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MATH 6030: Stochastic Processes
3.00 Credits
Tulane University of Louisiana
Staff. Pre-requisite: MATH 3010. Markov processes, Poisson processes, queueing models, introduction to Brownian Motion.
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MATH 6030 - Stochastic Processes
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MATH 6040: Linear Models
3.00 Credits
Tulane University of Louisiana
Staff. Pre-requisite: MATH 3010 and 3090 or equivalent. Overview of multivariate analysis, theory of least squares linear regression, regression diagnostics, introduction to generalized linear models with emphasis on logistic regression. The student will complete several extended data analysis assignments using SAS, S-Plus, or R.
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MATH 6040 - Linear Models
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MATH 6080: Introduction to Statistical Inference
3.00 Credits
Tulane University of Louisiana
Pre-requisite: MATH 2210, MATH 3070. Basics of Statistical inference. Sampling distributions, parameter estimation, hypothesis testing, optimal estimates and tests. Maximum likelihood estimates and likelihood ratio tests. Data summary methods, categorical data analysis. Analysis of variance and introduction to linear regression.
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MATH 6080 - Introduction to Statistical Inference
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MATH 6240: Ordinary Differential Equations
3.00 Credits
Tulane University of Louisiana
Pre-requisite: MATH 3090. 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 nonlinearsystems, 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). Students may not receive credit for both 2240 and 4240.
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MATH 6240 - Ordinary Differential Equations
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MATH 6250: 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 4250.)
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MATH 6250 - Mathematical Foundations of Computer Security
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MATH 6350: Optimization
3.00 Credits
Tulane University of Louisiana
Staff. Pre-requisite: MATH 3090 or equivalent. Constrained and unconstrained non-linear optimization; Linear programming, combinatorial optimization as time allows. Emphasis is on realistic problems whose solution requires computers, using Maple or Mathematica.
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MATH 6350 - Optimization
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MATH 6380: Introduction to Theory of Information
3.00 Credits
Tulane University of Louisiana
Co-requisite: MATH 305 or 309 and familiarity with discrete probability. This introduction to information theory will address fundamental concepts, such as information, entropy, relative entropy, and mutual information. In addition to giving precise definitions of these concepts, the course will include a probabilistic approach based on equipartitions. Many of the applications of information will be discussed, including Shannon’s basic theorems on channel capacity and related coding theorems. In addition to channels and channel capacity, the course will discuss applications of information theory to mathematics, statistics, and computer science.
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MATH 6380 - Introduction to Theory of Information
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MATH 6510: Topology I and II
3.00 Credits
Tulane University of Louisiana
Staff. Pre-requisite: MATH 3050 and 4060. Point set topology. Connectedness, product and quotient spaces, separation properties, metric spaces. Classification of compact connected surfaces. Homotopy. Fundamental group and covering spaces. Singular and simplicial homology. Eilenberg-Steenrod axioms. Computational techniques, including long exact sequences. Mayer-Vietoris sequences, excision, and cellular chain complexes. Introduction to singular cohomology.
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MATH 6510 - Topology I and II
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MATH 6520: Topology I and II
3.00 Credits
Tulane University of Louisiana
Staff. Pre-requisite: MATH 3050 and 4060. Point set topology. Connectedness, product and quotient spaces, separation properties, metric spaces. Classification of compact connected surfaces. Homotopy. Fundamental group and covering spaces. Singular and simplicial homology. Eilenberg-Steenrod axioms. Computational techniques, including long exact sequences. Mayer-Vietoris sequences, excision, and cellular chain complexes. Introduction to singular cohomology.
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MATH 6520 - Topology I and II
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MATH 6550: Differential Geometry I
3.00 Credits
Tulane University of Louisiana
Staff. Differentiable manifolds. Vector fields and flows. Tangent bundles. Frobenius theorem. Tensor fields. Differential forms, Lie derivatives. Integration and deRham’s theorem. Riemannian metrics, connections, curvature, parallel translation, geodesics, and submanifolds, including surfaces. First and second variation formulas, Jacobi fields, Lie groups. The Maurer-Cartan equation. Isometries, principal bundles, symmetric spaces, Kähler geometry.
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MATH 6550 - Differential Geometry I
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