T: Differential Geometry - 52444 - MATH 439 - 001 & Introduction to Differentiable manifolds MATH 536
(Spring 2022)
Instructor: Dimiter Vassilev Office : SMLC, Office 326 Email: vassilev@unm.edu
The class is hybrid: T 8:00-9:15 SMLC 352 & Th 8:00-9:15 on Microsoft Office Teams. You need to be registered for the course with a @unm.edu email. Any other email will disable features of Microsoft Teams.
Office Hours: Wednesday 10am-11am and 2pm-3pm on MS Teams.
Textbook: Introduction to Geometry and Topology, ISBN 9783034809825/ 3034809824, Ballmann, Werner (free on the UNM network)
Supplemental books:
Description: The main goal of the course is to familiarize you with topological and geometric notions and structures through a gentle introduction to some topics motivated by physics and geometry. Specific topics will include basic topology, smooth manifolds, vector field and their flows, differential forms, Stokes theorem, DeRham theory, Lie groups and algebras, Riemannian and semi-Riemannian metrics, vector and fiber bundles, connections. Some applications will be given to Maxwell's Equations and the Yang-Mills Equation. I will assume that you have taken Linear Algebra and Calculus III, preferably also MATH431. However, I will spend time on basic topology.
Please note the following guidelines for the course:
Grades: The final grade will be determined using the homework (100 pts), one midterm exam (100 pts) and a final exam (100 points). The Final Exam score will replace the midterm score if the latter is lower than the Final Exam score. There will be different expectations based on the registration in MATH439 or MATH536.
Final exam: check the Final Examination Schedule. Students having conflicts with this exam schedule must notify the appropriate instructor before April 4.
Homework: The homework will be posted in the class OneNote notebook. The Homework will be due the following Thursday and will be submitted through MS Teams. Instructions on how to submit can be found at Help inserting a printout in the homework (Web view). You can work together on the homework, but you have to write up your own solutions in your own words. To help the grader, please write your solutions up neatly and clearly and staple the sheets. It is best if you work and discuss the problems together and with me as questions arise. The highest 10 homeworks will be counted.
Missed Exams: Make-up exams can be arranged for exams missed with a VALID excuse (illness, family emergency, active participation in scholarly or athletic activities), and ONLY if prior notice is given.
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