MAT 401 Seminar in Mathematics

Birth of the Riemann Curvature Tensor

Fall 2020

SUNY at Stony Brook

This course is an introduction to the Riemann curvature tensor -- the basic invariant of Riemannian metrics. It is the generalization of the Gauss curvature for surfaces to arbitrary higher dimensional spaces. We will follow the path that Riemann blazed in his discovery of this remarkable, but complicated, invariant.
This is a rather advanced topic and so knowledge of the content of MAT 322 (Analysis in higher dimensions) and MAT 362 (Differential geometry of surfaces) is strongly encouraged.

  • Class Times: Tu/Th 1:15-2:35pm, online, Zoom

  • Grading:

    Your grade will be based on your lecture presentations, your lecture notes, and class participation.

    Course Text:

    Class Format:

    For the first three weeks of class, I will introduce the main concepts and issues that will be the focus of the semester. Following this, each student will give two (non-consecutive) lectures on an assigned topic; I will regularly provide individual assistance and guidance on this process. Students should make their lecture notes available to everyone in the class. Frequent disucssion and questions are encouraged.

    Volume II, Chapter 4 of the Spivak text is the main focus of the course.

    This will be an online class, meeting on Zoom through Blackboard.

    Required Syllabi Statements

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