Graduate Courses, Summer 2025 – Spring 2026

Summer 2025

For Detailed Course Outlines, click on course numbers.

7999-1 Problem Sessions in Algebra—practice for PhD Qualifying Exam in Algebra

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7999-2 Problem Sessions in Analysis—practice for PhD Qualifying Exam in Analysis

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7999-3 Problem Sessions in Topology—practice for PhD Qualifying Exam in Topology

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7999-4 Problem Sessions in Applied Math—practice for PhD Qualifying Exam in Applied Math

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7999-n Assorted Individual Reading Classes
  • No additional information.

8000-n Assorted Sections of MS-Thesis Research
  • No additional information.

9000-n Assorted Sections of Doctoral Dissertation Research
  • No additional information.

Fall 2025

For Detailed Course Outlines, click on course numbers. Core courses are listed in bold.

4997-1 Vertically Integrated Research: Combinatorial Topology. Profs. Bibby and Schreve

  • Time: 11:30-12:20 MWF
  • Instructor: Profs. Bibby and Schreve
  • Prerequisite: A first course in linear algebra; experience with topology or graph theory may be useful but not required
  • Text: None
  • Description: This is a project-based seminar class in geometry and topology. Students work together in small groups to tackle problems in combinatorial topology and geometric combinatorics.

4997-2 Vertically Integrated Research: Stochastic processes and partial differential equations. Prof. Fehrman

  • Time: 1:30-2:20 MWF
  • Instructor: Prof. Fehrman
  • Prerequisite: Calculus (necessary), real analysis (preferred, but not necessary), probability (preferred, but not necessary)
  • Text: The course will be based on notes provided by the professor. A good secondary reference is "Probability: Theory and Examples" by Rick Durrett (a free pdf copy is available on the author's website)
  • Description: The purpose of this course is to develop the heuristic connections between random processes and partial differential equations on both theoretic and numerical levels. The course will begin with an overview of measure theoretic probability theory, including probability spaces, sigma algebras, filtrations, (Gaussian) random variables, and independence. The well-posedness of ordinary differential equations with Lipschitz continuous coefficients will then be established in order to motivate the study of discrete stochastic differential equations, which are, roughly speaking, ordinary differential equations perturbed by a random noise. Such equations model everything from the diffusion of aerosols in the wind, the advection of passive quantities like dye or energy in a fluid, and the evolution of a stock price. By developing a version of Ito's formula, which is the fundamental theorem of calculus for stochastic processes, we will show that the density of the solution to a stochastic differential equation can be described using the solution to a certain partial differential equation. This connection is known as the Feynman--Kac formula, and it will be the fundamental result of the course. We will then spend a significant amount of time applying this connection to model stochastic processes with connections to biology, physics, finance, and machine learning. In particular, we will derive the Black--Scholes equation, which is the most fundamental partial differential equations used to estimate European-style options in finance; discuss diffusion models in machine learning, which are a state-of-the-art technique for generating synthetic data, including images, in machine learning; and analyze stochastic gradient descent algorithms.

4997-3 Vertically Integrated Research: TBA. Prof. Bălibanu

  • Time: 10:30-11:50 TT
  • Instructor: Prof. Bălibanu
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7001 Communicating Mathematics I. Prof. Shipman and Dr. Ledet

  • Time: 3:00-4:50 TT
  • Instructor: Prof. Shipman and Dr. Ledet
  • Prerequisite: Consent of department. This course is required for all first-year graduate students. It is a lab course meeting for an average of two hours per week throughout the semester for one-semester-hour's credit.
  • This course provides practical training in the teaching of mathematics at the pre-calculus level, how to write mathematics for publication, and treats other issues relating to mathematical exposition. Communicating Mathematics I and II are designed to provide training in all aspects of communicating mathematics. Their overall goal is to teach the students how to successfully teach, write, and talk about mathematics to a wide variety of audiences. In particular, the students will receive training in teaching both pre-calculus and calculus courses. They will also receive training in issues that relate to the presentation of research results by a professional mathematician. Classes tend to be structured to maximize discussion of the relevant issues. In particular, each student presentation is analyzed and evaluated by the class.

7210 Algebra I. Prof. X. Wang

  • Time: 8:30-9:20 MWF
  • Instructor: Prof. X. Wang
  • Prerequisite: Math 4200 or its equivalent
  • Text: Dummit and Foote, Abstract Algebra
  • Description: This is the first semester of the first year graduate algebra sequence. It will cover the basic notions of group, ring, and module theory. Topics will include symmetric and alternating groups, Cayley's theorem, group actions and the class equation, the Sylow theorems, finitely generated abelian groups, polynomial rings, Euclidean domains, principal ideal domains, unique factorization domains, finitely generated modules over PIDs and applications to linear algebra, field extensions, and finite fields.

