Prerequisite: MATH 254, 231 passed with grade C- or better (required); MATH 352, 332, 335, 454 (recommended)

Course Learning Outcomes: By the end of this course, students will be able to:

• Demonstrate a working knowledge of basics of modern differential geometry for further studies in geometry/geometrical analysis,
• Explain the concepts and language of differential geometry and its role in modern mathematics,
• Analyze and solve complex problems using appropriate techniques from differential geometry,
• Apply differential geometry techniques to diverse situations in physics, engineering or other mathematical contexts.

Program Learning Outcomes and Mission Statement of the Department of Mathematics

Course Requirements

• Textbook (required): T. Frankel, The Geometry of Physics, An Introduction, Cambridge University Press, 1997 (or later edition)
• Lecture Notes
• Goals and Objectives of the Course: This course provides a succinct yet comprehensive treatment of the essentials of modern di fferential geometry. It covers the basics of multilinear algebra, di fferentiation and integration on manifolds, Lie groups and Lie algebras, Riemannian geometry and features a variety of applications from mechanics, electromagnetism, general relativity and gauge theory.
• Class Procedures: The majority of each class period will be lecture oriented. You are expected to: attend the lectures and to take your own lecture notes, read the textbook and work out problems from that section covered in class, 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.
• Computers: Any electronic devices such as laptops, tablets and cell phones cannot be used during the class. Please set your cell phones on vibrate.

Grading

• Homework: There will be homework assignments that will count for 60%.
• Tests: There will be a final exam that will count for 20% of the total grade.
• Class Participation: A significant part of the grade, 20%, will depend on class participation.
• Make-ups: Make-up exams will be given only in cases of extremely properly documented emergencies. Late homework will not be accepted.
• Evaluation: Grades will be determined on a 100 point scale. The point totals near cutoff will be individually considered for the next higher grade. I do reserve the right to add some extra points depending on the class participation and outstanding exam performance.

Changes: The course plan may be modified during the semester. Such modifications will be announced in advance during class periods. You are responsible for keeping abreast of such changes.

Remarks: It is important to note that this course is cumulative (builds on itself) and it is assumed that all earlier parts covered are liable for any exam. It is strongly advised that you start working on this course from the very beginning. The course moves at a fast place, so it is very hard to catch up if you get behind.

Counseling and Disability Services. Reasonable 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. In addition, 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.