CRN 46166 Math 536 001 Intro Diff
Manifolds
Lecture MWF 11:0011:50 CENT1028 Vassilev, D.
Instructor: Dimiter Vassilev Office :
SMLC, Office 326
Email: vassilev@unm.edu
Phone
Number:
505 277 2136
Suggested Textbooks:
Lee J. M., Introduction to smooth manifolds (Springer, Graduate Texts in Mathematics)
Morita S., Geometry of Differential Forms (Translations of Mathematical Monographs, Vol. 201).
Boothby, W., An Introduction to Differentiable Manifolds and Riemannian Geometry.
Tu, L., An Introduction to Manifolds.
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: Makeup 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 2773506. In addition, they should see CATS
Counseling and Therapy Services;
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 

Jan. 21 (MLK) 


Jan. 28 
2. Smooth manifolds, smooth maps. 

Feb. 4 


Feb. 11 


Feb. 18 
5. Vector bundles  equivalent definitions, maps between vector bundles. 

Mar. 25 
6. Vector bundles. The cotangent bundle. 

Mar. 4 
7. Submanifolds: submersions, immersions, embeddings, regular submanifolds; the rank theorem; regular level sets; Sard's theorem. Midterm Exam 

Mar. 11 
Spring
Break 

Mar. 18 


Mar. 25 


Apr. 1 


Apr. 8 
10. Differential forms  operatiions, integration, de Rham cohomology 

Apr. 15 


Apr. 22 


Apr. 29 


May 6 Finals week 
Wednesday, May 8, 10:00–12:00 

HOLIDAYS/BREAKS
Spring Break March 1017, 2013
Finals Week May 611, 2013
Martin Luther King, Jr. Day: January 21, 2013