Graduate Courses, Summer 2025 – Spring 2026

Contact

Please direct inquiries about our graduate program to:
grad@math.lsu.edu

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: TBA. Profs. Bibby and Schreve

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  • Instructor: Profs. Bibby and Schreve
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4997-2 Vertically Integrated Research: TBA. Prof. Fehrman

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  • Instructor: Prof. Fehrman
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4997-3 Vertically Integrated Research: TBA. Prof. Bălibanu

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  • Instructor: Prof. Bălibanu
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7001 Communicating Mathematics I. 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.

7210 Algebra I. Prof. X. Wang

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  • 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. Prof. Kopp

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7250 Representation Theory. Prof. Ng

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  • Instructor: Prof. Ng
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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

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7311 Real Analysis (a.k.a. Analysis I). Prof. Lipton

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  • 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

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  • Instructor: Prof. Ólafsson
  • Prerequisite: Math 7311
  • Text:Lecture notes and Complex Analysis by Greene and Krantz
  • Description: Theory of holomorphic functions of one complex variable; path integrals, power series, singularities, mapping properties, normal families, other topics.

7360 Probability Theory: Prof. Ganguly

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  • 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

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  • Instructor: Prof. Fehrman
  • Prerequisite: Math 7360. This can be taken concurrently with Math 7365, provided that the student has a good background in measure theory and real analysis.
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  • Description: Math 7365 is a course on stochastic processes. A stochastic process can be thought of as a random function of time which originates in modeling temporal dynamics of many systems. Detailed modeling of such systems requires incorporation of their inherent randomness which deterministic methods, for example, through differential equations fail to capture. Examples of such systems are numerous and wide ranging - from biological networks to financial markets. Markov processes, in particular, form one of the most important classes of stochastic processes that are ubiquitous in probabilistic modeling. They also lead to probabilistic interpretations of a large class of PDEs. For example, Brownian motion is the underlying Markov process whose probability distribution satisfies the heat equation. The course will cover theory of martingales and Markov processes in discrete-time. Some specific topics include Doob's decomposition theorem, Doob's inequalities, Burkholder-Davis-Gundy inequality, Kolmogorov's equations, generators, stationary measures and some elementary stability theory. If time permits, we will also make some remarks about the continuous-time case and briefly discuss some stochastic algorithms like Markov Chain Monte Carlo, importance sampling, stochastic approximation methods which are instrumental in probabilistic approach to data-science. The course is also a gateway to the course on stochastic analysis (Math 7366).

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

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  • Instructor: Prof. Shipman
  • Prerequisite: Real and complex analysis
  • Text: Operator Theory by Barry Simon
  • Description: This material is foundational broadly in analysis and its applications. Salient aspects or applications of operator theory include spectral theory, index theory, PDE, and numerical analysis. Operator theory is ubiquitous in all flavors of mathematical physics. The topics include compact operators, index theory, and spectral theory.

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

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  • 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

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  • 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

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  • 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: Operator Theory. Prof. Bulut

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7400 Combinatorial Theory. Prof. Bibby

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  • 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

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  • 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.

7560 Riemannian Geometry. Prof. Vela-Vick

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  • Instructor: Prof. Vela-Vick
  • Prerequisite: MATH 7550
  • Text: Riemannian Geometry by Manfredo P. do Carmo
  • Description: Riemannian metrics and connections, geodesics, completeness, Hopf-Rinow theorem, sectional curvature, Ricci curvature, scalar curvature, Jacobi fields, second fundamental form and Gauss equations, manifolds of constant curvature, first and second variation formulas, Bonnet-Myers theorem, comparison theorems, Morse index theorem, Hadamard theorem, Preissmann theorem, and further topics such as sphere theorems, critical points of distance functions.

7590 Seminar in Geometry and Algebraic Topology. Prof. Dani

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Spring 2026

For Detailed Course Outlines, click on course numbers.

4997-1 Vertically Integrated Research: TBA. Profs. Novack and Wolenski

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  • Instructors: Profs. Novack and Wolenski
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4997-2 Vertically Integrated Research: TBA. Profs. Bibby and Z. Wang

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  • Instructors: Profs. Bibby and Z. Wang
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4997-3 Vertically Integrated Research: TBA. Prof. Drenska

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  • Instructors: Prof. Drenska
  • Prerequisite: Math 4200 or 4023
  • Text: None
  • Description: This is a project-based seminar course in geometry and topology focussing on complexes built out of polyhedra and the groups that act on them. Specific interesting examples that we will see are buildings, lattices in products of trees, and systolic complexes. Students will focus on understanding concrete classical examples through problem-solving.

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

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  • Instructors: Prof. Kopp
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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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7290 Seminar in Algebra and Number Theory: Category Theory. 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. Prof. Nguyen

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  • Instructor: Prof. Nguyen
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7390 Seminar in Analysis. Prof. Rubin

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7390 Seminar in Analysis. 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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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.