LSU College of Science
LSU
Mathematics

Graduate Course Outlines, Summer 2019-Spring 2020

Contact


All inquiries about our graduate program are warmly welcomed and answered daily:
grad@math.lsu.edu

Summer 2019

  • MATH 7999-1: Problem Lab in Algebra —practice for PhD Qualifying Exam in Algebra.
  • Instructor:
  • Prerequisite: Math 7210.
  • Text: Online Test Bank.
  • MATH 7999-2: Problem Lab in Real Analysis—practice for PhD Qualifying Exam in Analysis.
  • Instructor:
  • Prerequisite: Math 7311.
  • Text: Online Test Bank.
  • MATH 7999-3: Problem Lab in Topology—practice for PhD Qualifying Exam in Topology.
  • Instructor:
  • Prerequisite: Math 7510.
  • Text: Online Test Bank.

Fall 2019

  • MATH 4997-1: Vertically Integrated Research:
  • 12:00-1:20 TTh
  • Instructor:
  • Profs. Achar and Sage
  • Prerequisites:
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  • MATH 4997-2: Vertically Integrated Research:
  • 10:30-11:50 TTh
  • Instructor:
  • Profs. Vela-Vick and Wong
  • Prerequisites:
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  • MATH 7001: Communicating Mathematics I
  • 3:00-4:50 T Th
  • Instructor: Prof. Oxley.
  • Prerequisite: Consent of department. This course is required for all incoming 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.
  • MATH 7210: Algebra I
  • 12:30-1:20 MWF
  • Instructor: Prof. Ng.
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  • MATH 7230: Class Field Theory.
  • 10:30-11:50 TTh
  • Instructor: Prof. Mahlburg.
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  • MATH 7260: Homological Algebra.
  • 9:00-10:20 TTh
  • Instructor: Prof. Achar.
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  • MATH 7290: Modular Tensor Categories and Quantum Invariants.
  • 10:30-11:20 MWF
  • Instructor: Profs. Ng and Wang
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  • MATH 7311: Real Analysis I.
  • 10:30-11:20 MWF
  • Instructor: Prof. Sundar.
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  • MATH 7325: Finite Element Methods.
  • 12:00-1:20 TTh
  • Instructor: Prof. Walker.
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  • MATH 7350: Complex Analysis.
  • 1:30-2:50 TTh
  • Instructor: Prof. Sage.
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  • MATH 7360: Probability Theory.
  • 1030-11:50 TTh
  • Instructor: Prof. Ganguly.
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  • MATH 7380: Spherical Harmonics and Integral Geometry.
  • 8:30-9:20 MWF
  • Instructor: Prof. Rubin.
  • Prerequisites: Differential calculus in n-dimensional space (MATH 4035), Lebesgue integration (MATH 7311).
  • Text: Prof. Rubin will provide his notes following the book:
    B. Rubin: Introduction to Radon transforms: With elements of fractional calculus and harmonic analysis (Encyclopedia of Mathematics and its Applications), Cambridge University Press (2015).
  • Syllabus: The focus of this course/seminar is introduction to the Fourier analysis on the unit sphere in the n-dimensional real Euclidean space and related problems of integral geometry. This topic plays an important role in PDE, harmonic analysis, group representations, mathematical physics, geometry, and many other areas of mathematics and applications.
  • MATH 7384: Topics in Material Science:
  • 2:30-3:20 MWF
  • Instructor: Prof. Lipton.
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  • MATH 7386: Partial Differential Equations.
  • 12:00-1:20 MW
  • Instructor: Prof. Bulut.
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  • MATH 7390-1: Topics in Numerical Analysis.
  • 130-2:20 MWF
  • Instructor: Prof. Wan.
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  • MATH 7390-2: Introduction to Control Theory.
  • 9:00-10:20 TTh
  • Instructor: Prof. Malisoff.
  • Prerequisites: MATHs 4027 and 4035, or their equivalents or permission from instructor.
  • Text:
  • This course provides an introduction to basic ideas and results from control theory, which is an interdisciplinary field that provides the foundation for much current research in multiple branches of engineering.
    Course topics will be chosen from among the following: review of differential equations, linear control systems, open and closed loop control, Lyapunov functions, feedback control of nonlinear systems, robustness to uncertainty, adaptive control, and control systems with delays.
  • MATH 7510: Topology I
  • 9:30-10:20 MWF
  • Instructor: Prof. Dasbach.
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  • MATH 7520: Algebraic Topology.
  • 11:30-12:20 MWF
  • Instructor: Prof. Gilmer.
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  • MATH 7590: Trisections on smooth 4-manifolds.
  • 1:30-2:50 TTh
  • Instructor: Prof. Baldridge.
  • Prerequisites: Differential Geometry (7550) and Topology II (7512)
  • Text: 4-Manifolds and Kirby Calculus by R. Gompf and A. Stipsicz, and papers by Peter Lambert-Cole on trisections
  • In this course, we study trisections on smooth closed 4-manifolds with the goal of understanding the minimal genus of all embedded smooth surfaces representing a given homology class (The Thom Theorem). A trisection of a 4-manifold is analogous to a Heegaard decompositions of a 3-manifold. It is a cutting-edge tool that has already shown great promise in understanding and proving some of the hardest problems in 4-manifold theory. This course will benefit students who want an overview of 4-manifold constructions and want to learn how to use advanced techniques in topology and geometry to study smooth manifolds.

Spring 2020

  • MATH 4997-1: Vertically Integrated Research:
  • Instructor:
  • Prerequisites:
  • Text:
  • MATH 4997-2: Vertically Integrated Research:
  • Instructor:
  • Prerequisites:
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  • MATH 7002: Communicating Mathematics II
  • 3:00-4:50 T Th
  • Instructor: Prof. Oxley .
  • Prerequisite: Consent of department. This course is required for all incoming 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.
  • MATH 7211: Algebra II.
  • Instructor: Prof. Hoffman.
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  • MATH 7230: Introduction to Elliptic Curves and Modular Forms
  • Instructor: Prof. Tu.
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  • MATH 7280: D-modules
  • Instructor: Prof. Sage.
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  • MATH 7290: Group Schemes
  • Instructor: Prof. Casper.
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  • MATH 7320: Ordinary Differential Equations.
  • Instructor: Prof. Malisoff
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  • MATH 7330: Functional Analysis.
  • Instructor: Prof. He.
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  • MATH 7366: Stochastic Analysis.
  • Instructor: Prof. Kuo.
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  • MATH 7370: Lie Groups and Representations
  • Instructor: Prof. Olafsson.
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  • MATH 7375: Wavelets:
  • Instructor: Prof. Nguyen.
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  • MATH 7384: Topics in Material Science:
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  • MATH 7490: Combinatorial Optimization
  • Instructor: Prof. Ding.
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  • MATH 7550: Differential Geometry.
  • Instructor: Prof. Zeitlin.
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  • MATH 7590-1: Geometric Topology: Hyperbolic Geometry.
  • Instructor: Prof. Zimmer.
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  • MATH 7590-2: Modular categories and Reshetikhin-Turaev TQFTs
  • Instructor: Prof. Wang
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  • MATH 7710: Advanced Numerical Linear Algebra.
  • Instructor: Prof. Zhang.
  • Prerequisites:
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