewski theorem, potential theory, Dirichlet and Neumann problems, integral equations, elliptic equations. |
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College: School of Natural Sciences |
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Department: Mathematics |
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MATH 424 - PARTIAL DIFFERENTIAL EQUATIONS
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Credits: 3 |
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Continuation of MATH 423. |
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College: School of Natural Sciences |
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Department: Mathematics |
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Pre-requisites: MATH 423 |
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MATH 425 - INTEGRATION THEORY
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Credits: 3 |
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Lebesgue theory of measure and integration. |
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College: School of Natural Sciences |
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Department: Mathematics |
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MATH 426 - TOPICS IN REAL ANALYSIS
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Credits: 3 |
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Content varies from year to year. May include Fourier series, harmonic analysis, probability theory, advanced topics in measure theory, ergodic theory, and elliptic integrals. |
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College: School of Natural Sciences |
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Department: Mathematics |
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Pre-requisites: MATH 425 |
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MATH 427 - COMPLEX ANALYSIS
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Credits: 3 |
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Study of the Cauchy-Riemann equation, power series, Cauchy's integral formula, residue calculus, and conformal mappings. Emphasis on the theory. Credit may not be received for both MATH 382 and MATH 427. Equivalency: MATH 382. |
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College: School of Natural Sciences |
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Department: Mathematics |
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MATH 428 - TOPICS IN COMPLEX ANALYSIS
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Credits: 3 |
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Special topics include Riemann mapping theorem, Runge's Theorem, elliptic function theory, prime number theorem, Riemann surfaces, et al. |
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College: School of Natural Sciences |
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Department: Mathematics |
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Pre-requisites: MATH 382
OR MATH 427 |
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MATH 435 - DYNAMICAL SYSTEMS
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Credits: 3 |
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Existence and uniqueness for solutions of ordinary differential equations and difference equations, linear systems, nonlinear systems, stability, periodic solutions, bifurcation theory. Cross-list: CAAM 435. |
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College: School of Natural Sciences |
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Department: Mathematics |
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Pre-requisites: MATH 211
AND CAAM 335
OR MATH 355
AND CAAM 401
OR MATH 321 |
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MATH 443 - GENERAL TOPOLOGY
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Credits: 3 |
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Study of basic point set topology. Includes a treatment of cardinality and well ordering, as well as metrization. |
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College: School of Natural Sciences |
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Department: Mathematics |
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MATH 444 - GEOMETRIC TOPOLOGY
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Credits: 3 |
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Introduction to algebraic methods in topology and differential topology. Elementary homotopy theory. Covering spaces. |
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College: School of Natural Sciences |
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Department: Mathematics |
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Pre-requisites: MATH 443
or permission of department |
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MATH 445 - ALGEBRAIC TOPOLOGY
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Credits: 3 |
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Introduction to the theory of homology. Includes simplicial complexes, cell complexes and cellular homology and cohomology, as well as manifolds, and Poincare duality. |
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College: School of Natural Sciences |
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Department: Mathematics |
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Pre-requisites: MATH 444 |
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MATH 463 - ABSTRACT ALGEBRA II
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Credits: 3 |
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Ring theory: ideals, polynomials, factorization. Advanced linear algebra: quadratic forms, canonical forms. Field theory: extensions, Galois theory, soluability in radicals. Continuation of MATH 356. |
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College: School of Natural Sciences |
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Department: Mathematics |
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Pre-requisites: MATH 356
or permission of instructor |
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MATH 464 - ABSTRACT ALGEBRA III
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Credits: 3 |
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Continuation of MATH 463. Advanced topics may include representations of finite groups, modules, commutative algebra, and homological algebra. |
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College: School of Natural Sciences |
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Department: Mathematics |
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Pre-requisites: MATH 463
or permission of instructor |
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MATH 465 - TOPICS IN ALGEBRA
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Credits: 3 |
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Content varies from year to year. |
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College: School of Natural Sciences |
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Department: Mathematics |
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MATH 466 - TOPICS IN ALGEBRA II
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Credits: 3 |
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Content varies from year to year. |
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College: School of Natural Sciences |
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Department: Mathematics |
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MATH 468 - POTPOURRI
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Credits: 3 |
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This course deals with miscellaneous special topics not covered in other courses. |
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College: School of Natural Sciences |
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Department: Mathematics |
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MATH 490 - SUPERVISED READING
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Credits: Hours Variable |
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College: School of Natural Sciences |
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Department: Mathematics |
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MATH 498 - RESEARCH THEMES IN THE MATHEMATICAL SCIENCES
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Credits: Hours Variable |
| A seminar course that will cover selected themes of general research in the mathematical sciences from the perspectives of mathematics, computational and applied mathematics and statistics.
