The texts we will be following are ``Principles of mathematical analysis" (3rd edition) by Walter Rudin, and the 2 volume series ``Analysis" by Terence Tao. We will largely follow Rudin. The syllabus is roughly the first 8 chapters of Rudin. (Subject to change.)
Instructor :
Vamsi Pritham Pingali, vamsipingali@math.iisc.ernet.in.
Office : N23 in the mathematics building. (It might be a good
idea to email me if you plan on coming to my office.)
Teaching assistants : Nimisha Pahuja (nimisha14@math.iisc.ernet.in) and S. Aiyyapan (aiyappan12@math.iisc.ernet.in).
Classroom and timings : Wednesday, Thursday, Friday from 11-12 in the morning in Room G2 (Old physics building).
The Grading policy : 10% for Homeworks (one HW to be handed in on stapled sheets of paper on Fridays in the classroom), Midterm-40%, and
50% for the Final. Under NO circumstances will makeup exams be held
for the midterms. If you have a valid and provable excuse, (Schedule
conflicts with other courses do NOT constitute as valid excuses. You
are supposed to resolve them before registering for the courses.)
then your performance on the other exams shall determine your grade on your midterms.
Late HW is unacceptable.
Exams : The dates for the midterm and the final will be announced later on.
Ethics: Read the information on the
IISc student ethics page. In short, cheating is a silly thing. Don't do
it. As for homeworks, write them up on your own. You are allowed to
discuss them amongst yourselves but please write the solutions on
your own. That said I must hasten to add that you learn mathematics
best when you solve the problems entirely by yourself.
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.)
|
Wk |
Dates |
Syllabus to be covered |
|
1 |
2 Jan - 6 Jan |
Introduction, Naive set theory (done correctly) (Wednesday notes), Natural numbers, Cardinality (Thursday notes), Rational numbers (Friday notes) |
|
2 |
9 Jan - 13 Jan |
Real numbers (Wednesday notes) and (Thursday notes), Complex numbers (Friday notes) |
|
3 |
16 Jan - 20 Jan |
Euclidean space, Topology (Wednesday notes) and (Thursday notes). 20th is a holiday on account of Pravega. (The opening drama was cute :)) |
|
4 |
23 Jan - 27 Jan |
More topology (Wednesday notes) and (Friday notes), Thursday (26th) is a holiday. |
|
5 |
30 Jan - 3 Feb |
Sequences (Wednesday notes) , Series (Thursday notes), The number e, Tests of convergence (Friday notes) |
|
6 |
6 Feb - 10 Feb |
Absolute and conditional convergence (Wednesday notes), Revision ((Thursday notes) and (Friday notes)) |
|
7 |
13 Feb - 17 Feb |
Midterm week. Midterm solutions(Your midterm will be held on Tuesday, 14th Feb from 9:30-11:30 in the morning in the rooms G1 and G21. The syllabus is everything we have done until (and including) Sequences (but no series).) |
8 |
20 Feb - 24 Feb |
Rearrangements (Wednesday notes), Continuity (Thursday notes), Friday (24 Feb) is a holiday |
|
9 |
27 Feb - 3 March |
Continuity cont'd.. (Wednesday notes), Differentiation, Mean value theorems (Thursday notes), L' Hospital rule, Higher order derivatives, Taylor's theorem (Friday notes) |
|
10 |
6 March - 10 March |
Vector-valued functions, Riemann-Stieltjes integral (Wednesday notes), (Thursday notes), (Friday notes) |
|
11 |
13 March - 17 March |
Riemann-Stieltjes integral, Fundamental theorem of calculus (Wednesday notes), Uniform convergence (Thursday notes), (Friday notes) |
|
12 |
20 March - 24 March |
More on uniform convergence (Wednesday notes), Equicontinuity (Thursday notes), and Arzela-Ascoli (Friday notes) |
|
13 |
27 March - 31 March |
Wednesday (29 March) is a holiday, Weierstrass approximation theorem (Thursday notes), Special functions ((Friday notes) |
|
14 |
3 April - 7 April |
Special functions (Wednesday notes), (Thursday notes), Revision ((Friday notes) |
|
Wk |
To be handed to me on |
Homework (subject to changes; please check regularly) |
|
1 |
6th Jan |
No HW due |
|
2 |
13th Jan |
No HW due |
|
3 |
19th Jan (Note that it is a Thursday) |
|
|
4 |
27th Jan |
No HW due |
|
5 |
3rd Feb |
|
|
6 |
10th Feb |
No HW due |
|
7 |
17th Feb |
No HW due (Midterm week) |
|
8 |
23rd Feb (Note the unusual day - Thursday) |
No HW due (Grace) |
|
9 |
3rd March |
|
|
10 |
10th March |
|
|
11 |
17th March |
No HW due |
|
12 |
24th March |
|
|
13 |
31st March |
No HW due |
|
14 |
7th April |