MATH 401
Introduction to Analysis I (3) Review of calculus, properties of real numbers, infinite series, uniform convergence, power series. Students who have passed Math. 403 may not schedule this course.
Effective: Fall 1983
Prerequisite:
MATH 230 orMATH 231
MATH 403
Classical Analysis I (3) Topology of Rn, compactness, continuity of functions, uniform convergence, Arzela-Ascoli theorem in the plane, Stone-Wierstrass theorem.
Effective: Spring 1996
Prerequisite:
MATH 312
MATH 403H
Honors Classical Analysis I (3) Development of a thorough understanding and technical mastery of foundations of classical analysis in the framework of metric spaces.
Effective: Spring 2010
Prerequisite:
MATH 311M, MATH 312H
MATH 404
Classical Analysis II (3) Differentiation of functions from Rn to Rm, implicit function theorem, Riemann integration, Fubini's theorem, Fourier analysis.
Effective: Fall 1985
Prerequisite:
MATH 403
MATH 405
Advanced Calculus for Engineers and Scientists I (3) Vector calculus, linear algebra, ordinary and partial differential equatinos. Students who have passed MATH 411 or 412 may not take this course for credit.
Effective: Spring 1994
Prerequisite:
MATH 231;MATH 250 orMATH 251
MATH 406
Advanced Calculus for Engineers and Scientists II (3) Complex analytic functions, sequences and series, residues, Fourier and Laplace transforms. Students who have passed MATH 421 may not take this course for credit.
Effective: Spring 1994
Prerequisite:
MATH 405
MATH 408
Advanced Calculus (3) Differential and integral calculus of functions of several variables, line and surface integrals, infinite series, series of functions, power series.
Effective: Spring 2007
Prerequisite:
MATH 141
MATH 411
Ordinary Differential Equations (3) Linear ordinary differential equations; existence and uniqueness questions; series solutions; special functions; eigenvalue problems; Laplace transforms; additional topics and applications.
Effective: Fall 1983
Prerequisite:
MATH 230 orMATH 231;MATH 250 orMATH 251
MATH 412
Fourier Series and Partial Differential Equations (3) Orthogonal systems and Fourier series; derivation and classification of partial differential equations; eigenvalue function method and its applications; additional topics.
Effective: Spring 2009
Prerequisite:
MATH 230;MATH 250 orMATH 251
MATH 414
(STAT 414)
Introduction to Probability Theory (3) Probability spaces, discrete and continuous random variables, transformations, expectations, generating functions, conditional distributions, law of large numbers, central limit theorems. Students may take only one course from MATH(STAT) 414 and 418 for credit.
Effective: Fall 2001
Prerequisite:
MATH 230 orMATH 231
MATH 415
(STAT 415)
Introduction to Mathematical Statistics (3) A theoretical treatment of statistical inference, including sufficiency, estimation, testing, regression, analysis of variance, and chi-square tests.
Effective: Fall 1989
Prerequisite:
MATH 414
MATH 416
(STAT 416)
Stochastic Modeling (3) Review of distribution models, probability generating functions, transforms, convolutions, Markov chains, equilibrium distributions, Poisson process, birth and death processes, estimation.
Effective: Spring 1984
Prerequisite:
MATH 318 orMATH 414;MATH 230
MATH 417
Qualitative Theory of Differential Equations (3) Linear differential equations, stability of stationary solutions, ordinary bifurcation, exchange of stability, Hopf bifurcation, stability of periodic solutions, applications.
Effective: Spring 2009
Prerequisite:
MATH 220;MATH 250 orMATH 251
MATH 418
(STAT 418)
Introduction to Probability and Stochastic Processes for Engineering (3) Introduction to probability axioms, combinatorics, random variables, limit laws, and stochastic processes. Students may take only one course from MATH(STAT) 414 and 418 for credit.
Effective: Fall 2011
Prerequisite:
MATH 230 orMATH 231
MATH 419
(PHYS 419)
Theoretical Mechanics (3) Principles of Newtonian, Lagrangian, and Hamiltonian mechanics of particles with applications to vibrations, rotations, orbital motion, and collisions.
Effective: Spring 2007
Prerequisite:
MATH 230 orMATH 231;MATH 250 orMATH 251;PHYS 212, PHYS 213 andPHYS 214
MATH 421
Complex Analysis (3) Infinite sequences and series; algebra and geometry of complex numbers; analytic functions; integration; power series; residue calculus; conformal mapping, applications.