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College: School of Natural Sciences |
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Department: Mathematics |
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MATH 499 - MATHEMATICAL SCIENCES VIGRE SEMINAR
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Credits: Hours Variable |
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Graduate/Undergraduate Equivalency: MATH 699. |
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College: School of Natural Sciences |
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Department: Mathematics |
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MATH 501 - TOPICS IN DIFFERENTIAL GEOMETRY
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Credits: 3 |
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Topic to be announced. |
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College: School of Natural Sciences |
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Department: Mathematics |
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MATH 502 - TOPICS IN DIFFERENTIAL GEOMETRY
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Credits: 3 |
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The Atiyah-Singer theorem, secondary invariants, and related topics. |
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College: School of Natural Sciences |
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Department: Mathematics |
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MATH 521 - ADVANCED TOPICS IN REAL ANALYSIS
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Credits: 3 |
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Topic to be announced. |
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College: School of Natural Sciences |
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Department: Mathematics |
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MATH 522 - TOPICS IN ANALYSIS
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Credits: 3 |
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Topic to be announced. |
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College: School of Natural Sciences |
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Department: Mathematics |
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MATH 523 - FUNCTIONAL ANALYSIS
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Credits: 3 |
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Topic to be announced. |
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College: School of Natural Sciences |
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Department: Mathematics |
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MATH 527 - ERGODIC THEORY AND TOPOLOGICAL DYNAMICS
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Credits: 3 |
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Topic to be announced. |
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College: School of Natural Sciences |
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Department: Mathematics |
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MATH 528 - ERGODIC THEORY AND TOPOLOGICAL DYNAMICS
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Credits: 3 |
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College: School of Natural Sciences |
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Department: Mathematics |
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MATH 541 - TOPICS IN TOPOLOGY
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Credits: 3 |
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Topic to be announced. |
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College: School of Natural Sciences |
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Department: Mathematics |
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MATH 542 - TOPICS IN ADVANCED TOPOLOGY
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Credits: 3 |
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Topic to be announced. |
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College: School of Natural Sciences |
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Department: Mathematics |
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MATH 543 - TOPICS IN LOW DIMENSIONAL TOPOLOGY
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Credits:Variable |
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Topic to be announced. |
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College: School of Natural Sciences |
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Department: Mathematics |
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MATH 567 - TOPICS IN ALGEBRAIC GEOMETRY
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Credits: 3 |
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Possible topics include rational points on algebraic varieties, moduli spaces, deformation theory, and Hodge structures.
Recommended prerequisite(s): Mathematics 463 - 464. |
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College: School of Natural Sciences |
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Department: Mathematics |
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MATH 590 - CURRENT MATHEMATICS SEMINAR
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Credits: 1 |
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Lectures on topics of recent research in mathematics delivered by mathematics graduate students and faculty. |
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College: School of Natural Sciences |
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Department: Mathematics |
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MATH 591 - GRADUATE TEACHING SEMINAR
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Credits: 1 |
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Discussion on teaching issues and practice lectures by participants as preparation for classroom teaching of mathematics. |
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College: School of Natural Sciences |
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Department: Mathematics |
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MATH 698 - RESEARCH THEMES IN THE MATHEMATICAL SCIENCES
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Credits: Hours Variable |
| A seminar course that will cover selected themes of general research in the mathematical sciences from the perspectives of mathematics, computational and applied mathematics and statistics.
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College: School of Natural Sciences |
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Department: Mathematics |
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MATH 699 - MATHEMATICAL SCIENCES VIGRE SEMINAR
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Credits: Hours Variable |
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Graduate/Undergraduate Equivalency: MATH 499. |
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College: School of Natural Sciences |
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Department: Mathematics |
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MATH 777 - VISITING RESEARCH TRAINEE
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Credits: 0 |
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College: School of Natural Sciences |
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Department: Mathematics |
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MATH 800 - THESIS AND RESEARCH
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Credits: Hours Variable |
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College: School of Natural Sciences |
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Department: Mathematics |
