TEW - Real Analysis, Algebra and Number Theory with some Applications (2023)
Speakers and Syllabus
| S.No. | Name | Affiliation | Number of Lecture hours (L) and Tutorial hours (T) |
| 1 | Prof. Kalyan Chakraborty (Main Speaker-1) | Director & Professor, KSCSTE-Kerala School of Mathematics, Kozhikode, Kerala, India |
6 L + 2 T |
| 2 | Prof. Geetha Venkataraman (Main Speaker-2) | Professor of Mathematics, School of Liberal Studies, Dr. B. R. Ambedkar University Delhi, India |
8 L + 2 T |
| 3 | Prof. Varadharaj R. Srinivasan (Main Speaker-3) | Associate Professor, Department of Mathematical Sciences, IISER Mohali, India |
8 L + 2 T |
| 4 | Dr. Jyoti Singh (Guest Speaker-1) | Assistant Professor, Department of Mathematics, VNIT, Nagpur, India |
1 L |
| 5 | Dr. Charu Goel (Guest Speaker-2) |
Assistant Professor of Mathematics, Department of Basic Sciences, IIIT Nagpur, India |
1 L |
| 6 | Dr. Richa Sharma (Tutor-1) | PostDoc Fellow, Institute of Mathematical Sciences (IMSc), India |
2 T |
| 7 | Ms. Neelam (Tutor-2) | Teaching Assistant, Department of Mathematics, Ashoka University, India |
2 T |
| 8 | Dr. Rahul V. Mapari (Tutor-3) | Assistant Professor, Department of Mathematics, Government Vidarbha Institute of Science and Humanities, Amravati, India |
2 T |
(B) Course Contents
| Topic | Number of lecture hours | Number of tutorial hours | Syllabus to be covered | Name of the Speaker |
| Real Analysis | 8 | 2 | Finite, countable and uncountable sets, R as complete ordered field, Sequences and their convergence, Continuous functions and their properties. | Prof. Varadharaj R. Srinivasan |
| Algebra | 8 | 2 | Some history, Quick review of basic group theory: groups, subgroups, homomorphisms, quotient groups, Groups Acting on Sets, Burnside's Lemma and Applications. Cayley's Theorem, Cauchy's Theorem, Class equation, Sylow's Theorems and applications, Exploring Symmetry with an emphasis on the group of rigid motions of a plane. | Prof. Geetha Venkataraman |
| Number Theory | 6 | 2 | Multiplicative functions (basics, Mobius inversion formula), Modular arithmetic (Wilson's theorem, Fermat little theorem, etc.), Primitive roots modulo some prime powers, Quadratic residues, Representation of integers by some quadratic forms, Continues fractions. | Prof. Kalyan Chakraborty |
Reference Books:
(i) Introduction to real analysis by Robert G. Bartle and Donald R. Sherbert
(ii)Introduction to real analysis by William F. Trench
(iii) Contemporary Abstract Algebra by Joseph A. Gallian
(iv)Abstract Algebra by D. S. Dummit and R. M. Foote
(v)Reciprocity Laws: from Euler to Eisenstein by F. Lemmermeyer
(vi)Elementary Number Theory by G. A. Jones and J. M. Jones
(vii) A comprehensive course in number theory by A. Baker
Time Table
| Day | Date | Lecture 1 09:30 AM to 10:30 AM |
10.30 to 11.00 AM | Lecture 2 11.00 AM to 12.00 PM |
Lecture 3 12:00 PM to 01.00 PM |
Break 01.00 PM to 02.30 PM |
Lecture 4 02.30 PM to 03:30 PM |
03.30 PM to 04:00 PM |
Discussion/ Tutorial 04.00 PM to 05:00 PM |
05.00 PM to 05.30 PM |
| Mon | 03rd July | KC (L) | KC (L) | KC (L) | GV (L) | KC + RS (T) | S | |||
| Tue | 04th July | GV (L) | T | KC (L) | KC (L) | L | KC (L) | T | KC + RS (T) | N |
| Wed | 05th July | VS (L) | E | VS (L) | GV (L) | U | GV (L) | E | GV + N (T) | A |
| Thu | 06th July | GV (L) | A | GV (L) | VS (L) | N | VS (L) | A | VS + RM (T) | C |
| Fri | 07th July | GV (L) | GV (L) | VS (L) | C | VS (L) | GV + N (T) | K | ||
| Sat | 08 th July | VS (L) | VS (L) | JS (L) | H | CG (L) | VS+ RM (T) | S |