CRN 46166 Math 536 001 Intro Diff Manifolds

Lecture MWF 11:00-11:50 CENT-1028 Vassilev, D.

 

                                                                 

Instructor: Dimiter Vassilev     Office :  SMLC, Office 326  Email: vassilev@unm.edu  Phone Number: 505 277 2136

 

Office Hours: Monday & Friday 9am-10am, Wednesday 10am-11am or by appointment. 

 

Final exam: Wednesday, May 8, 10:00–12:00 Please see Final Examination Schedule.

Students having conflicts with this examination schedule must notify the appropriate instructor before April 5, 2013. Any student having more than three examinations scheduled in any one day may notify the instructor of the last examination listed. If notified before April 5, 2013, the instructor shall make arrangements to give a special examination. Conflicts arising as a result of scheduling out of normal hours-pattern or day sequences must be resolved by the instructor of the off-pattern courses. Changes in this examination schedule are not permitted except by formal approval of the instructor’s College Dean.       

Suggested Textbooks:

Please note the following guidelines for the course:

 

Description: Math 536  Introduction to Differentiable Manifolds

Concept of a manifold, differential structures, vector bundles, tangent and cotangent bundles, embedding, immersions and submersions, transversality, Stokes' theorem.

 

Prerequisite: Math 511.


Grades: The final grade will be determined by homework (100 points), one midterm exam (100 pts) and a final exam (200 points).  All grades will be posted on UNM Learn.

 

Homework:  You can work together on the homework, but you do need 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.   Each homework has 5 problems (2 pts each) for a total of 10 points.  The Extra Credit Problems are not due and are truly extra credit (4 pts each).

 

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. 

 

Disability Statement: We will accommodate students with documented disabilities. During the first two weeks of the semester, those students should inform the instructor of their particular needs and they should also contact Accessibility Services in Mesa Vista Hall, Room 2021, phone 277-3506.  In addition, they should see CATS- Counseling and Therapy Services; Student Health Center (277-4537). (They can help if you suffer from exam anxiety).    

 

 

 

                                             Syllabus and Homework – Spring 2013 (please check after class as advanced postings of homework could change)

Week of

Topics Covered

Homework due following Monday.

Jan. 14

1. Topological manifolds,  paracompactness and partitions of unity, existence of smooth cut-off functions.

HW

Jan. 21 (MLK)

 

HW

Jan. 28

2. Smooth manifolds, smooth maps.

HW

Feb. 4

3. The tangent space.

 

HW

Feb. 11

4. The tangent bundle.

HW

Feb. 18

5. Vector bundles - equivalent definitions, maps between vector bundles.

HW 

Mar. 25

6. Vector bundles. The cotangent bundle.

HW

Mar. 4

7. Submanifolds: submersions, immersions, embeddings, regular submanifolds; the rank theorem; regular level sets; Sard's theorem.

Midterm Exam

HW

Mar. 11

Spring Break

 

Mar. 18

 

 

 

HW

Mar. 25

 

 8.  Examples – matrix Lie groups.

 

HW

Apr. 1

 9. Lie brackets, flows of vector fields.

 

 

HW

Apr. 8

10. Differential forms - operatiions, integration, de Rham cohomology

 

HW

Apr. 15

 

HW

Apr. 22

 

 

HW

Apr. 29

 

HW

May 6 Finals week

Wednesday, May 8, 10:00–12:00

 

 

 

 

 

HOLIDAYS/BREAKS


Spring Break March 10-17, 2013
Finals Week May 6-11, 2013
Martin Luther King, Jr. Day: January 21, 2013