Convener(s)
| Name: | Prof. Arvind | Dr. Ved Prakash Gupta | Dr. Manisha Saini |
| Mailing Address: | Professor, Department of Mathematics Hansraj College, Mahatama Hansraj Marg Malka Ganj, Delhi 110007 |
Assistant Professor School of Physical Sciences Jawaharlal Nehru University New Delhi 110067 |
Assistant Professor, Department of Mathematics Hansraj College, Mahatama Hansraj Marg Malka Ganj, Delhi 110007 |
| Email: | drarvind at hrc.du.ac.in | vedgupta at jnu.ac.in | manishasaini at hrc.du.ac.in |
A Teachers’ Enrichment Workshop is funded by the National Center for Mathematics (NCM) to introduce college mathematics teachers to interesting topics in the basic subjects they teach at graduation or post-graduation level. This workshop is basically aimed at teachers of different colleges and universities of NCR Delhi. (Interested teachers from other regions, who can manage their travel, lodging and food on their own, may also apply.)
Objective of the workshop: With the inclusion of courses on Functional Analysis and Galois Theory as core courses in the 4-year BSc curriculum, it has become imperative to refresh the knowledge and understanding of the fundamental topics associated to these theories among the college teachers.
With this objective, this workshop intends to revisit some fundamental concepts of Functional Analysis and Galois Theory in an interactive way so as to rekindle the joy of learning concepts and solving problems related to these indispensable branches of modern Mathematics. The participants are expected to have rigorous interactive sessions and derive maximum benefit from this workshop.
Dates:
Venue:
Venue Address:
Hansraj College, University of Delhi
Mahatama Hansraj Marg, Malka Ganj
Delhi 110007
Venue State:
Venue City:
PIN:
Syllabus:
|
Name of the Speaker with affiliation |
No. of Lectures |
Detailed Syllabus |
|
Dr. A. Satyanarayana Reddy
Department of Mathematics, |
6 |
Field Extensions, Algebraic Extensions, Splitting FieldsTopics: Fields, prime subfields, Field extensions, degree, tower theorem, Algebraic and transcendental elements / extensions, Monomorphisms of field extensions, Splitting fields, Uniqueness of splitting field Normal extensions, Introduction to cyclotomic fields, Ruler and compass constructions (brief, if time permits) Tutorial 1: Problems on degree of extensions, tower theorem, finding splitting fields, constructing monomorphisms. Suggested Texts:
|
|
Dr. Anuj Bishnoi,
Department of Mathematics, University of Delhi |
6 |
Galois Extensions, Fundamental Theorem of Galois TheoryTopics Covered: Separability, separable extensions, Automorphism groups, Galois groups, Fixed fields, Galois extensions, Fundamental theorem of Galois theory, Galois theory of polynomials, Solution by radicals (if time permits)
Tutorial 2: Normal and separable extensions, computation of Galois groups Tutorial 3: Applications of the Fundamental Theorem (correspondence, intermediate fields) Suggested Texts:
|
| Dr. Aparajita Dasgupta, Department of Mathematics, IIT Delhi |
6 |
Basics of normed spaces Basics aspects of normed spaces, Some examples, Finite dimensional normed spaces and local compactness, Local compactness lost in infinite dimensional normed spaces, Separability in normed spaces Suggested Texts:
|
| Dr. Ved Prakash Gupta School of Physical Sciences, Jawaharlal Nehru University |
6 |
Fundamental theorems, Hilbert spaces and bounded operators Operators between normed spaces, Hahn-Banach Theorem (statement) and applications, Some category theorems (statements) and applications, Hilbert spaces, Riesz representation theorem, various types of operators between Hilbert spaces Suggested Texts:
|
Name of the tutors:
|
S. No. |
Name |
Affiliation |
|
1 (For Functional Analysis) |
Dr. Rachna Aggarwal
|
Department of Mathematics, |
|
Dr. Ashutosh Pandey
|
Department of Applied Sciences and Humanities, |
|
|
2 (For Galois Theory) |
Dr. Manisha Saini
|
Department of Mathematics, |
|
Dr. Ashima |
Department of Mathematics, |
Time Table:
|
09:30 - 10:30 |
10:30-11:00 |
11:00-12:00 |
12:00 - 13:00 |
13:00-14:30 |
14:30 - 15:30 |
15:30 - 16:00 |
16:00 - 17:00 |
|
|
Day 1 |
AD |
Tea Break |
ASR |
AD |
Lunch Break |
ASR |
Tea Break |
RA + AP + AD |
|
Day 2 |
AD |
ASR |
AD |
ASR |
MS + AA + ASR |
|||
|
Day 3 |
AD |
ASR |
AD |
ASR |
RA + AP + AD |
|||
|
Day 4 |
VPG |
AB |
VPG |
AB |
MS + AA + AB |
|||
|
Day 5 |
VPG |
AB |
VPG |
AB |
RA + AP + VPG |
|||
|
Day 6 |
VPG |
AB |
VPG |
AB |
MS + AA + AB |
Full forms for the abbreviations of speakers and tutors:
-
Speakers
Tutors
Dr. Aparajita Dasgupta (AD)
Dr. A. Satyanaraya Reddy (ASR)
Dr. Ved Prakash Gupta (VPG)
Dr. Anuj Bishnoi (AB)
Dr. Rachna Aggarwal (RA)
Dr. Ashuthosh Pandey (AP)
Dr. Manisha Saini (MS)
Dr. Ashima (AA)
Selected Applicants:
How to Reach:
TBA