TEW - Groups, Rings and Number Theory (2022)
Speakers and Syllabus
Speaker |
Affiliation |
Topic(s) |
Number of lecture hours |
Number of tutorial hours |
ShantaLaishram | ISI Delhi | Number Theory | 6 | 4 |
B.Sury | ISI Bangalore | Groups | 6 | 4 |
RamdinMawia | ISI Bangalore | Rings | 6 | 4 |
S.SaratSingh | Mizoram University, Aizawl | Group/NumberTheory | 0 | 3 |
JayPSingh | Mizoram University, Aizawl | Number Theory/Fields | 0 | 3 |
JamalHussain | Mizoram University, Aizawl | Number Theory/Ring | 0 | 3 |
M.Sundararajan | Mizoram University, Aizawl | Ring/Group | 0 | 3 |
Detailed Syllabus
- Syllabus to be covered by B. Sury: Group Representations
- Basic definitions and first examples
- Irreducible Representations
- Unitary Representations
- Maschke’s theorem and complete reducibility
- Character Theory and the Orthogonality Relations
- Schur’s Lemma
- Proof of the Orthogonality Relations
- Representations of SU2
- Reference books: Chapter 10 of Algebra by M Artin and Representation Theory of Finite Groups by B. Steinberg
- Syllabus to be covered by S. Laishram: Primitive Roots and Quadratic Reciprocity Law
- Motivation
- Polynomials and Primitive Roots
- Existence of primitive roots
- Primitive Roots to Composite Moduli
- Explicit description of the group U (Z/nZ) for arbitrary n.
- Power Residues and Quadratic Residues
- Gauss’s Lemma and Quadratic Reciprocity Law
- Applications
- Reference book: Chapter 4 and 5 of A Classical Introduction to Modern Number Theory by K. Ireland and M. Rosen; Chapter 3 of Elementary Methods in Number Theory by M. Nathanson.
- Syllabus to be covered by R. Mawia: Quadratic Number Fields
- Algebraic Integers
- Factoring Algebraic Integers
- Ideal Multiplication and Factoring Ideals
- Prime Ideals and Prime Integers
- Ideal Classes
- Computing the Class Group
- Real Quadratic Fields
- Reference book: Chapter 13 of Algebra by M Artin.
Time Table
Time Table
Time | 0930 to 1100 |
1130 to 1300 |
1400 to 1500 |
1530 to 1630 |
||||
Mon 12 Dec | BSL1 | SLL1 | L | BS/SST1 | SL/JPT1 | S | ||
Tue 13 Dec | SLL2 | T | RML1 | U | SL/JHT2 | T | RM/MST1 | N |
Wed 14 Dec | RML2 | E | BSL2 | N | RM/JPT2 | E | BS/SST2 | A |
Thu 15 Dec | BSL3 | A | SLL3 | C | BS/MST3 | A | SL/JHT3 | C |
Fri 16 Dec | SLL4 | RML3 | H | SL/SST4 | RM/JPT3 | K | ||
Sat 17 Dec | RML4 | BSL4 | RM/JHT4 | BS/MST4 |