The calendar here is tentative, and the topics discussed and specific dates are subject to change. Numbers in parentheses denote the corresponding section from Guillemin and Pollack, Differential Topology, unless otherwise noted.

Week 1:
Fri. 8/29	Topologies, open and closed sets, interior, closure, and boundary (Hatcher pp. 1-7)
Week 2:
Mon. 9/1	No class
Wed. 9/3	Bases, metric spaces, and subspaces (Hatcher pp. 7-12)
Fri. 9/5	Continuity, product spaces (Hatcher pp. 12-16)
Week 3:
Mon. 9/8	Connectedness, compactness (Hatcher pp. 18-21, 30-33)
Wed. 9/10	Separation axioms (Hatcher pp. 34-38)
Fri. 9/12	Smooth manifolds, smooth maps, coordinate systems (1.1)
Week 4:
Mon. 9/15	Derivatives and tangents (1.2)
Wed. 9/17	Derivatives and tangents (1.2)
Fri. 9/19	Inverse function theorem (1.3)
Week 5:
Mon. 9/22	Immersions (1.3)
Wed. 9/24	Embeddings and submersions (1.3, 1.4)
Fri. 9/26	Transversality (1.5)
Week 6:
Mon. 9/29	Homotopy and stability (1.6)
Wed. 10/1	Homotopy and stability (1.6)
Fri. 10/3	Review: manifolds and tangent spaces
Week 7:
Mon. 10/6	Measure and Sard's theorem (1.7)
Wed. 10/8	Weak Whitney immersion theorem (1.8)
Fri. 10/10	Whitney embedding theorem (1.8)
Week 8:
Mon. 10/13	Chapter 1 exercises
Wed. 10/15	Chapter 1 exercises
Fri. 10/17	Chapter 1 exercises
Week 9:
Mon. 10/20	Midterm
Wed. 10/22	Manifolds with boundary (2.1)
Fri. 10/24	Manifolds with boundary (2.1)
Week 10:
Mon. 10/27	Morse functions, one manifolds (1.7, Appendix 2)
Wed. 10/29	Brouwer fixed point theorem (2.2)
Fri. 10/31	Tranversality (2.3)
Week 11:
Mon. 11/3	Epsilon neighborhood theorem (2.3)
Wed. 11/5	Intersection Theory Mod 2 (2.4)
Fri. 11/7	Intersection Theory Mod 2 (2.4)
Week 12:
Mon. 11/10	Winding numbers, Jordan-Brouwer separation theorem (2.5) --with Hongbin Sun
Wed. 11/12	Winding numbers, Jordan-Brouwer separation theorem (2.5)--with Kathryn Mann
Fri. 11/14	Winding numbers, Jordan-Brouwer separation theorem (2.5)
Week 13:
Mon. 11/17	Application: S2 and T2 are not diffeomorphic
Wed. 11/19	Borsuk-Ulam Theorem (2.6)
Fri. 11/21	Borsuk-Ulam Theorem (2.6)
Week 14:
Mon. 11/24	Epsilon neighborhood theorem for compact manifolds, partitions of unity (2.3, 1.8)
Wed. 11/26	Epsilon neighborhood theorem and Whitney embedding theorem for non-compact manifolds (1.8, 2.3)
Fri. 11/28	No class
Week 15:
Mon. 12/1	Overview of oriented intersection theory (3.1-6)
Wed. 12/3	Overview of integration (4.1-9)
Fri. 12/5	Overview of Morse theory
RRR Week:
TBD	Review
Final Examinations:
Thurs. 12/18	Final exam 7-10pm