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

Prof. K. Sumesh
Department of Mathematics
IIT Madras

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
Department of Mathematics
IIT Madras

 6

Compactness, Characterization of compact sets, Heine Borel theorem, Cauchy sequence and Complete metric space

Dr. G. Arunkumar
Department of Mathematics
IIT Madras

 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
Department of Mathematics
IIT Roorkee

 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
Department of Mathematics
IIT Madras

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
Department of Mathematics
IIT Delhi

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:

  1. L. Lorentzen and H. Waadeland, Continued Fractions, Volume 1: Convergence Theory, Atlantis Studies in Mathematics, 2nd edition, World Scientific, 2008.

  2. H. N. Mhaskar and D. V. Pai, Fundamentals of Approximation Theory, Narosa Publishing House, 2007.

  3. W. Rudin, Principles of Mathematical Analysis, Mcgraw-Hill, 1976.

  4. G. F. Simmons, Topology and Modern Analysis, Kreiger, 2003.

  5. D. F. Walnut, An Introduction to Wavelet Analysis, Birkhauser Boston, MA, 2003.

  6. 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,
SSN College of Engineering

2

Dr. M. Sundarakannan

Assistant Professor, Department of Mathematics,
SSN College of Engineering

3

Mr. Nitin Bartwal

Research Scholar, Department of Mathematics,
IIT Madras

4

Ms. Puja Sonawane

Research Scholar, Department of Mathematics,
IIT Madras

5

Mr. Arpan Kumar Dey

Research Scholar, Department of Mathematics,
IIT Madras

6

Mr. M. Surya

Research Scholar, Department of Mathematics,
IIT Madras

Time Table

  

 

 

 

 

Day

 

 

 

 

Date

Lecture 1

(9.30–11.00)

Tea

(11.00-11.30)

Lecturer 2

(11.30–01.00)

Lunch

(1.00 – 2.30)

Tutorial 1

(2.30-3.30)

Tea

(3.30 -4.00)

Tutorial 2

(4.00-500)

Snacks

(5.00 – 5.30)

 

 

 

 

(Speaker’s name)

(Speaker’s name)

(Speaker’s name)

(Tutor’s name)

Mon

01.06.26

KS

GA

KS, NB, AKD

GA, NB, AKD

Tue

02.06.26

KS

GA

KS, NB, AKD

GA, NB, AKD

Wed

03.06.26

KS

GA

MSK, MS, PS

MSK, MS, PS

Thu

04.06.26

KS

GA

MSK, MS, PS

MSK, MS, PS

Fri

05.06.26

SK

ASK

SK, SY, MSK

MSK, SY, PS

Sat

06.06.26

SK

ASK

SK, SY, MSK

ASK, SY, MSK

Sunday

Mon

08.06.26

ASK

Tea

(11.00-11.30)

SK

Lunch

(1.00 – 2.30)

ASK, NB, AKD

Tea

(3.30 -4.00)

PS, NB, AKD

Snacks

(5.00 – 5.30)

Tue

09.06.26

ASK

SK

SY, MS, PS

SY, MS, PS

Wed

10.06.26

AS

SS

NB, PS, MS

SS, MS, AKD

Thu

11.06.26

AS

SS

SY, NB, AKD

SS, NB, AKD

Fri

12.06.26

SS

AS

PS, NB, AKD

AS, NB, AKD

Sat

13.06.26

SS

AS

AS, SY, MS

SY, MS, PS

 

Full forms for the abbreviations of speakers and tutors:

 AS: Prof. A. Swaminathan

SS: Prof. S. Sivananthan

KS: Dr. K. Sumesh

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

MS: Mr. M. Surya

 

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