Effective: Summer 1993
Prerequisite:
MATH 230, MATH 232 orMATH 405;MATH 401 orMATH 403
MATH 422
Wavelets and Fourier Analysis: Theory and Applications (3) Fundamental mathematical issues of the theory of wavelets for senior undergraduate and graduate students in mathematics, engineering, physics, and computer science.
Effective: Summer 2000
Prerequisite:
complete one of the following:MATH 312, MATH 401, MATH 403, MATH 405 orMATH 412
MATH 425
Introduction to Operations Research (3) Nature of operations research, problem formulation, model construction, deriving solution from models, allocation problems, general linear allocation problem, inventory problems.
Effective: Spring 2012
Prerequisite:
MATH 141 andMATH 220
MATH 426
Introduction to Modern Geometry (3) Plane and space curves; space surfaces; curvature; intrinsic geometry of surfaces; Gauss-Bonnet theorem; covariant differentiation; tensor analysis.
Effective: Spring 1994
Prerequisite:
MATH 401 orMATH 403
MATH 427
Foundations of Geometry (3) Euclidean and various non-Euclidean geometries and their development from postulate systems. Students who have passed MATH 427 may not schedule MATH 471.
Effective: Spring 1994
Prerequisite:
MATH 230 orMATH 231
MATH 428
Geometry for Teachers (1) Research in mathematics education using ideas from Euclidean and non-Euclidean geometry. Students who have passed MATH 471 may not schedule MTHBD 478.
Effective: Spring 2007
Prerequisite:
MATH 311W . Prerequisite or concurrent:MATH 427
MATH 429
Introduction to Topology (3) Metric spaces, topological spaces, separation axioms, product spaces, identificaiton spaces, compactness, connectedness, fundamental group.
Effective: Spring 1994
Prerequisite:
MATH 311W
MATH 430
Linear Algebra and Discrete Models I (3) Vector spaces, linear transformations, matrices determinants, characteristic values and vectors, systems of linear equations, applications to discrete models.
Effective: Spring 2010
Prerequisite:
MATH 220
MATH 431
Linear Algebra and Discrete Models II (3) Vector spaces and linear transformations, matrices, determinants, characteristics values and vectors, systems of linear equations, applications to discrete models.
Effective: Spring 2007
Prerequisite:
MATH 430
MATH 435
Basic Abstract Algebra (3) Elementary theory of groups, rings, and fields. Students who have passed MATH 435 may not schedule MATH 470.
Effective: Spring 2010
Prerequisite:
MATH 311W orMATH 315
MATH 436
Linear Algebra (3) Vector spaces and linear transformations, canonical forms of matrices, elementary divisors, invariant factors; applications. Students who have passed MATH 436 may not schedule MATH 441.
Effective: Fall 1983
Prerequisite:
MATH 311W
MATH 437
Algebraic Geometry (3) Study of curves in the plane defined by polynomial equations p(x,y)= 0. Projective equivalence, singular points, classification of cubics.
Effective: Spring 2009
Prerequisite:
MATH 230 orMATH 231;MATH 311W
MATH 441
Matrix Algebra (3) Determinants, matrices, linear equations, characteristic roots, quadratic forms, vector spaces. Students who have passed Math 436 may not schedule this course.
Effective: Fall 1985
Prerequisite:
MATH 220
MATH 444
Mathematical Statistics and Applications I (3) Distributions of random variables, special distributions, limiting distributions, sampling, statistical inference, point and interval estimation, orthogonal polynomials, and least squares.
Effective: Spring 2007
Prerequisite:
MATH 141
MATH 445
Mathematical Statistics and Applications II (3) Further topics in point estimation, statistical hypotheses, other statistical tests, nonparametric methods.
Effective: Spring 2007
Prerequisite:
MATH 444
MATH 446
Introduction to Applied Statistics I (3) Descriptive statistics, probability theory, discrete and continuous probability distributions, statistical inferences for means and proportions.
Effective: Spring 2007
Prerequisite:
MATH 022 orMATH 040
MATH 447
Introduction to Applied Statistics II (3) Regression, correlation, analysis of variance, contingency tables, nonparametric methods, time series, index numbers.
Effective: Spring 2007
MATH 449
Applied Ordinary Differential Equations (3) Differential and difference equations and their application to biology, chemistry, and physics; techniques in dynamical systems theory.
Effective: Spring 2007
Prerequisite:
MATH 250 orMATH 251
MATH 450
Mathematical Modeling (3) Constructing mathematical models of physical phenomena; topics include pendulum motion, polymer fluids, chemical reactions, waves, flight, and chaos.
