Convener(s)
| Name: | Prof. Pratulananda Das | Dr. Bikash Chakraborty |
| Mailing Address: | Professor of Mathematics Department of Mathematics Jadavpur University Kolkata - 700032 |
Assistant Professor in Mathematics Department of Mathematics Ramkrishna Mission Vivekananda Centenary College Rahara, Khardaha West Bengal Pin – 700118 |
| Email: | pratulananda at yahoo.co.in | bikashchakrabortyy at gmail.com |
In this workshop we will deal with two different directions, one being real analysis, in particular Riemann integration followed by measure theory and the other being functional analysis. These topics are being (going to be) taught in the third year and fourth year in Mathematics honours courses (4 year course under NEP which is now being implemented in West Bengal and most states from the year 2023). The main aim is to make the participants aware as to how to introduce these topics to the students in interesting ways with lots of examples and to emphasis the interplay between the topics.
Dates:
Venue:
Venue Address:
Ramakrishna Mission Vivekananda Centenary College
Rahara, Khardaha
West Bengal
Pin – 700118
Venue State:
Venue City:
PIN:
Syllabus:
|
Name of the Speaker with affiliation |
No. of Lectures |
Detailed Syllabus |
|
Prof. Shibananda Biswas IISER Kolkata |
6 |
Normed linear spaces and Banach spaces, basic properties, bounded linear operators, duals of normed linear spaces, Hahn Banach theorem, uniform boundedness principle, open mapping and closed graph theorems. Examples and applications |
|
Prof. Jaydeb Sarkar ISI Bangalore
|
6 |
Compact operators in Banach spaces and their importance, spectral theorem for compact operators. Integral operators, basic results about these operators. Computational aspects of integral operators, specifically Volterra operator. Applications and examples |
|
Dr. Bikash Chakraborty RKMVCC |
6 |
Riemann Integral, properties of Riemann integrable functions, Fundamental theorems of integral calculus, Mean value theorem, Change of variable in Riemann integration, improper Riemann integration |
|
Prof. Pratulananda Das Jadavpur University, Kolkata |
6 |
Lebesgue outer measure, Extension of the idea of length function, Lebesgue measure, measurable sets, existence of non-measurable sets, idea of measurable functions, Lebesgue integration, advantages over Riemann integration. Applications and examples |
References:
1. Topology of metric spaces, S. Kumaresan
2. Topology, J.R. Munkres
3. Topology, J.F. Simmons
(Lecture notes from the speakers, if available)
Name of the tutors:
|
S. No. |
Name |
Affiliation |
|
1 |
TBD |
Ramkrishna Mission Vivekananda Centenary College |
|
2 |
TBD |
Ramkrishna Mission Vivekananda Centenary College |
|
3 |
|
|
Time Table:
|
Day |
Date |
Lecture 1 (9.30–10.30) |
Tea (10.35-10.55) |
Lecturer 2 (11.00–12.00) |
Lecture 3 (12.00–1.00) |
Lunch (1.00 – 2.20) |
Lecture 4 (2.30-3.30) |
Tea (3.35 -3.55) |
Discussion (4.00-500) |
Snacks (5.05 – 5.30) |
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|
|
(Speaker’s name) |
|
(Speaker’s name) |
(Speaker’s name) |
|
(Speaker’s name) |
|
(Tutor’s name) |
|
|
Mon |
|
SB |
|
SB |
BC |
|
BC |
|
BC, -, - |
|
|
Tue |
|
SB |
|
JS |
PD |
|
PD |
|
PD, -, - |
|
|
Wed |
|
BC |
|
SB |
SB |
|
JS |
|
JS, -, - |
|
|
Thu |
|
JS |
|
JS |
BC |
|
SB |
|
SB, -, - |
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|
Fri |
|
BC |
|
PD |
PD |
|
JS |
|
JS, -, - |
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|
Sat |
|
PD |
|
PD |
BC |
|
JS |
|
BC, -, - |
Selected Applicants:
How to Reach:
TBA