Ph229: Advanced Mathematical
Methods of Physics

Textbook: C. Nash and S. Sen.
"Topology and Geometry for Physicists".

Other useful books: V. A. Vassiliev, "Introduction to Topology," A. Hatcher, "Algebraic Topology", S. Morita, "Geometry of differential forms".

Topics to be covered:

topological spaces

homotopy groups

homology and cohomology

manifolds and calculus on manifolds

vector and principal bundles and connections on them

spinors and the Dirac equation,

characteristic classes of vector bundles

index theorems

My office: 420 Downs. Office hour: Friday 1:30-2:30.

TA: Lev Spodyneiko, 446 Lauritsen. Office hours: Wednesday 4-7 pm.

HW will be posted on this page every week on Friday. Due next Thursday by 12 pm. Please put the HW into Lev's mailbox on the 4th floor of Downs-Lauritsen.

Passing grade: >50% of the maximal possible total number of points on HW. Each problem (or a sub-problem of a problem, if it has sub-problems) is worth 10 pts. Ask me for an extension if you need one, otherwise the HW will not be accepted.

**Homework **

Week 1 (due Oct. 10) Week 2 (due Oct. 17) Week 3 (due Oct. 24) Week 4 (due Oct. 31) Week 5 (due Nov. 7)

Week 6 (due Nov. 14) Week 7 (due Nov. 21) Week 8 (Dec. 2)

Other useful books: V. A. Vassiliev, "Introduction to Topology," A. Hatcher, "Algebraic Topology", S. Morita, "Geometry of differential forms".

Topics to be covered:

topological spaces

homotopy groups

homology and cohomology

manifolds and calculus on manifolds

vector and principal bundles and connections on them

spinors and the Dirac equation,

characteristic classes of vector bundles

index theorems

My office: 420 Downs. Office hour: Friday 1:30-2:30.

TA: Lev Spodyneiko, 446 Lauritsen. Office hours: Wednesday 4-7 pm.

HW will be posted on this page every week on Friday. Due next Thursday by 12 pm. Please put the HW into Lev's mailbox on the 4th floor of Downs-Lauritsen.

Passing grade: >50% of the maximal possible total number of points on HW. Each problem (or a sub-problem of a problem, if it has sub-problems) is worth 10 pts. Ask me for an extension if you need one, otherwise the HW will not be accepted.

Week 1 (due Oct. 10) Week 2 (due Oct. 17) Week 3 (due Oct. 24) Week 4 (due Oct. 31) Week 5 (due Nov. 7)

Week 6 (due Nov. 14) Week 7 (due Nov. 21) Week 8 (Dec. 2)