Convener(s)
| Name: | Prof. Brundaban Sahu | Prof. Binod Kumar Sahoo |
| Mailing Address: | Professor School Mathematical Sciences National Institute of Science Education and Research (NISER) Bhubaneswar Via-Jatni, Khurda-752050, Odisha, India |
Professor School Mathematical Sciences National Institute of Science Education and Research (NISER) Bhubaneswar Via-Jatni, Khurda-752050, Odisha, India |
| Email: | brundaban.sahu at niser.ac.in | bksahoo at niser.ac.in |
The objective is to increase the knowledge of the fundamentals of the college teachers and Ph.D. scholars working in Algebra and increase problem-solving abilities. Emphasis will be given on basic examples. The program will be largely interactive.
The syllabus of the proposed summer school has been designed in such a way so that the major part of the school will be devoted to foundational concepts. This Instructional School for Teachers will discuss the topics from linear algebra, group theory, ring theory and field theory, primarily using the book Algebra by M. Artin and Abstract Algebra by D. S. Summit and R. M. Foote.
Dates:
Venue:
Venue Address:
School Mathematical Sciences
National Institute of Science Education and Research (NISER) Bhubaneswar Via-Jatni, Khurda-752050, Odisha, India
Venue State:
Venue City:
PIN:
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 |
||
Selected Applicants:
How to Reach:
TBA