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MATH 4250: Mathematical Foundations of Computer Security
3.00 Credits
Tulane University of Louisiana
Pre-requisite: Calculus, MATH 2170 and MATH 3110 or permission of 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 analysis of secure information flow. (Same as MATH 6250.)
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MATH 4300: Complex Analysis
3.00 Credits
Tulane University of Louisiana
Staff. Pre-requisite: MATH 3050. The complex number system, complex integration and differentiation, conformal mapping, Cauchy’s theorem, calculus of residues.
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MATH 4300 - Complex Analysis
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MATH 4410: Topology
3.00 Credits
Tulane University of Louisiana
Staff. Pre-requisite: MATH 3050. 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.
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MATH 4410 - Topology
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MATH 4411: Introduction to Algebraic Topology with Applications
3.00 Credits
Tulane University of Louisiana
Prof. Rafal Komendarczyk. An introduction to algebraic topology with perspectives on applications to sensor networks, target detection and learning theory." " Elementary algebraic topology:" " fundamental group, simplicial complexes, homology, long exact sequences, excision, Lefschetz fixed point theorem, persistent homology." " Applications to coverage in sensor networks, deSilva-Ghrist criterium, target enumeration." "
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MATH 4411 - Introduction to Algebraic Topology with Applications
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MATH 4470: Analytical Methods of Applied Mathematics
3.00 Credits
Tulane University of Louisiana
Staff. Pre-requisite: MATH 2210 and 2240 or 4240. Derivations of transport, heat/reaction-diffusion, wave, Poisson’s equations; well-posedness; characteristics methods 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 eigen-expansions; 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.
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MATH 4470 - Analytical Methods of Applied Mathematics
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MATH 4780: Introduction to Concurrency
3.00 Credits
Tulane University of Louisiana
Staff. Pre-requisite: MATH 2170 and MATH 3100 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.
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MATH 4780 - Introduction to Concurrency
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MATH 4900: Advanced Topics in Mathematics
3.00 Credits
Tulane University of Louisiana
Staff. Pre-requisite: Approval of instructor. This course covers a variety of advanced topics in mathematics and exposes students to recent developments not available in other parts of the mathematics curriculum. Topics covered will vary from semester to semester. Recent topics offered include Knot Theory and 3-Manifolds, Algebraic Combinatorics, Cardiac Modeling, Number Theory. Note: Each section will have the specific topic listed as a subtitle and will have specific prerequisites at the 300 level or above. It meets in conjunction with graduate level courses MATH 771-779. Students may receive credit for MATH 490 more than once, when the topics covered are distinct.
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MATH 4900 - Advanced Topics in Mathematics
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MATH 4910: Independent Studies
3.00 Credits
Tulane University of Louisiana
Staff. Pre-requisite: Approval of the department. No more than four hours of 4910-4920 may be counted toward satisfying the major requirements.
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MATH 4910 - Independent Studies
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MATH 4920: Independent Studies
3.00 Credits
Tulane University of Louisiana
Staff. Pre-requisite: Approval of the department. No more than four hours of 4910-4920 may be counted toward satisfying the major requirements.
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MATH 4920 - Independent Studies
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MATH 6020: Mathematical Statistics
3.00 Credits
Tulane University of Louisiana
Staff. Pre-requisite: MATH 3010 and 2210. Thorough review of key distributions for probability and statistics, including the multivariate calculus needed to develop them. Full derivation of sampling distribution. Classical principles of inference including best tests and estimations. Methods of finding tests and estimators. Introduction to Bayesian estimators.
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MATH 6020 - Mathematical Statistics
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