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MATH 7350: Scientific Computing I
3.00 Credits
Tulane University of Louisiana
Pre-requisite: MATH 3310 or MATH 7310-7320. Introduction to numerical analysis: well-posedness and condition number, stability and convergence of numerical methods, a priori and a-posteriori analysis, source of error in computational models, machine representation of numbers. Linear operators on normed spaces. Root finding for nonlinear equations. Polynomial interpolation. Numerical integration. Orthogonal polynomials in approximation theory. Numerical solution of ordinary differential equations.
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MATH 7350 - Scientific Computing I
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MATH 7360: Data Analysis
3.00 Credits
Tulane University of Louisiana
This course covers the statistical analysis of datasets using R software package. The R environment, which is an Open Source system based on the S Language, is one of the most versatile and powerful tools available for statistical data analysis, and is widely used in both academic and industrial research. Key topics include graphical methods, generalized linear models, clustering, classification, time series analysis and spatial statistics. No prior knowledge of R is required.
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MATH 7360 - Data Analysis
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MATH 7510: Differential Geometry I
3.00 Credits
Tulane University of Louisiana
Differential 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 7510 - Differential Geometry I
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MATH 7520: Differential Geometry II
3.00 Credits
Tulane University of Louisiana
Differential 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 7520 - Differential Geometry II
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MATH 7540: Partial Differential Equations II
3.00 Credits
Tulane University of Louisiana
Pre-requisite: MATH 7530 or by instructor’s approval. A brief introduction to elliptic and parabolic regularity theory, the L^p and Schauder estimates. Nonlinear elliptic equations, variational methods, methods of upper and lower solutions, fixed point method, bifurcation method. Nonlinear parabolic equations, global existence, stability of steady states, traveling wave solutions. Conservation laws, Rankine-Hugonoit jump condition, uniqueness issue,, entropy condition, Reimann problem for Burger’s equation and p-systems.
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MATH 7540 - Partial Differential Equations II
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MATH 7550: Probability and Statistics I
3.00 Credits
Tulane University of Louisiana
Various types of convergence, independent incraments, stable laws, central limit problem. Central limit theorems, x^2 distribution, contingency tables. Sampling distributions for normal populations (t, x^2, F). Estimation of parameters: minimum variance, maximum likelihood, sufficiency, nonparametric estimation. Hypothesis testing: Neyman-Pearson lemmas, general linear models, analysis of variances and covariance, regression. Introduction to time series, sampling design, and Bayesian theory.
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MATH 7550 - Probability and Statistics I
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MATH 7560: Probability and Statistics II
3.00 Credits
Tulane University of Louisiana
Various types of convergence, independent incraments, stable laws, central limit problem. Central limit theorems, x^2 distribution, contingency tables. Sampling distributions for normal populations (t, x^2, F). Estimation of parameters: minimum variance, maximum likelihood, sufficiency, nonparametric estimation. Hypothesis testing: Neyman-Pearson lemmas, general linear models, analysis of variances and covariance, regression. Introduction to time series, sampling design, and Bayesian theory.
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MATH 7560 - Probability and Statistics II
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MATH 7570: Scientific Computation I
3.00 Credits
Tulane University of Louisiana
Pre-requisite: MATH 7350. Floating point arithmetic (limitations and pitfalls). Numerical linear algebra, solving linear system by direct and iterative methods, eigenvalue problems, singular value decompositions, numerical integrations, interpolations. Unconstrained optimization.
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MATH 7570 - Scientific Computation I
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MATH 7580: Scientific Computation II
0.00 Credits
Tulane University of Louisiana
Pre-requisite: MATH 7350 and 7570. Numerical ODE, both initial and boundary value problems. Numerical PDE. Introduction to fluid dynamics and other areas of application.
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MATH 7580 - Scientific Computation II
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MATH 7710: Special Topics
3.00 Credits
Tulane University of Louisiana
No course description available.
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MATH 7710 - Special Topics
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