Effective: Spring 2007
Prerequisite:
MATH 315 andMATH 430 orMATH 405 orMATH 412
MATH 451
(CMPSC 451)
Numerical Computations (3) Algorithms for interpolation, approximation, integration, nonlinear equations, linear systems, fast FOURIER transform, and differential equations emphasizing computational properties and implementation. Students may take only one course for credit from MATH 451 and 455.
Effective: Spring 2008
Prerequisite:
3 credits of programming;MATH 230 orMATH 231
MATH 455
(CMPSC 455)
Introduction to Numerical Analysis I (3) Floating point computation, numerical rootfinding, interpolation, numerical quadrature, direct methods for linear systems. Students may take only one course for credit from MATH 451 and MATH 455.
Effective: Spring 2008
Prerequisite:
CMPSC 201, CMPSC 202 orCMPSC 121;MATH 220;MATH 230 orMATH 231
MATH 456
(CMPSC 456)
Introduction to Numerical Analysis II (3) Polynomial and piecewise polynomial approximation, matrix least squares problems, numerical solution of eigenvalue problems, numerical solution of ordinary differential equations.
Effective: Spring 2008
Prerequisite:
MATH 455
MATH 457
Introduction to Mathematical Logic (3) Propositional logic, first-order predicate logic, axioms and rules of inference, structures, models, definability, completeness, compactness.
Effective: Summer 2011
Prerequisite:
MATH 311W ; 3 additional credits in philosophy
MATH 461
(PHYS 461)
Theoretical Mechanics (3) Continuation of Math.(Phys.) 419. Theoretical treatment of dynamics of a rigid body, theory of elasticity, aggregates of particles, wave motion, mechanics of fluids.
Effective: Fall 1986
Prerequisite:
MATH 419
MATH 465
Number Theory (3) Elements, divisibility of numbers, congruences, residues, and forms.
Effective: Spring 2009
Prerequisite:
MATH 311W
MATH 467
(CMPSC 467)
Factorization and Primality Testing (3) Prime sieves, factoring, computer numeration systems, congruences, multiplicative functions, primitive roots, cryptography, quadratic residues. Students who have passed MATH 465 may not schedule this course.
Effective: Spring 1995
Prerequisite:
MATH 311W
MATH 468
Mathematical Coding Theory (3) Shannon's theorem, block codes, linear codes, Hamming codes, Hadamard codes, Golay codes, Reed-Muller codes, bounds on codes, cyclic codes.
Effective: Fall 1983
Prerequisite:
MATH 311W ; advanced calculus
MATH 470
Algebra for Teachers (3) An introduction to algebraic structures and to the axiomatic approach, including the elements of linear algebra. Designed for teachers and prospective teachers. Students who have passed Math 435 may not schedule this course.
Effective: Fall 1988
Prerequisite:
MATH 311W
MATH 471
Geometry for Teachers (4) Problem solving oriented introduction to Euclidean and non-Euclidean geometries; construction problems and geometrical transformations via "Geometer's Sketchpad" software. Intended primarily for those seeking teacher certification in secondary mathematics. Students who have passed MATH 427 may not schedule this course.
Effective: Spring 1996
Prerequisite:
MATH 311W
MATH 475W
(US;IL)
History of Mathematics (3) A global survey of the history of mathematics as viewed as a human response to cultural, political, economic, and societal pressures.
Effective: Spring 2012
Prerequisite:
MATH 315 orMATH 311W
MATH 479
(PHYS 479)
Special and General Relativity (3) Mathematical description, physical concepts, and experimental tests of special and general relativity.
Effective: Spring 2007
Prerequisite:
PHYS 237, PHYS 400, PHYS 419;MATH 250 orMATH 251;MATH 230 orMATH 231
MATH 482
Mathematical Methods of Operations Research (3) Survey of linear and nonlinear programming; mathematics of optimization; queues; simulation.
Effective: Spring 2007
Prerequisite:
MATH 220, MATH 230, STAT 301
MATH 484
Linear Programs and Related Problems (3) Introduction to theory and applications of linear programming; the simplex algorithm and newer methods of solution; duality theory.
Effective: Spring 1987
Prerequisite:
MATH 220;MATH 230 orMATH 231
MATH 485
Graph Theory (3) Introduction to the theory and applications of graphs and directed graphs. Emphasis on the fundamental theorems and their proofs.
Effective: Spring 1987
Prerequisite:
MATH 311W
MATH 486
Mathematical Theory of Games (3) Basic theorems, concepts, and methods in the mathematical study of games of strategy; determination of optimal play when possible.
