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400 level courses
100 level| 200 level | 300 level| 400 level | Graduate courses
Math 406
Real Analysis II (3)
Prerequisites: Math 305 and 309. An in-depth treatment
of multivariable calculus. Extends the material covered in Mathematics
221. Chain rule, inverse and implicit function theorems, Riemann
integration in Euclidean n-space, Gauss-Green-Stokes theorems,
applications.
Math 412
Abstract Algebra II (3)
Prerequisites: Math 309 and 311. Abstract vector spaces,
quotient spaces, linear transformations, dual spaces, determinants.
Solvable groups. Field extensions, Galois theory, solvability of
equations by radicals.
Math 421/621
Differential Geometry (3)
Prerequisites: Math 305 and 309. Theory of plane and
space curves including arc length, curvature, torsion, Frenet
equations, surfaces in three-dimensional space. First and second
fundamental forms, Gaussian and mean curvature, differentiable mappings
of surfaces, curves on a surface, special surfaces.
Math 424/624 Ordinary Differential Equations (3)
Prerequisites: Math 309. Review of linear algebra, first-order equations (models, existence, uniqueness, Euler method, phase line, stability of equilibria), higher-order linear equations, Laplace transforms and applications, power series of solutions, linear first-order, systems (autonomous systems, phase plane), application of matrix normal forms, linearization and stability of nonlinear systems, bifurcation, Hopf bifurcation, limit cycles, Poincare-Bendixson theorem, partial differential equations (symmetric boundary-value problems on an interval, eigenvalue problems, eigenfunction expansion, initial-value problems in 1D).
Math 425/625 Mathematical Foundations of Computer Security (3)
Prerequisites: Calculus, Math 217 and Math 311 or the permission of the instructor.
This course studies the mathematics underlying computer security, including both public key and symmetric key cryptography, crypto-protocols and information flow. The course includes a study of the RSA encryption scheme, stream and clock ciphers, digital signatures and authentication. It also considers semantic security and an analysis of secure information flow.
Math 430/630
Complex Analysis (3)
Prerequisite: Math 305. The complex number system,
complex integration and differentiation, conformal mapping, Cauchy’s
theorem, calculus of residues.
Math 441
Topology (3)
Prerequisite: Math 305. An introduction to topology.
Elementary point set topology: topological spaces, compactness,
connectedness, continuity, homeomorphisms, product and quotient spaces.
Classification of surfaces and other geometric applications.
Math 447/647
Analytical Methods of Applied Mathematics (3)
Prerequisites: Math 221 and 224. Derivations of transport, heat/reaction-diffusion, wave. Poisson's equations; well-posedness; characteristics for first order PDE's; D'Alembert formula and conservation of energy for wave equations; propagation of waves; Fourier transforms; heat kernel, smoothing effect; maximum principles; Fourier series and Sturm-Liouville eigenexpansions; method of separation of variables; frequencies of wave equations, stable and unstable modes, long-time behavior of heat equations; delta function; fundamental solution of Laplace equation, Newton potential; Green's function and Poisson formula; Dirichlet Principle.
Math 478
Introduction to Concurrency (3)
Prerequisites: Math 217 and Math 310 or approval of
instructor. This course is a general introduction to Concurrency,
i.e., the Mathematical modeling of systems made up of several processes
interacting with each other. The process algebra CSP (Communicating
Sequential Processes) will be studied, both on the syntactic and
semantic level. The denotational, operational, and algebraic models
used to reason about the language will be presented, and examples will
be used throughout to illustrate the theory.
Math 490 (3)
Prerequisite: Permission of the Instructor. This course
covers a variety of advances in topics in mathematics and exposes
students to recent developments not available in other parts of the
mathematics curriculum. It meets ini conjunction with graduate level
courses MATH 771-779. Topics covered will vary from semester to
semester. Recent topics offered include Knot Theory and 3-Manifolds,
Algebraic Combinatorics, Cardiac Modeling, Number Theory. Students may
receive credit for MATH 490 more than once, when the topics covered are
distinct. Each section will have the specific topic listed as a
subtitle and will have specific prerequisites to the 300 level or
above.
Math 491,
492 Independent Studies (1-3, 1-3)
Prerequisite: approval of the department. No more than
four hours of 491-492 may be counted toward satisfying the major
requirements.
Math
H499-H500 Honors Thesis (3, 4)
Prerequisite: approval of the department. Thesis may
serve to satisfy part of the departmental honors requirements.
| Mathematics
Department Tulane University 6823 St. Charles Ave New Orleans, LA 70118 phone: (504) 865-5727 fax: (504) 865-5063 |
Last Updated:
February 20, 2008
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