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Catalog Course Descriptions

View the Course Descriptions from the University Catalog

Fall 2022 Undergraduate Courses

MATH 4080 Differential Geometry - John Krueger

Textbook: "Elementary Differential Geometry", Andrew Pressley

Prerequisites: Linear Algebra (Math 2700), Multivariable Calculus (Math 2730), Real Analysis (Math 3000)

This course is an introduction to differential geometry. We will learn how to apply multivariable calculus and linear algebra to study curves and surfaces in three dimensional space. Topics include the Frenet apparatus for curves, isometries, the Gauss map, the fundamental forms for surfaces, and geodesics. In addition to being a beautiful area of pure mathematics, differential geometry also serves as a mathematical foundation to areas of theoretical physics such as general relativity.

Students who take this course will receive geometry or analysis credit towards their math major. This is a new class starting this year and will appear in the UNT 2022-23 catalog.

Spring 2023 Graduate Courses

  • MATH 6150 - Functional Analysis Bunyamin Sari (Syllabus MATH 6510)

  • MATH 6510 - Topics in Modular Forms Ralf Schmidt

    This course is appropriate for students who took Dr. Richter's modular forms course in Fall 2022. After a review of the basic theory of modular forms, we will consider some advanced topics. One of our main goals will be to develop the representation-theoretic point of view, which necessitates the introduction of p-adic numbers and adeles. We will also consider L-functions and how they capture the "essence" of an automorphic object.

  • MATH 6610 - Topics in Topology and Geometry Anne Sheppler

    Topic: Arrangements of Hyperplanes
    An arrangement of hyperplanes is a collection of hyperplanes (codim 1 subspaces) in a finite dimensional vector space. Arrangements of hyperplanes have served as a unifying theory for many problems in topology and discrete and computational geometry with strong connections to algebraic combinatorics and representation theory. We will delve into the captivating topology, geometry, and combinatorics of arrangements encoded by the lattice of intersections, the Mobius function, and the characteristic polynomial. Topics include braid groups, Weyl chambers, and the cohomology of the complement. No previous knowledge is assumed.

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