Effective: Spring 2006
Prerequisite:
MATH 220
MATH 494
Research Project (1-12) Supervised student activities on research projects identified on an individual or small-group basis.
Effective: Spring 1995
MATH 494H
Research Project (1-12) Supervised student activities on research projects identified on an individual or small-group basis.
Effective: Fall 2007
MATH 495
Internship (1-18) Supervised off-campus, nongroup instruction including field experiences, practica, or internships. Written and oral critique of activity required.
Effective: Spring 2007
Prerequisite:
prior approval of proposed assignment by instructor
MATH 496
Independent Studies (1-18) Creative projects, including research and design, which are supervised on an individual basis and which fall outside the scope of formal courses.
Effective: Fall 1983
MATH 496A
Mathematical Models in Biology (1-6) Covers mathematical modeling in Biology; there are two major components: analytical modeling techniques and computational modeling techniques.
Effective: Summer 2013 Ending: Summer 2013
Prerequisite:
MATH 250, MATH 220
MATH 496B
Elementary Combinatorics (1-6) Fundamental techniques of enumeration and construction of combinatorial structures, permutations, recurrences, inclusion-exclusion, permanents, 0, 1-, matrices, Latin squares, combinatorial designs.
Effective: Fall 2013 Ending: Fall 2013 Future: Fall 2013
Prerequisite:
MATH 220
MATH 497
Special Topics (1-9) Formal courses given infrequently to explore, in depth, a comparatively narow subject which may be topical or of special interest.
Effective: Fall 1983
MATH 497A
Number Theory in the Spirit of Ramanujan (4) Formal courses given infrequently to explore, in depth, a comparatively narow subject which may be topical or of special interest.
Effective: Fall 2013 Ending: Fall 2013 Future: Fall 2013
MATH 497B
Elements of Functional Analysis (4) Formal courses given infrequently to explore, in depth, a comparatively narow subject which may be topical or of special interest.
Effective: Fall 2013 Ending: Fall 2013 Future: Fall 2013
MATH 497C
The Winding Number in Topology and Geometry (and the rest of Mathematics) (4) Formal courses given infrequently to explore, in depth, a comparatively narow subject which may be topical or of special interest.
Effective: Fall 2013 Ending: Fall 2013 Future: Fall 2013
MATH 497D
MASS Interdisciplinary Seminar (3) Formal courses given infrequently to explore, in depth, a comparatively narow subject which may be topical or of special interest.
Effective: Fall 2013 Ending: Fall 2013 Future: Fall 2013
MATH 497E
MASS Colloquium (1) Formal courses given infrequently to explore, in depth, a comparatively narow subject which may be topical or of special interest.
Effective: Fall 2013 Ending: Fall 2013 Future: Fall 2013
MATH 498
Special Topics (1-9) Formal courses given infrequently to explore, in depth, a comparatively narrow subject which may be topical or of special interest.
Effective: Fall 1992
MATH 499
(IL)
Foreign Studies (1-12) Courses offered in foreign countries by individual or group instruction.
Effective: Summer 2005
MATH 501
Real Analysis (3) Legesgue measure theory. Measurable sets and measurable functions. Legesgue integration, convergence theorems. Lp spaces. Decomposition and differentiation of measures. Convolutions. The Fourier transform.
Effective: Spring 2013
Prerequisite:
MATH 404
MATH 502
Complex Analysis (3) Complex numbers. Holomorphic functions. Cauchy's theorem. Meromorphic functions. Laurent expansions, residue calculus. Conformal maps, topology of the plane.
Effective: Spring 2013
Prerequisite:
MATH 501
MATH 503
Functional Analysis (3) Banach spaces and Hilbert spaces. Dual spaces. Linear operators. Distributors, weak derivatives. Sovolev spaces. Applications to linear differential equations.
Effective: Spring 2013
Prerequisite:
MATH 501
MATH 504
Analysis in Euclidean Space (3) The Fourier transform in L1 and L2 and applications, interpolation of operators, Riesz and Marcinkiewics theorems, singular integral operators.
Effective: Spring 1992
Prerequisite:
MATH 502
MATH 505
Mathematical Fluid Mechanics (3) Kinematics, balance laws, constitutive equations; ideal fluids, viscous flows, boundary layers, lubrication; gas dynamics.
Effective: Spring 1992
Prerequisite:
MATH 402 orMATH 404
MATH 506
Ergodic Theory (3) Measure-preserving transformations and flows, ergodic theorems, ergodicity, mixing, weak mixing, spectral invariants, measurable partitions, entropy, ornstein isomorphism theory.
