MA 235-Introduction to Differentiable Manifolds Spring 2024 - Vamsi Pritham Pingali


The texts we will be referring to are as follows :
1. John Lee, Introduction to Smooth Manifolds (primary text).
2. Frank Warner, Foundations of Differentiable Manifolds and Lie Groups.

The course description (along with pre-requisites) can be found on this webpage.

Instructors : Vamsi Pritham Pingali, vamsipingali@iisc.ac.in

Classroom and timings : LH-4, Tu, Thu 3:30-5

Teaching Assistant: Aashirwad N. Ballal

Tutorials: Wed from 4-5

The Grading policy : 20% for the HW, 30% for the Midterm, and 50% for the Final.

Exams:

The Midterm shall be held on Feb 22 (Thur) 3-5 PM in LH-4. The syllabus is everything taught until then (including all of Harish's lectures).

The Final shall be held on TBA. The syllabus will be everything taught in this course.

Ethics: Read the information on the IISc student ethics page. In short, cheating is a silly thing. Don't do it. As for the quizzes based on HW, write them up on your own. You are NOT allowed to discuss them amongst yourselves.

Here is the tentative schedule. (It is subject to changes and hence visiting this webpage regularly is one of the best ideas in the history of best ideas.)

Week

 Dates

 Syllabus covered

1

1 Jan - 7 Jan

Logistics, review of multivariable calculus - continuity, differentiability, chain rule (Tuesday notes), review of multivariable calculus - Clairaut's theorem, Taylor's theorem, second derivative test (Thursday notes)

2

8 Jan - 14 Jan

Bump functions, Inverse function theorem (Tuesday notes), Implicit function theorem and Lagrange's multipliers (Thursday notes)

3

15 Jan - 21 Jan

Smooth manifolds - definition and examples (Tuesday notes), Manifolds-with-boundary (Thursday notes)

4

22 Jan - 28 Jan

Smooth functions on manifolds (Tuesday notes), Partitions-of-unity (Thursday notes)

5

29 Jan - 4 Feb

Tangent spaces (Tuesday notes), Thursday-taught by Harish

6

5 Feb - 11 Feb

Harish's lectures

7

6 Feb - 18 Feb

Harish's lectures (My take on the material taught by him)

8

19 Feb - 25 Feb

Midterm week

9

26 Feb - 3 Mar

Regular value theorem, definition of smooth vector fields (Tuesday notes), Tangent bundle and vector bundles (Thursday notes)



The power of the HW compels you

Week

 HW to be submitted on

 Homework (subject to changes; please check regularly)

1

12 Jan

HW 1

2

31 Jan

HW 2

4

7 Feb

HW 3

5

14 Feb

HW 4

10

8 Mar

HW 5