Prerequisite: MATH 442 (or consent of the instructor)

• Lecture Notes
• Textbook (required):
  • T. Frankel, The Geometry of Physics, Cambridge University Press, 1997
• Books (recommended):
  • M. Nakahara, Geometry, Topology and Physics, IOP, 2003
  • C. Nash and S. Sen, Topology and Geometry for Physicists, Academic Press, 1983
  • A. S. Schwarz, Topology for Physicists, Springer, 1996
• Goals and Objectives of the Course: Study of advanced topics in differential geometry such as: Brouwer degree, fundamental group, homology groups, De Rham cohomology, Betti numbers, fibre bundles, Morse theory, Lie groups, covering spaces, homotopy groups.
• Class Procedures: The majority of each class period will be lecture oriented. You are expected to attend the lectures, take your own lecture notes, read the textbook and do the homework problems.
• Attendance Requirements: Regular attendance is expected. You are responsible for all material covered in this class as well as material from the textbook which is assigned but not covered in class.
• Grading Scheme: There will be homework assignments that may or may not be graded. A significant part of the grade will depend on the homework and the class participation.
• Changes: The course plan may be modified during the semester. Such modifications will be announced during class periods. You are responsible for keeping abreast of such changes.
• Disability Accommodations: New Mexico Tech is committed to protecting the rights of individuals with disabilities. Qualified individuals who require reasonable accommodations are invited to make their needs known to the Office of Counseling and Disability Services (OCDS) as soon as possible. To schedule an appointment, please call 835-6619.
• Counseling Services: New Mexico Tech offers mental health and substance abuse counseling through the Office of Counseling and Disability Services. The confidential services are provided free of charge by licensed professionals. To schedule an appointment, please call 835-6619.
• Academic Honesty: NEW MEXICO TECH’S ACADEMIC HONESTY POLICY AND GUIDE TO CONDUCT AND CITIZENSHIP FOR STUDENTS (pp. 11-21)