Effective: Spring 1992
Prerequisite:
MATH 502
MATH 507
Dynamical Systems I (3) Fundamental concepts; extensive survey of examples; equivalence and classification of dynamical systems, principal classes of asymptotic invariants, circle maps.
Effective: Spring 1992
Prerequisite:
MATH 502
MATH 508
Dynamical Systems II (3) Hyperbolic theory; stable manifolds, hyperbolic sets, attractors, Anosov systems, shadowing, structural stability, entropy, pressure, Lyapunov characteristic exponents and non-uniform hyperbolicity.
Effective: Spring 1992
Prerequisite:
MATH 507
MATH 511
Ordinary Differential Equations I (3) Existence and uniqueness, linear systems, series methods, Poincare-Bendixson theory, stability.
Effective: Spring 1992
Prerequisite:
MATH 411 orMATH 412
MATH 512
Ordinary Differential Equations II (3) Floquet theory, regular and singular boundary value problems, Green's functions, eigenfunction expansions.
Effective: Spring 1992
Prerequisite:
MATH 511
MATH 513
Partial Differential Equations I (3) First order equations, the Cauchy problem, Cauchy-Kowalevski theorem, Laplace equation, wave equation, heat equation.
Effective: Spring 1992
Prerequisite:
MATH 411 orMATH 412
MATH 514
Partial Differential Equations II (3) Sobolev spaces and Elliptic boundary value problems, Schauder estimates. Quasilinear symmetric hyperbolic systems, conservation laws.
Effective: Spring 1992
Prerequisite:
MATH 502, MATH 513
MATH 515
Classical Mechanics and Variational Methods (3) Introduction to the calculus of variations, variational formulation of Lagrangian mechanics, symmetry in mechanical systems, Legendre transformation, Hamiltonian mechanics, completely integrable systems.
Effective: Spring 1992
Prerequisite:
MATH 401, MATH 411 orMATH 412
MATH 516
Stochastic Processes (3) Markov chains; generating functions; limit theorems; continuous time and renewal processes; martingales, submartingales, and supermartingales; diffusion processes; applications.
Effective: Summer 1995
Prerequisite:
MATH 416
MATH 517
(STAT 517)
Probability Theory (3) Measure theoretic foundation of probability, distribution functions and laws, types of convergence, central limit problem, conditional probability, special topics.
Effective: Summer 2000
Prerequisite:
MATH 403
MATH 518
(STAT 518)
Probability Theory (3) Measure theoretic foundation of probability, distribution functions and laws, types of convergence, central limit problem, conditional probability, special topics.
Effective: Fall 1983
Prerequisite:
STAT 517
MATH 519
(STAT 519)
Topics in Stochastic Processes (3) Selected topics in stochastic processes, including Markov and Wiener processes; stochastic integrals, optimization, and control; optimal filtering.
Effective: Fall 1984
Prerequisite:
STAT 516, STAT 517
MATH 521
Complex Analysis: Theory and Applications I (3) Conformal mappings, Schwarz-Cristoffel transformations, Dirichlet and Neumann problems, electrostatics and fluid flow, transform methods, asymptotic methods, Runge approximation theorems.
Effective: Spring 1992
Prerequisite:
MATH 502
MATH 523
Numerical Analysis I (3) Approximation and interpolation, numerical quadrature, direct methods of numerical linear algebra, numerical solutions of nonlinear systems and optimization.
Effective: Summer 2002
Prerequisite:
MATH 456
MATH 524
Numerical Linear Algebra (3) Matrix decompositions. Direct method of numerical linear algebra. Eigenvalue computations. Iterative methods.
Effective: Spring 2013
Prerequisite:
MATH 535
MATH 527
Metric and Topological Spaces (3) Metric spaces, continuous maps, compactness, connectedness, and completeness. Topolocial spaces, products, quotients, homotopy, fundamental group, simple applications.
Effective: Spring 2013
Prerequisite:
MATH 429
MATH 528
Differentiable Manifolds (3) Smooth manifolds, smooth maps, Sard's theorem. The tangent bundle, vector fields, differential forms, integration on manifolds. Foliations. De Rham cohomology; simple applications. Lie groups, smooth actions, quotient spaces, examples.
Effective: Spring 2013
Prerequisite:
MATH 527
MATH 529
Algebraic Topology (3) Manifolds, Poincare duality, vector bundles, Thom isomorphism, characteristic classes, classifying spaces for vector bundles, discussion of bordism, as time allows.
