TEW - Real Analysis and Group Theory (2025)
Speakers and Syllabus
|
Name of the Speaker with affiliation |
No. of Lectures |
Detailed Syllabus |
|
Dr. Surinder Pal Singh Kainth Associate Professor Department of Mathematics Panjab University |
6 |
Completeness axiom, Sequences and their limits, Convergent sequence, Limit theorems, Monotone sequences, Monotone convergence theorem, Subsequences, Bolzano Weierstrass theorem for sequences, Limit superior and limit inferior for sequence, Cauchy sequence, Cauchy’s convergence criterion |
|
Dr Saurabh Verma Assistant Professor Department of Applied Sciences IIIT Allahabad |
6 |
Limits of functions, sequential criterion for limits, divergence criteria, Continuous functions and its properties, Uniform continuity, Differentiability of a real-valued function, Chain rule, Relative extrema, Interior extremum theorem, Rolle’s theorem, Mean-value theorem and its applications, Intermediate value theorem for derivatives |
|
Dr. Dinesh Khurana Professor Department of Mathematics Panjab University |
6 |
Groups, subgroups, Lagrange theorem, quotient groups, isomorphism theorems, symmetric groups, alternating groups, simple groups, simplicity of alternating groups, Group action, Sylow theorems and applications |
|
Dr. Amit Kulshrestha Professor Department of Mathematical Sciences, IISER, Mohali |
6 |
Classification of finite abelian groups. Finitely-generated abelian groups, Free groups, Composition series, Jordan-Hölder theorem, Nilpotent and solvable groups |
References:
1. Algebra, M. Artin, Second Edition
2. Contemporary Abstract Algebra, Joseph Gallian
3. Abstract Algebra, David S. Dummit and Richard M. Foote.
4. Elementary Analysis: The Theory of Calculus, Ross, Kenneth A.
5. A Course in Calculus and Real Analysis, Ghorpade, Sudhir R. and Limaye, B. V. (2006)
6. Introduction to Real Analysis, Bartle, Robert G., & Sherbert, Donald R.
Name of the tutors:
|
S. No. |
Name |
Affiliation |
|
1 |
Dr. Ridhima Thakral |
Punjab Engineering College |
|
2 |
Dr. Swati Bhardwaj |
Punjab Engineering College |
|
3 |
Mr. Kushal Singh |
Punjab Engineering College |
|
4 |
Ms. Kamalpreet Kaur |
Punjab Engineering College |
Time Table
Time-table (with names of speakers and tutors):
|
Day |
Date |
Lecture 1 (9.30–10.30) |
Tea (10.35-10.55) |
Lecturer 2 (11.00–12.00) |
Lecture 3 (12.00–1.00) |
Lunch (1.00 – 2.20) |
Lecture 4 (2.30-3.30) |
Tea (3.35 -3.55) |
Discussion (4.00-500) |
Snacks (5.05 – 5.35) |
|
Mon |
|
SP |
|
SP |
DK |
|
DK |
|
SP+KS+KK |
|
|
Tue |
|
SP |
|
SP |
DK |
|
DK |
|
DK+SB+RT |
|
|
Wed |
|
SP |
|
SP |
DK |
|
DK |
|
SP+KS+KK |
|
|
Thu |
|
SV |
|
SV |
AK |
|
AK |
|
SV+KS+KK |
|
|
Fri |
|
SV |
|
SV |
AK |
|
AK |
|
AK+SB+RT |
|
|
Sat |
|
SV |
|
SV |
AK |
|
AK |
|
AK+SB+RT |
|
Full forms for the abbreviations of speakers and tutors:
Speakers:
SP: Surinder Pal Singh Kainth
SV: Saurabh Verma
DK: Dinesh Khurana
AK: Amit Kulshrestha
Tutors:
RT: Ridhima Thakral
SB: Swati Bhardwaj
KS: Kushal Singh
KK: Kamalpreet Kaur