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 1112 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), Midterm40%, 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 9:3011:30 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 
Vectorvalued functions, RiemannStieltjes integral (Wednesday notes), (Thursday notes), (Friday notes) 
11 
13 March  17 March 
RiemannStieltjes 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 ArzelaAscoli (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 