Effective: Spring 1992
Prerequisite:
MATH 528
MATH 530
Differential Geometry (3) Distributions and Frobenius theorem, curvature of curves and surfaces, Riemannian geometry, connections, curvature, Gauss-Bonnet theorem, geodesic and completeness.
Effective: Spring 1992
Prerequisite:
MATH 528
MATH 531
Differential Topology (3) DeRham's theorem, geometry of smooth mappings, critical values, Sard's theorem, Morse functions, degree of mappings, smooth fiber bundles.
Effective: Spring 1992
Prerequisite:
MATH 528
MATH 533
Lie Theory I (3) Lie groups, lie algebras, exponential mappings, subgroups, subalgebras, simply connected groups, adjoint representation, semisimple groups, infinitesimal theory, Cartan's criterion.
Effective: Spring 1992
Prerequisite:
MATH 528
MATH 534
Lie Theory II (3) Representations of compact lie groups and semisimple lie algebras, characters, orthogonality, Peter-Weyl theorem, Cartan-Weyl highest weight theory.
Effective: Spring 1992
Prerequisite:
MATH 533
MATH 535
Linear Algebra (3) Vector spaces. Linear transformations. Bilinear forms. Canonical forms for linear transformations. Multilinear algebra.
Effective: Spring 2013
Prerequisite:
MATH 436
MATH 536
Abstract Algebra (3) Groups. Sylow's theorems. Rings. Ideals, unique factorization domains. Finitely generated modules. Fields. Algebraic and transcendental field extensions, Galois theory.
Effective: Spring 2013
Prerequisite:
MATH 535
MATH 537
Field Theory (3) Finite and infinite algebraic extensions; cyclotomic fields; transcendental extensions; bases of transcendence, Luroth's theorem, ordered fields, valuations; formally real fields.
Effective: Fall 1983
Prerequisite:
MATH 536
MATH 538
Commutative Algebra (3) Topics selected from Noetherian rings and modules, primary decompositions, Dedekind domains and ideal theory, other special types of commutative rings or fields.
Effective: Winter 1978
Prerequisite:
MATH 536
MATH 542
Group Theory I (3) Topics selected by instructor from abelian, solvable, and nilpotent groups; finite presentations; free products; group extensions; group representations.
Effective: Fall 1983
Prerequisite:
MATH 535
MATH 547
Algebraic Geometry I (3) Affine and projective algebraic varieties; Zariski topology; Hilbert Nullstellensatz; regular functions and maps; birationality; smooth varieties normalization; dimension.
Effective: Spring 1992
Prerequisite:
MATH 536
MATH 548
Algebraic Geometry II (3) Topics may include algebraic curves, Riemann-Roch theorem, linear systems and divisors, intersectino theory, schemes, sheaf cohomology, algebraic groups.
Effective: Spring 1992
Prerequisite:
MATH 547
MATH 550
(CSE 550)
Numerical Linear Algebra (3) Solution of linear systems, sparse matrix techniques, linear least squares, singular value decomposition, numerical computation of eigenvalues and eigenvectors.
Effective: Summer 1996
Prerequisite:
MATH 441 orMATH 456
MATH 551
(CSE 551)
Numerical Solution of Ordinary Differential Equations (3) Methods for initial value and boundary value problems; convergence and stability analysis, automatic error control, stiff systems, boundary value problems.
Effective: Summer 1996
Prerequisite:
MATH 451 orMATH 456
MATH 552
(CSE 552)
Numerical Solution of Partial Differential Equations (3) Finite difference methods for elliptic, parabolic, and hyperbolic differential equations; solutions techniques for discretized systems; finite element methods for elliptic problems.
Effective: Summer 1996
Prerequisite:
MATH 402 orMATH 404;MATH 451 orMATH 456
MATH 553
(CSE 553)
Introduction to Approximation Theory (3) Interpolation; remainder theory; approximation of functions; error analysis; orthogonal polynomials; approximation of linear functionals; functional analysis applied to numerical analysis.
Effective: Summer 1996
Prerequisite:
MATH 401 3 credits of computer science and engineering
MATH 554
Approximation Theory (3) Approximation in normed spaces; existence, uniqueness, characterization, computation of best approximations; error bounds; degree of approximation; approximation of linear functionals.
Effective: Spring 1992
Prerequisite:
MATH 451 orMATH 456;MATH 501
MATH 555
(CSE 555)
Numerical Optimization Techniques (3) unconstrained and constrained optimization methods, linear and quadratic programming, software issues, ellipsoid and Karmarkar's algorithm, global optimization, parallelism in optimization.
