Lectures: Wednesday, 16:30 ~ 17:20 and Friday 10:20 ~ 12:10 at Astro-Math 102
Office hours: Tuesday 11:00 ~ 11:45 and 16:00 ~ 17:00, or by appointment, at Astro-Math 458 Office hour during the exam week: 16:00 ~ 17:00 on January 13th and 14th (Tuesday and Wednesday).
Grading scheme:
Homework 30%
You have three jokers: the lowest three grades will be discarded.
Midterm 30%
Final Exam 35%
The final exam will be held on January 16th (Friday), from 9:30 to 12:10.
Course participation 5%
Course Assistant: Yu-Ching Sun, whose office is Astro-Math 445.
(10/03) tangent bundle and cotangent bundle. Reference: [T, §3]
(10/08) vector field and derivation, maps between vector bundles. Reference: [T, §3]
(10/15) subbundle and quotient bundle. Reference: [T, §4] and note1015
(10/17) pull-back bundle, symmetric square and exterior powers of cotangent bundle, push-forward and pull-back, exterior derivative. Reference: [T, §4, §5 and §12.1]
(10/22) exterior derivative, orientation and integration, de Rham cohomologies. Reference: [T, §12.1 and §12.2] and [BT, §3]
(10/24) manifold with boundary, Stokes theorem, the notion of left/right invariant for Lie groups, exponential map for matrix groups. Reference: [BT, §3] and [T, §5.4 and §5.5]
(10/29) exponential map (continued), almost complex structure. Reference: [T, §2.4 and §6]
(10/31) complex vector bundle, orientation for vector bundle, metric on vector bundle. Reference: [T, §6 and §7]