IST - Algebra
Speakers and Syllabus
|
Name of the Speaker with affiliation |
No. of Lectures |
Detailed Syllabus |
|
Sasmita Barik (SB) |
6 | Course-1 (Vector Spaces ): Matrices (basic operations, row reduction, system of linear equations, determinants), vector space: examples, bases and dimension, computing with bases, direct sum, linear transformations, The rank-nullity theorem, The matrix of a linear transformations, Dual vector spaces, linear operators, eigenvectors, eigenvalues, characteristic polynomials, triangulations, diagonalisations, Jordan forms |
|
Binod Kumar Sahoo (BKS), NISER Bhubaneswar. |
6 | Course-2 (Group Theory) : Groups: examples (dihedral groups, symmetric groups matrix groups, The quaternion group), homomorphisms, subgroups (examples, Alternating groups, centralizers, normalizers), subgroup generated by subset of a group, lattice of subgroups, cosets, Lagrange’s Theorem, normal subgroups, quotient groups, Isomorphism Theorems, Direct product of groups, Group actions: examples, permutation representations, Cayley’s Theorem, The Class equation, Sylow’s Theorem, symmetries of plane figures. |
|
Kamal Lochan Patra (KLP) |
6 | Course-3 (Ring Theory) Rings: examples of rings, polynomial rings, homomorphisms, ideals, quotient rings, properties of ideals, Ring of fractions, prime and maximal ideals, Chinese Reminder Theorem, Euclidean Domains, Principal Ideal Domains, Unique Factorization Domains. Gauss’s Lemma, Polynomial rings over a Field, Irreducibility Criteria. |
|
Brundaban Sahu (BS) |
6 | Course-4 (Field Theory) : Fields: examples of fields, finite fields, Field extension, algebraic elements, degree of field extensions, ruler and compass constructions, adjoining roots and splitting fields, separable extension, algebraically closed fields and algebraic closure, cyclotomic polynomials, Galois group, The Fundamental Theorem of Galois Theory. |
Course Associates:
1. Ms. Raveena Ganash (RG), (4th year Ph. D. Student), NISER Bhubaneswar
2. Mr. Arnab Mitra (AM), (3rd year Ph. D. Student), NISER Bhubaneswar
3. Mr. Devjyoti Das (DD), (4th year Ph. D. Student), NISER Bhubaneswar
4. Mr. Akash De (AD), (3rd year Ph.D. student), NISER Bhubaneswar
Time Table
Time-Table (with names of speakers and course associates/tutors):
|
Day |
Date |
9:30-11.00 |
11.00-11:30 |
11:30-1:00 |
1:00-2:30 |
2:30-3:30 |
3:30-4:00 |
4.00-5.00 |
||
|
|
|
(nameofthe speaker) |
|
(name of thespeaker) |
|
(nameofthe speaker + tutors) |
|
(name of the speaker+tutors) |
||
|
Mon |
01-06-26 |
L1 (SB) |
T |
L2 (BKS) |
L |
SB+T1,T2 |
T |
BKS+T3,T4 |
||
|
Tues |
02-06-26 |
L3 (SB) |
|
L4 (BKS) |
U |
SB+T1,T2 |
E |
BKS+T3,T4 |
||
|
Wed |
03-06-26 |
L5 (SB) |
E |
L6 (BKS) |
N |
SB+T1,T2 |
A |
BKS+T3,T4 |
||
|
Thu |
04-06-26 |
L7 (SB) |
|
L8 (BKS) |
C |
SB+T1,T2 |
|
BKS+T3,T4 |
||
|
Fri |
05-06-26 |
L9 (SB) |
A |
L10(BKS) |
H |
SB+T1,T2 |
|
BKS+T3,T4 |
||
|
Sat |
06-06-26 |
L11(SB) |
|
L12(BKS) |
|
SB+T1,T2 |
|
BKS+T3,T4 |
||
|
Sun |
07-06-26 |
Off |
||||||||
|
Mon |
08-06-26 |
L13(KLP) |
T |
L14(BS) |
L |
KLP+T1,T2 |
T |
BS+T3,T4 |
||
|
Tues |
09-06-26 |
L15(KLP) |
|
L16(BS) |
U |
KLP+T1,T2 |
E |
BS+T3,T4 |
||
|
Wed |
10-06-26 |
L17(KLP) |
E |
L18(BS) |
N |
KLP+T1,T2 |
A |
BS+T3,T4 |
||
|
Thu |
11-06-26 |
L19(KLP) |
|
L20(BS) |
C |
KLP+T1,T2 |
|
BS+T3,T4 |
||
|
Fri |
12-06-26 |
L21(KLP) |
A |
L22(BS) |
H |
KLP+T1,T2 |
|
BS+T3,T4 |
||
|
Sat |
13-06-26 |
L23(KLP) |
|
L24(BS) |
|
KLP+T1,T2 |
|
BS+T3,T4 |
||