Announcements. Lectures will begin on Monday, January 01, 2024! The second lecture will be held during the UM 205 tutorial slot on Tuesday, January 02, in G-21 (OPB). The third lecture will be on Wednesdary, January 03, during the usual lecture time. There will be no tutorial on Thursday, January 05 and no lectures on Friday, January 05, and Monday, January 08.

To join the MS Teams page for this course, please drop me an email.

Course Description. Coming up.

Broadly speaking, we will cover the topics listed here. However, to keep track of the precise syllabus, see the calendar at the bottom of this page. It will be updated on a weekly basis.

Suggested books.
  • (Main reference) W. Rudin, Principles of Mathematical Analysis, 3rd edition.
  • T. Tao, Analysis–I, 3rd Ediition.
  • T. M. Apostol, Mathematical Analysis, 2nd edition.

Instructor. Purvi Gupta
Office. L-25 (Math)
Email. purvigupta
  • Biltu Dan (✉biltudan)
  • Rumpa Masanta (✉rumpamasanta)

Lecture timings. MW Noon - 12:50 pm, Th. 9-9:50 am.
Lecture room. G21, Old Physics Building
Tutorials Fridays, 12 - 12:50 pm
Section Location Instructor
A G01, OPB Rumpa
B G21, OPB Biltu

Office hours will be held

by in during for
Purvi L25 (Math) W 5-6 pm the entire class

by in during for
Rumpa L26 (Math) Tu 6-7 pm Section A
Biltu R28 (Math) Tu 5-6 pm Section B

HW Assignments. A list of problems will be posted on MS TEAMS (almost) every Wednesday evening. These are not meant for submission, but only for self-study. You are expected to work on these problems on your own (this is not a team sport) before the subsequent tutorial, where (1) the TA will moderate a discussion on this problem set, and (2) you will answer a written based on it. The TA will not be helpful if they perceive any lack of preparation.

Evaluation Scheme.  

Course materials. You will be added to the UM 204 MS Teams page, where you can access your grades and other course materials.

Course Calendar. Topics and assignments will be updated here. Tutorials are highlighted in yellow.

Lec.# Date Topics Assignments, etc.
Week 1
1. 01/01 From natural numbers to integers
2. 02/01 From integers to rational numbers
3. 03/01 Gaps in Q; complete ordered fields HW 1 posted
04/01 NO CLASS
05/01 No tutorial this week
Week 2
08/01 NO CLASS
4. 10/01 R via Dedekind cuts
5. 11/01 R via Cauchy sequences HW 2 posted
12/01 Tutorial 1 + Quiz 1
Week 3
6. 15/01 The l.u.b. property of R
7. 17/01 Complex numbers; metric spaces: definitions, examples
8. 18/01 Open & closed sets I
19/01 Tutorial 2 + Quiz 2
Week 4
9. 22/01 Open and closed sets II HW 3 to be posted
10. 24/01 Compact sets
11. 25/01 Compact sets in Euclidean spaces
26/01 No tutorial this week
Week 5
12. 29/01 Connectedness
13. 31/01 The Cantor set
14. 01/02 Sequences in metric spaces HW 4 to be posted
02/02 Tutorial 3+ Quiz 3
Week 6
15. 05/02 Subsequences and Cauchy sequences
16. 07/02 Completeness of metric spaces
17. 08/02 The extended real line, lim inf & lim sup HW 5 to be posted
09/02 Tutorial 4+ Quiz 4
Week 7
18. 12/02 lim inf & lim sup contd.
14/02 Class cancelled
15/02 Recap
16/02 No tutorial this week.
Week 8
Midterm Week
Week 9
19. 26/02 Series, definition, examples & properties
20. 28/02 Cauchy condensation test, defining the constant e, power series
21. 29/02 Combining series (addition, termwise product, product)
01/03 Quiz 5
Week 10
22. 04/03 Rearrangements, functional limits HW 6 to be posted
23. 06/03 Continuity
24. 07/03 Discontinuities
08/03 No tutorial this week