Effective: Summer 1996
Prerequisite:
MATH 456
MATH 556
(CSE 556)
Finite Element Methods (3) Sobolev spaces, variational formulations of boundary value problems; piecewise polynomial approximation theory, convergence and stability, special methods and applications.
Effective: Summer 1996
Prerequisite:
MATH 502, MATH 552
MATH 557
Mathematical Logic (3) The predicate calculus; completeness and compactness; Godel's first and second incompleteness theorems; introduction to model theory; introduction to proof theory.
Effective: Spring 1992
Prerequisite:
MATH 435 orMATH 457
MATH 558
Foundations of Mathematics I (3) Decidability of the real numbers; computability; undecidability of the natural numbers; models of set theory; axiom of choice; continuum hypothesis.
Effective: Spring 1992
Prerequisite:
any 400 level math course
MATH 559
Recursion Theory I (3) Recursive functions; degrees of unsolvability; hyperarithmetic theory; applications to Borel combinatorics. Computational complexity. Combinatory logic and the Lambda calculus.
Effective: Summer 2011
Prerequisite:
MATH 557 orMATH 558
MATH 561
Set Theory I (3) Models of set theory. Inner models, forcing, large cardinals, determinacy. Descriptive set theory. Applications to analysis.
Effective: Spring 1992
Prerequisite:
MATH 557 orMATH 558
MATH 565
Foundations of Mathematics II (3) Subsystems of second order arithmetic; set existence axioms; reverse mathematics; foundations of analysis and algebra.
Effective: Spring 1992
Prerequisite:
MATH 557, MATH 558
MATH 567
Number Theory I (3) Congruences, quadratic residues, arithmetic functions, partitions, classical multiplicative ideal theory, valuations and p-adic numbers; primes in arithmetic progression, distribution of primes.
Effective: Spring 1994
Prerequisite:
MATH 421
MATH 568
Number Theory II (3) Congruences, quadratic residues, arithmetic functions, partitions, classical multiplicative ideal theory, valuations and p-adic numbers; primes in arithmetic progression, distribution of primes.
Effective: Spring 1994
Prerequisite:
MATH 421
MATH 569
Algebraic Number Theory I (3) Dedekind rings; cyclotomic and Kummer extensions; valuations; ramification, decomposition, inertial groups; Galois extensions; locally compact groups of number theory.
Effective: Spring 1992
Prerequisite:
MATH 536, MATH 568
MATH 570
Algebraic Number Theory II (3) Topics chosen from class field theroy; integral quadratic forms; algebraic and arithmetic groups; algebraic function of one variable.
Effective: Spring 1992
Prerequisite:
MATH 569
MATH 571
Analytic Number Theory I (3) Improvements of the prime number theorem, L-functions and class numbers, asymptotic and arithmetic properties of coefficients of modular forms.
Effective: Spring 1994
Prerequisite:
MATH 421
MATH 572
Analytic Number Theory II (3) Distribution of primes, analytic number theory in algebraic number fields, transcendental numbers, advanced theory of partitions.
Effective: Spring 1992
Prerequisite:
MATH 571
MATH 574
Topics in Logic and Foundations (3-6 per semester) Topics in mathematical logic and the foundations of mathematics.
Effective: Spring 1992
Prerequisite:
MATH 558
MATH 577
(M E 577)
Stochastic Systems for Science and Engineering (3) The course develops the theory of stochastic processes and linear and nonlinear stochastic differential equations for applications to science and engineering.
Effective: Summer 1998
Prerequisite:
MATH 414 orMATH 418;M E 550 orMATH 501
MATH 578
(M E 578)
Theory & Applications of Wavelets (3) Theory and physical interpretation of continuous and discrete wavelet transforms for applications in different disciplines.
Effective: Spring 2012
Prerequisite:
MATH 501 orM E 550
MATH 580
Introduction to Applied Mathematics I (3) A graduate course of fundamental techniques including tensor, ordinary and partial differential equations, and linear transforms.
Effective: Fall 2003
Prerequisite:
Basic knowledge of linear algebra vector calculus and ODEMATH 405
MATH 581
Introduction to Applied Mathematics II (3) A graduate course of fundamental techniques including Ordinary, Partial, and Stochastic Differential Equations, Wavelet Analysis, and Perturbation Theory.