7230 Topics in Number Theory: A Tour of Analytic Number Theory. Prof. Kopp

  • Time: 12:00-1:20 TT
  • Instructor: Prof. Kopp
  • Prerequisite: Math 7210, Math 7311, Math 7350 (recommended)
  • Text: To be determined
  • Description: This course will be split into three parts, each visiting a different realm within the vast landscape of analytic number theory. Part 1 covers multiplicative number theory, including Dirichlet series and the proof of the prime number theorem. Part 2 covers additive number theory, including the Hardy–Littlewood circle method as applied to partitions. Part 3 covers topics in computational number theory or other topics determined by student interest. Coursework will include problem sets due regularly and student presentations to be given at the end of the course.

7250 Representation Theory. Prof. Ng

  • Time: 9:00-10:20 TT
  • Instructor: Prof. Ng
  • Prerequisite:
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  • Description: Representations of finite groups, group algebras, character theory, induced representations, Frobenius reciprocity, Lie algebras and their structure theory, classification of semisimple Lie algebras, universal enveloping algebras and the PBW theorem, highest weight representations, Verma modules, and finite-dimensional representations.

7260 Homological Algebra. Prof. Hoffman

  • Time: 8:30-9:20 MWF
  • Instructor: Prof. Hoffman
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7311 Real Analysis (a.k.a. Analysis I). Prof. Lipton

  • Time: 9:30-10:20 MWF
  • Instructor: Prof. Lipton
  • Prerequisite: Undergraduate real analysis
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  • Description: This is a standard introductory course on analysis based on measure theory and integration. We start by introducing sigma algebras and measures. We will then discuss measurable functions and integration of real and complex valued functions. As an example we discuss the Lebesgue integral on the line and n-dimensional Euclidean space. We also discuss the Lebesgue integral versus the Riemann integral. Important topics here are the convergence theorems, product measures and Fubini’s theorem and the Radon-Nikodym derivative. We give a short discussion of Banach spaces and Hilbert spaces. We then introduce Lp spaces and discuss the main properties of those spaces. Further topics include functions of bounded variations Lebesgue differentiation theorems, Lp and its dual. Other topics might be included depending on the time.

7350 Complex Analysis. Prof. Ólafsson

  • Time: 12:30-1:20 MWF
  • Instructor: Prof. Ólafsson
  • Prerequisite: Math 7311
  • Text: Lecture notes and Complex Analysis by Elias Stein and Rami Shakarchi, Princeton Lectures in Analysis II.
  • Description: Theory of holomorphic functions of one complex variable; path integrals, power series, singularities, mapping properties, normal families, other topics.

    Detailed Description: This is a standard course in complex analysis in one variable. We start out by discussing basic definitions concerning the complex numbers and continuous functions. Then we will cover the following material: Holomorphic functions; power series; path integrals, Cauchy’s integral singularities, sequences of holomorphic functions; singularities and meromorphic functions; Schwarz reflection principle. The Fourier transform in the complex plane. Paley-Wiener theorem. Entire functions including Jensen's formula and infinite products. Conformal mapping including the Riemann mapping theorem. Some special functions including the Gamma function, the Zeta functions and an introduction to the theory of elliptic functions. Other topics might be discussed depending on the time and requests from the students. We will use our own lecture notes which follows closely the book by E. Stein and R. Shakarchi, but some of the material will be taken from other books.

7360 Probability Theory: Prof. Ganguly

  • Time: 1:30-2:50 TT
  • Instructor: Prof. Ganguly
  • Prerequisite: Math 7311
  • Text: Probability and Stochastics by Erhan Cinlar
  • Description: Probability spaces, random variables and expectations, independence, convergence concepts, laws of large numbers, convergence of series, law of iterated logarithm, characteristic functions, central limit theorem, limiting distributions, martingales.

    This is a self-contained introduction to modern probability theory. Starting from the concept of probability measures, it would introduce random variables, and independence. After a study of various modes of convergence, the Kolmogorov strong law of large numbers and results on random series will be established. Weak convergence of probability measures will be discussed in detail, which would lead to the central limit theorem and its applications. A main goal of the course is to develop the concept of conditional probability and its basic properties. Stochastic processes such as Brownian motion and martingales will be introduced, and their essential features, studied.

