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  • MATH 6820: Applied Mathematics II

    3.00 Credits
    Tulane University of Louisiana

    Staff. Pre-requisite: MATH 3050, 3090, 3470, and 4060. Formulating mathematical models. Introduction to differential equations and integral equations. Fourier series and transforms, Laplace transforms. Generating functions. Dimensional analysis and scaling. Regular and singular perturbations. Asymptotic expansions. Boundary layers. The calculus of variations and optimization theory. Similarity solutions. Difference equations. Stability and bifurcation. Introduction to probability and statistics, and applications. Note: Mathematics 651, 652, 655, 656, 661, 662, 665, 666, 671, 672, 675, 676, 681, 682 are particularly recommended for students planning to do graduate work in mathematics.
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  • MATH 6840: Numerical Methods in Partial Differential Equations

    3.00 Credits
    Tulane University of Louisiana

    Staff. Pre-requisite: MATH 3310 and 3470 or approval of instructor. This course will present a detailed analysis of the methods for numerically approximating the solution of ordinary and partial differential equations typically encountered in applications from engineering and physics. Mathematical theory, practical implementation and applications will be emphasized equally. Typical applications to be discussed include population dynamics, particle dynamics, waves, diffusion processes.
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  • MATH 7010: Topology I

    3.00 Credits
    Tulane University of Louisiana

    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 7020: Topology II

    3.00 Credits
    Tulane University of Louisiana

    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 7110: Algebra I

    3.00 Credits
    Tulane University of Louisiana

    Pre-requisite: Math 3090 and 3110. Vector spaces: matrices, eigenvalues, Jordan canonical form. Elementary number theory: primes, congruences, function, linear Diophantine equations, Pythagorean triples. Group theory: cosets, normal subgroups, homomorphisms, permutation groups, theorems of Lagrange, Cayley, Jordan-Hölder, Sylow. Finite abelian groups, free groups, presentations. Ring theory: prime and maximal ideals, fields of quotients, matrix and Noetherian rings. Fields: algebraic and transcendental extensions, survey of Galois theory. Modules and algebras: exact sequences, projective and injective and free modules, hom and tensor products, group algebras, finite dimensional algebras. Categories: axioms, subobjects, kernels, limits and colimits, functors and adjoint functors.
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  • MATH 7120: Algebra II

    3.00 Credits
    Tulane University of Louisiana

    Pre-requisite: Math 3090 and 3110. Vector spaces: matrices, eigenvalues, Jordan canonical form. Elementary number theory: primes, congruences, function, linear Diophantine equations, Pythagorean triples. Group theory: cosets, normal subgroups, homomorphisms, permutation groups, theorems of Lagrange, Cayley, Jordan-Hölder, Sylow. Finite abelian groups, free groups, presentations. Ring theory: prime and maximal ideals, fields of quotients, matrix and Noetherian rings. Fields: algebraic and transcendental extensions, survey of Galois theory. Modules and algebras: exact sequences, projective and injective and free modules, hom and tensor products, group algebras, finite dimensional algebras. Categories: axioms, subobjects, kernels, limits and colimits, functors and adjoint functors.
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  • MATH 7240: Mathematical Statistics

    3.00 Credits
    Tulane University of Louisiana

    Pre-requisite: Math 6070, 6080 and 7210 or permission of the instructor. Consists of Math 602 and additional meetings and readings to cover advanced limit theorems and foundations of mathematical statistics.
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  • MATH 7260: Linear Models

    3.00 Credits
    Tulane University of Louisiana

    Pre-requisite: Math 3070/6070, 3080/6080. Co-requisite: Math 309 or approval of instructor. Review of linear algebra pertinent to least squares regression. Review of multivariate normal, chi-square, t, F distributions. Classical theory of linear regression and related inference. Regression diagnostics. Extensive practice in data analysis.
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  • MATH 7310: Applied Mathematics I

    3.00 Credits
    Tulane University of Louisiana

    This is a first year graduate course in Applied Mathematics. A solid working knowledge of linear algebra and advanced calculus is the necessary background for this class. The topics covered include a mix of analytical and numerical methods that are used to understand models described by differential equations. We will emphasize applications from science and engineering, as they are the driving force behind each of the topics addressed.
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  • MATH 7320: Applied Mathematics II

    3.00 Credits
    Tulane University of Louisiana

    This is a first year graduate course in Applied Mathematics. A solid working knowledge of linear algebra and advanced calculus is the necessary background for this class. The topics covered include a mix of analytical and numerical methods that are used to understand models described by differential equations. We will emphasize applications from science and engineering, as they are the driving force behind each of the topics addressed.
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