IST - Real Analysis and its Applications to Approximation and Learning Theory (2026)
Speakers and Syllabus
|
Name of the Speaker with affiliation |
No. of Lectures |
Detailed Syllabus |
|
Dr. B. Sriram |
6 |
Review of the real number system, Infimum and Supremum, Euclidean spaces and Metric spaces, Open and closed sets, Limit points, Bolzano-Weierstrass theorem, liminf and limsup of a sequence. |
|
Dr. Surjit Kumar |
6 |
Compactness, Characterization of compact sets, Heine Borel theorem, Cauchy sequence and Complete metric space |
|
Dr. G. Arunkumar |
6 |
Limits of functions, Continuous functions, Types of discontinuities, Uniform continuity, Differentiable functions and Mean value theorem, Convergence of sequences and series of numbers. |
|
Prof. A. Swaminathan |
6 |
Sequences and series of functions, Weierstrass M-test, Uniform convergence and its relation to continuity, Differentiation, and integration, Continued fractions, Fundamental results, Convergence, Best approximation and applications, Pade approximation and Real analytic functions. |
|
Dr. A. Sathish Kumar |
6 |
Approximation of real valued functions, Bernstein operators and its properties, Weierstass approximation theorem, Korovkin theorem, Shannon sampling theorem, Convergence of sampling operators and Universal approximation theorem. |
|
Prof. S. Sivananthan |
6 |
Reproducing kernel Hilbert space, Gaussian kernel and their RKHSs, Mercer’s theorem, Probabilistic inequalities, Tikhonov-type regularization, Representer theorem and Convergence analysis of regularized learning algorithm. |
References:
-
L. Lorentzen and H. Waadeland, Continued Fractions, Volume 1: Convergence Theory, Atlantis Studies in Mathematics, 2nd edition, World Scientific, 2008.
-
H. N. Mhaskar and D. V. Pai, Fundamentals of Approximation Theory, Narosa Publishing House, 2007.
-
W. Rudin, Principles of Mathematical Analysis, Mcgraw-Hill, 1976.
-
G. F. Simmons, Topology and Modern Analysis, Kreiger, 2003.
-
D. F. Walnut, An Introduction to Wavelet Analysis, Birkhauser Boston, MA, 2003.
-
D-X. Zhou and F. Cucker, Learning Theory: An Approximation Theory Viewpoint, Cambridge University Press, 2007.
Name of the tutors:
|
S. No. |
Name |
Affiliation |
|
1 |
Dr. S. Yugesh |
Assistant Professor, Department of Mathematics, |
|
2 |
Dr. M. Sundarakannan |
Assistant Professor, Department of Mathematics, |
|
3 |
Mr. Nitin Bartwal |
Research Scholar, Department of Mathematics, |
|
4 |
Ms. Puja Sonawane |
Research Scholar, Department of Mathematics, |
|
5 |
Mr. Arpan Kumar Dey |
Research Scholar, Department of Mathematics, |
|
6 |
Mr. M. Surya |
Research Scholar, Department of Mathematics, |
Time Table
|
Day |
Date |
Lecture 1 (9.30–11.00) |
Tea (11.00 to |
Lecturer 2 (11.30–01.00) |
Lunch (1.00 |
Tutorial 1 (2.30-3.30) |
Tea (3.30 to |
Tutorial 2 (4.00-500) |
Snacks (5.00 |
|
|
|
|
|
||||||
|
(Speaker’s name) |
(Speaker’s name) |
(Speaker’s name) |
(Tutor’s name) |
||||||
|
Mon |
01.06.26 |
BS |
SK |
BS, NB, AKD |
SK, NB, AKD |
||||
|
Tue |
02.06.26 |
BS |
SK |
BS, NB, AKD |
SK, NB, AKD |
||||
|
Wed |
03.06.26 |
BS |
SK |
MSK, MS, PS |
MSK, MS, PS |
||||
|
Thu |
04.06.26 |
BS |
SK |
MSK, MS, PS |
MSK, MS, PS |
||||
|
Fri |
05.06.26 |
GA |
AS |
GA, SY, MSK |
MSK, SY, PS |
||||
|
Sat |
06.06.26 |
GA |
AS |
GA, SY, MSK |
AS, SY, MSK |
||||
|
Sunday |
|||||||||
|
Mon |
08.06.26 |
AS |
Tea (11.00 |
GA |
Lunch (1.00 |
AS, NB, AKD |
Tea (3.30 to |
PS, NB, AKD |
Snacks (5.00
|
|
Tue |
09.06.26 |
AS |
GA |
SY, MS, PS |
SY, MS, PS |
||||
|
Wed |
10.06.26 |
ASK |
SS |
NB, PS, MS |
SS, MS, AKD |
||||
|
Thu |
11.06.26 |
ASK |
SS |
SY, NB, AKD |
SS, NB, AKD |
||||
|
Fri |
12.06.26 |
SS |
ASK |
PS, NB, AKD |
ASK, NB, AKD |
||||
|
Sat |
13.06.26 |
SS |
ASK |
ASK, SY, MS |
SY, MS, PS |
||||
Full forms for the abbreviations of speakers and tutors:
AS: Prof. A. Swaminathan
SS: Prof. S. Sivananthan
BS: Dr. B. Sriram
SK: Dr. Surjit Kumar
GA: Dr. G. Arunkumar
ASK: Dr. A. Sathish Kumar
SY: Dr. S. Yugesh
MSK: Dr. M. Sundarakannan
NB: Mr. Nitin Bartwal
PS: Ms. Puja Sonawane
AKD: Mr. Arpan Kumar Dey