7365 Applied Stochastic Analysis. Prof. Fehrman

  • Time: 11:30-12:20 MWF
  • Instructor: Prof. Fehrman
  • Prerequisite: Calculus (necessary), real analysis (necessary), probability (preferred, but not necessary). The course can be taken concurrently with Math 7360.
  • Text: Probability: Theory and Examples by Rick Durrett (a pdf copy is available on the author's website)
  • Description: The evolution of many physical systems is fundamentally random. Even relatively simple processes, like random walks generated by a sequence of independent coin flips, can exhibit remarkably interesting behaviors, and such systems form the basis of our understanding of diverse phenomena in physics and biology and several of the computational techniques used in finance and machine learning. This course will focus, in particular, on stochastic processes in discrete time. We will develop the theory of discrete time martingales and Markov processes. Topics will include Doob's decomposition theorem, Doob's Martingale inequalities, the Burkholder-Davis-Gundy inequality, Kolmogorov's equations, generators, stationary measures, and some results in ergodic theory. We will also discuss some stochastic algorithms like Markov Chain Monte Carlo and diffusion models in machine learning. The course is provides the necessary background for Math 7366, which builds on Math 7365 to develop the theory of continuous-time martingales and Markov processes and and the theory of stochastic differential equations.

7380 Seminar in Functional Analysis: Operator Theory. Prof. Shipman

  • Time: 2:30-3:20 MWF
  • Instructor: Prof. Shipman
  • Prerequisite: Real and complex analysis
  • Text: Operator Theory by Barry Simon, AMS
  • Description: This material is foundational broadly in analysis and its applications. Operator theory is ubiquitous in all flavors of mathematical physics, including PDE, quantum mechanics, and quantum field theory. The topics include compact operators, index theory, and spectral theory, and perhaps orthogonal polynomials and/or Banach algebras.

7390-1 Seminar in Functional Analysis: Iterative Methods for Linear Systems. Prof. Brenner

  • Time: 10:30-11:50 TT
  • Instructor: Prof. Brenner
  • Prerequisite: Math 7710
  • Text: Iterative Methods for Solving Linear Systems by Anne Greenbaum (This book can be downloaded for free through the LSU library.)
  • Description: Basic Iterative Methods, Krylov Subspace Methods, Preconditioning, Domain Decomposition, Multigrid

7382 Introduction to Applied Mathematics. Prof. Tarfulea

  • Time: 10:30-11:50
  • Instructor: Prof. Tarfulea
  • Prerequisite: Simultaneous enrollment in Math 7311
  • Text: Lecture notes by Massatt and Shipman
  • Description: Overview of modeling and analysis of equations of mathematical physics, such as electromagnetics, fluids, elasticity, acoustics, quantum mechanics, etc. There is a balance of breadth and rigor in developing mathematical analysis tools, such as measure theory, function spaces, Fourier analysis, operator theory, and variational principles, for understanding differential and integral equations of physics.

7386 Theory of Partial Differential Equations. Prof. Zhu

  • Time: 10:30-11:20 MWF
  • Instructor: Prof. Zhu
  • Prerequisite: Math 7330
  • Text: Partial Differential Equations by L. C. Evans
  • Description: Introduction to PDE. Sobolev spaces. Theory of second order scalar elliptic equations: existence, uniqueness and regularity. Additional topics such as: Direct methods of the calculus of variations, parabolic equations, eigenvalue problems.

7390-2 Seminar in Analysis: TBA. Prof. Bulut

  • Time: 12:00-1:20 TT
  • Instructor: Prof. Bulut
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7400 Combinatorial Theory. Prof. Bibby

  • Time: 9:30-10:20 MWF
  • Instructor: Prof. Bibby
  • Prerequisite: Calculus (Math 1552), linear algebra (Math 2085), and abstract algebra (Math 4200)
  • Text: Enumerative Combinatorics Volume 1 by Stanley (pdf available through LSU Library here)
  • Description: Problems of existence and enumeration in the study of arrangements of elements into sets; combinations and permutations; other topics such as generating functions, recurrence relations, inclusion-exclusion, Polya’s theorem, graphs and digraphs, combinatorial designs, incidence matrices, partially ordered sets, matroids, finite geometries, Latin squares, difference sets, matching theory.