Effective: Summer 2003
Prerequisite:
MATH 580 or consent of instructor
MATH 582
Introduction to C* Algebra Theory (3) Basic properties of C* algebras, representation theory, group C* algebras and crossed products, tensor products, nuclearity and exactness.
Effective: Summer 2006
Prerequisite:
MATH 503
MATH 583
Introduction to K-Theory (3) K-theory groups for compact spaces and C*-algebras. Long exact sequences, Bott periodicity, index theory and the Pimsner-Voiculescu theorem.
Effective: Summer 2006
Prerequisite:
MATH 503
MATH 584
Introduction to von Neumann Algebras (3) Comparison of projections, traces, tensor products, ITPFI factors and crossed products, the Jones index, modular theory, free probability.
Effective: Summer 2006
Prerequisite:
MATH 503
MATH 585
Topics in Mathematical Modeling (3) Introduction to mathematical modeling, covering the basic modeling and common mathematical techniques for problems from physical, biological and social sciences.
Effective: Summer 2012
Prerequisite:
MATH 403, MATH 411 andMATH 412
MATH 588
(CSE 588)
Complexity in Computer Algebra (3) Complexity of integer multiplication, polynomial multiplication, fast Fourier transform, division, calculating the greatest common divisor of polynomials.
Effective: Spring 2008
Prerequisite:
CMPSC 465
MATH 590
Colloquium (1-3) Continuing seminars which consist of a series of individual lectures by faculty, students, or outside speakers.
Effective: Spring 1987
MATH 596
Individual Studies (1-9) Creative projects, including nonthesis research, which are supervised on an individual basis and which fall outside the scope of formal courses.
Effective: Spring 1987
MATH 597
Special Topics (1-9) Formal courses given on a topical or special interest subject which may be offered infrequently; several different topics may be taught in one year or term.
Effective: Spring 1987
MATH 597A
Nonlinear PDEs (3) The course will cover topics in the theory of nonlinear PDEs, mainly from Part III of Evan's book. In particular: - Variational methods. The Euler- Lagrange equation, Coercivity, lower semicontinity, weak solutions. Regularity of solutions. Critical points, the mountain pass theorem, and existence of solutions to semilinear elliptic PDEs. - Fixed point methods. Schauder's fixed point. - Monotonicity methods. Upper and lower solutions. - Hamilton-Jacobi equations. Viscosity solutions. Relations with optimal control theory and the principle of dynamic programming. - Introduction to hyperbolic systems of conservation laws. Weak solutions. Rankine-Hugoniot equations. Entropy admissibility conditions. The Riemann problem.
Effective: Fall 2013 Ending: Fall 2013 Future: Fall 2013
MATH 597B
q-series and Partitions (3) In the course, the topics to be covered include partition function p(n), congruences for p(n) and tau(n), the Rogers-Ramanujan identities, partition rank and crank, Eisenstein series, theta functions, and basic hypergeometric functions.
Effective: Fall 2013 Ending: Fall 2013 Future: Fall 2013
MATH 597C
Numerical Methods for Stochastic Differential Equations (3) The course is about numerical methods for the solution of differential equations involving random input and stochastic sources. Main topics include: Basic concepts of random variables and stochastic processes, differential equations involving random terms, simulation of Brownian motion, numerical methods for lto stochastic differential equations, basic strong and weak convergence analysis, spectral representations of random fields, methods for stochastic PDEs, methods for estimating rare events, methods for quantifying uncertainties.
Effective: Fall 2013 Ending: Fall 2013 Future: Fall 2013
MATH 598
Special Topics (1-9) Formal courses given on a topical or special interest subject which may be offered infrequently; several different topics may be taught in one year or semester.
Effective: Spring 1994
MATH 599
(IL)
Foreign Studies (1-12 per semester, maximum of 24) Full-time graduate-level foreign study at an overseas institution with whom linkages have been established.
Effective: Summer 2005
MATH 600
Thesis Research (1-15) No description.
Effective: Fall 1983
MATH 601
Ph.D. Dissertation Full-Time (0) No description.
Effective: Winter 1978
MATH 602
Supervised Experience in College Teaching (1-3 per semester/maximum of 6) Teaching of mathematics undergraduate recitation classes with senior faculty instruction supervision.
Effective: Fall 1983
MATH 610
Thesis Research Off Campus (1-15) No description.
Effective: Fall 1983
MATH 611
Ph.D. Dissertation Part-Time (0) No description.
Effective: Winter 1978
NOTE: Courses in computer science and statistics are listed separately.
Last Import from UCM: May 18, 2013 3:00 AM