Math 622: Differential Geometry 1

Syllabus     |     HW     |     Lee Errata     |     Jan 20 handout.

Midterms.
    1 : Friday, March 05.
    2 : Friday, April 09 [Solutions].

Final. Monday, May 10, 10:30 - 12:30.

E-mail. I will be contacting the class though the TAMU e-mail system. Be sure to check your neo.tamu.edu account regularly, or have those e-mails forwarded to your preferred account.

Prerequisites. We will use some basic concepts from Linear Algebra and Topology. See, for example, the appendices of Lee's text. If you are short on the prerequisites, or would prefer to study classical surface theory, then you might consider Math 439.

Course texts. Introduction to Smooth Manifolds, John M. Lee, Springer [primary];
Differential Forms and Applications, Manfredo P. do Carmo, Springer [secondary].

Material. We will cover material from the following chapters of Lee's text: 1 - 8, 10 - 14, 17, 19. We will also go over the classical surface theory (from a modern perspective); see do Carmo's text. If time allows we will work though Chapters 9, 18, 20 of Lee. See the syllabus for more detail.

Additional references that you may like to consult include:

• An Introduction to Differentiable Manifolds and Riemannian Geometry, William M. Boothby [one of my favorite reference texts];
• Calculus on Manifolds, Michael Spivak [good reference for the Inverse and Implicit Function Theorems];
• A Comprehensive Introduction to Differential Geometry, v.1-5, Michael Spivak.

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