7510 Topology I. Prof. Bălibanu

  • Time: 9:00-10:20 TT
  • Instructor: Prof. B&alibanu
  • Prerequisite: Advanced Calculus (Math 4031)
  • Text: Topology (2nd ed.) by James R. Munkres.
  • Description: This course is a preparation course for the Core I examination in topology. It will cover general (point set) topology, the fundamental group, and covering spaces. We will also introduce simplicial complexes and manifolds. A good supplementary reference is Chapter 1 of Algebraic Topology by Allen Hatcher, available online.

7520 Algebraic Topology. Prof. Cohen

  • Time: 1:30-2:50 TT
  • Instructor: Prof. Cohen
  • Prerequisite: MATH 7512
  • Text: <\em>Algebraic Topology by Allen Hatcher (freely available online)
  • Description: This is a continuation of Math 7512 (for students from any prior offering of this course). We will discuss various forms of duality involving homology and cohomology, basic homotopy theory, and related topics potentially including the theory of fiber bundles, spectral sequences, etc.

7590 Seminar in Geometry and Algebraic Topology: Sigma-invariants of finitely generated groups. Prof. Dani

  • Time: 10:30-11:20 MWF
  • Instructor: Prof. Dani
  • Prerequisite: MATH 7210 and 7512
  • Text: Notes on the Sigma invariants by Ralph Strebel (available on arXiv)
  • Description: The Sigma-invariants of a finitely generated group (also called BNSR-invariants) are an important tool in geometric group theory, with connections to many other topics, such as the Thurston norm and fibering of manifolds over S^1, Novikov homology, and resonance varieties. Defined in the 1980s by Bieri-Neuman-Strebel (in dimension 1) and Bieri-Renz (in higher dimensions), they are certain subsets of the character sphere of a group G, which encode a vast amount of information about the finiteness properties of subgroups of G. Recently, they have been successfully used in the study of interesting group theoretic questions such as virtual algebraic fibering and commensurability. Although they are rather hard to compute in general, they are now understood, at least in low dimensions, for various well-known classes of groups, such as generalized Baumslag-Solitar groups as well as many Artin and braid groups. In this course, we will begin with the geometric approach to the 1-dimensional Sigma invariants, following Strebel's "Notes on the Sigma invariants". Following that, we will explore further applications, explicit computations in specific classes of groups, and connections to other topics, to be determined by the interests of the class.

Spring 2026

For Detailed Course Outlines, click on course numbers.

4997-1 Vertically Integrated Research: TBA. Dr. Rios and Prof. Wolenski

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  • Instructors: Dr. Rios and Prof. Wolenski
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4997-2 Vertically Integrated Research: Topics in Combinatorics. Profs. Bibby and Z. Wang

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  • Instructors: Profs. Bibby and Z. Wang
  • Prerequisite: Linear Algebra (Math 2085 or 2090)
  • Text: None
  • Description: This is a project-based seminar class in combinatorics. Students work together in small groups to tackle problems in topics such as graph theory; matroid theory; order theory; enumerative and algebraic combinatorics; geometric and topological combinatorics. Previous experience in combinatorics is not required.

4997-3 Vertically Integrated Research: TBA. Prof. Drenska

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  • Instructors: Prof. Drenska
  • Prerequisite: 2085 or equivalent, as well as a 4000-level mathematics course with a grade of C or better, or obtain permission of the department
  • Text: Gilbert Strang, Linear Algebra and Learning from Data
  • Description: This is a project-based course that involves real-world applications of machine learning. The course provides opportunities for students to consolidate their mathematical knowledge, and to obtain a perspective on the meaning and significance of that knowledge. Course work will emphasize communication skills, including reading, writing, and speaking mathematics.

4997-4 Vertically Integrated Research: Arithmetic of subspace packings and quantum designs. Prof. Kopp

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  • Instructors: Prof. Kopp
  • Prerequisite: Multivariable calculus (Math 2057, Math 2058, or equivalent) and linear algebra (Math 2085, Math 2090, or equivalent) are required. Some experience reading and writing mathematical proofs and some experience writing computer code is highly recommended. Some projects, but not all, will use elementary number theory (Math 4181) and abstract algebra including Galois theory (Math 4200 and Math 4201). As project leaders, PhD students in the course should have Math 7210 and should have some knowledge of algebraic number theory.
  • Text: Waldron, An Introduction to Finite Tight Frames
  • Description: In this research-focused course, we will use computational tools to search for structures of interest to algebraic number theory, quantum information theory, and coding theory. These structures (called subspace packings, quantum designs, and/or fusion frames) are arrangements of subspaces in a finite-dimensional Hilbert space satisfying highly restrictive geometric constraints or symmetries. The prototypical examples are SIC-POVMs (symmetric, informationally complete positive operator-valued measures), or sets of d^2 complex equiangular lines in d-dimensional Hilbert space, whose conjectural classification ties them to deep number theory (class field theory for real quadratic fields). SIC-POVMs make up a small sliver of a vast space of potentially interesting subspace packings. The discovery of the number-theoretic features of SIC-POVMs was an accident made possibly by massive computer searches, and such searches are needed in other directions. Background on finite frame theory and connections to number theory will be provided through lectures, and students will pursue computational research projects in groups. Half of the in-class time will be spent in a computer lab.

4997-5 Vertically Integrated Research: TBA. Profs. Achar and Balibanu

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  • Instructors: Profs. Achar and Bălibanu
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7002 Communicating Mathematics II. Prof. Shipman and Dr. Ledet

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  • Instructor: Prof. Shipman and Dr. Ledet
  • Prerequisite: Consent of department. This course is required for all first-year graduate students. It is a lab course meeting for an average of two hours per week throughout the semester for one-semester-hour's credit.
  • This course provides practical training in the teaching of mathematics at the pre-calculus level, how to write mathematics for publication, and treats other issues relating to mathematical exposition. Communicating Mathematics I and II are designed to provide training in all aspects of communicating mathematics. Their overall goal is to teach the students how to successfully teach, write, and talk about mathematics to a wide variety of audiences. In particular, the students will receive training in teaching both pre-calculus and calculus courses. They will also receive training in issues that relate to the presentation of research results by a professional mathematician. Classes tend to be structured to maximize discussion of the relevant issues. In particular, each student presentation is analyzed and evaluated by the class.

7211 Algebra II. Prof. Long

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  • Instructor: Prof. Long
  • Prerequisite: Math 7210 or equivalent
  • Text: David Dummit and Richard Foote, Abstract Algebra, 3rd Edition, John Wiley and Sons, 2003
  • Description: Fields: algebraic, transcendental, normal, separable field extensions; Galois theory, simple and semisimple algebras, Wedderburn theorem, group representations, Maschke’s theorem, multilinear algebra.

7230 Topics in Number Theory. Prof. Tu

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7240 Topics in Algebraic Geometry: Sheaf Theory. Prof. Achar

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  • Instructors: Prof. Achar
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7290 Seminar in Algebra and Number Theory: Category Theory. Prof. Ng

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  • Instructor: Prof. Ng
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7320 Ordinary Differential Equations. Prof. Neubrander

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  • Instructor: Prof. Neubrander
  • Prerequisite: The basics of Real Analysis or even just Advanced Calculus.
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  • Description: The course will cover the qualitative theory of Ordinary Differential Equations. This includes the usual existence and uniqueness theorems, linear systems, stability theory, hyperbolic systems (the Grobman-Hartman Theorem), phase portraits, and discrete systems. if time permits, an introduction to Control Theory will be included. The course will be accessible to those who do not aspire to be analysts, but expect at some point to teach an undergraduate course in ODEs.

7330 Functional Analysis (a.k.a. Analysis II). Prof. Vempati

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  • Instructor: Prof. Vempati
  • Prerequisite: Math 7311 or its equivalent
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7366 Stochastic Analysis. Prof. Fehrman

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  • Instructor: Prof. Fehrman
  • Prerequisite: Math 7311, and Math 7360 or its equivalent
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  • Description: First, the essential features of Brownian motion, martingale theory, and Markov processes are studied. Next, stochastic integrals are constructed with respect to Brownian motion and in general, semimartingales. A central role in stochastic analysis is played by the It\^o formula with far-reaching consequences. After its proof and applications, the theory of stochastic differential equations driven by a Brownian motion is presented. The fundamental connection between stochastic differential equations and a class of parabolic partial differential equations will be established.

7375 Wavelets. Prof. Huang

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7380 Seminar in Functional Analysis: Topics in Harmonic Analysis. Prof. Nguyen

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  • Instructor: Prof. Nguyen
  • Prerequisite: Math 7311
  • Text: Loukas Grafakos, Classical Fourier Analysis, Third Edition, GTM 249, Springer, New York, 2014. xviii+638 pp. ISBN: 978-1-4939-1193-6.

    Recommended References: 1. E. M. Stein, Singular Integrals and Differentiability Properties of Functions, Princeton Univ. Press,Princeton, 1970. 2. Elias M. Stein, Harmonic analysis: real-variable methods, orthogonality, and oscillatory integrals, Princeton University Press, Princeton, NJ, 1993. 3. Javier Duoandikoetxea, Fourier Analysis, Graduate Studies in Math., Vol. 29. Translated and revised by David Cruz-Uribe, SFO, 2000.

  • Description: This is an introductory course that covers basic topics of Harmonic Analysis. Topics include Fourier transform, Lorentz spaces, interpolation theorems, the Hardy-Littlewood maximal function, and Calderon-Zygmund singular integral operators. Moreover, the Littlewood-Paley theory will also be discussed if time permits.

7390 Seminar in Analysis. Prof. Rubin

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7390 Seminar in Analysis. Prof. Zhang

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  • Instructor: Prof. Zhang
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7410 Graph Theory. Prof. Z. Wang

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  • Instructor: Prof. Z. Wang
  • Prerequisite: None
  • Text: Graph Theory by Reinhard Diestel, Fifth Edition, Springer, 2016
  • Description: The main theme of this course will be graph theory. We will discuss a wide range of topics, including spanning trees, Eulerian trails, matching theory, connectivity, hamiltonian cycles, coloring, planarity, integer flows, surface embeddings, Turan theorems, Ramsey theorems, regularity lemma, and graph minors.

7490 Seminar in Combinatorics, Graph Theory, and Discrete Structures: Matroid Theory. Profs. Oxley

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  • Instructor: Prof. Oxley and Schreve
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7512 Topology II. Prof. Vela-Vick

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  • Instructor: Prof. Vela-Vick
  • Prerequisite: Math 7510
  • Text: Algebraic Topology by Hatcher
  • Description: This course covers the basics of homology and cohomology theory. Topics discussed may include singular and cellular (co)homology, Brouwer fixed point theorem, cup and cap products, universal coefficient theorems, Poincare duality, Alexander duality, Kunneth theorems, and the Lefschetz fixed point theorem.

7550 Differential Geometry. Prof. Baldridge

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  • Instructor: Prof. Baldridge
  • Prerequisite: Math 7210 and 7510; or equivalent.
  • Text: Topology and Geometry by Glen Bredon
  • Description: Manifolds, vector fields, vector bundles, transversality, deRham cohomology, metrics, other topics.

7590-1 Seminar in Geometry and Algebraic Topology: Rational Homotopy Theory. Prof. Bibby

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  • Instructor: Prof. Bibby
  • Prerequisite: Strongly recommend some familiarity with homotopy theory (as in Math 7520 Algebraic Topology) and differential forms (as in Math 7550 Differential Geometry)
  • Text: Rational Homotopy Theory and Differential Forms by Griffiths & Morgan (pdf available through LSU Library here)
  • Description: The course will start with some basics of homotopy theory, fibrations, Postnikov towers, and de Rham cohomology. The goal is then to study the rational homotopy type of a simply-connected space X, which is the homotopy type of its localization (or rationalization). The homotopy and homology groups of the rationalization are rationalizations of those for X, killing all torsion. The rational homotopy type of X has the advantage of being more computable than the (ordinary) homotopy type of X, thanks to the algebraic models (using differential graded algebras or Lie algebras) from Sullivan and Quillen. The story is more complicated when X is not simply connected, when one needs to make sense of how to "rationalize" the (possibly non-abelian) fundamental group.

7590-2 Seminar in Geometry and Algebraic Topology. Prof. Schreve

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  • Instructor: Prof. Schreve
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7710 Advanced Numerical Linear Algebra. Prof. Wan

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  • Instructor: Prof. Brenner
  • Prerequisite: Linear Algebra and Advanced Calculus and Programming Experience
  • Text: Fundamentals of Matrix Computations (Second Edition), D.S. Watkins (available for download through the LSU library)
  • Description: This is an introductory course in numerical linear algebra at the graduate level. Topics include

    • mathematical tools: norms, projectors, Gram-Schmidt process, orthogonal matrices, spectral theorem, singular value decomposition
    • error analysis: round-off errors, backward stability and conditioning
    • general systems: LU decomposition, partial pivoting, Cholesky decomposition and QR decomposition
    • sparse systems: the methods of Jacobi, Gauss-Seidel, steepest descent and conjugate gradient
    • eigenvalue problems: power methods, Rayleigh quotient iteration and QR algorithm

7999-n Assorted Individual Reading Classes
  • No additional information.

8000-n Assorted Sections of MS-Thesis Research
  • No additional information.

9000-n Assorted Sections of Doctoral Dissertation Research
  • No additional information.