Real Analysis and its Applications to Approximation and Learning Theory (2026)

Convener(s)
Name: Prof. A. Swaminathan Prof. B. Praba Dr. A. Sathish Kumar Dr. S. Yugesh
Mailing Address: Professor
Deparment of Mathematics
IIT Roorkee, Roorkee
247667		 Professor & Head
Department of Mathematics
SSN College of Engineering,
Kalavakkam , Tamil Nadu.
603 110		 Assistant Professor
Deparment of Mathematics
IIT Madras, Chennai
600 036		 Assistant Professor 
Department of Mathematics
SSN College of Engineering,
Kalavakkam ,Tamil Nadu,
603 110
Email: a.swaminathan at ma.iitr.ac.in prabab at ssn.edu.in sathishkumar at iitm.ac.in yugeshs at ssn.edu.in

Real Analysis forms the foundation of modern mathematics and plays a central role in various branches of analysis, with significant applications in approximation theory and learning theory. A solid understanding of real analysis is essential not only for exploring the structure and properties of functions and spaces, but also for developing rigorous methods in approximation and data-driven learning.

The instructional school aims to provide participants with a guided tour of the core concepts in Real Analysis and their connections to Approximation Theory and Learning Theory. It will also introduce advanced tools and applications such as best approximation, Padé approximation and real analytic functions, Shannon’s sampling theorem, convergence of sampling operators, the universal approximation theorem, reproducing kernel Hilbert spaces, and convergence analysis of regularized learning algorithms.

The topics are chosen to give participants exposure to both classical and modern perspectives in analysis and its applications, thereby strengthening their background for further research in mathematics, applied analysis, and data science.

Dates: 

Monday, June 1, 2026 - 19:00 to Saturday, June 13, 2026 - 19:00

Venue: 

Venue Address: 

 

Sri Sivasubramaniya Nadar College of Engineering
Rajiv Gandhi Salai(OMR), Kalavakkam – 603 110, Tamil Nadu.

 

Venue State: 

Venue City: 

PIN: 

603110

Syllabus: 

 

Name of the Speaker with affiliation

No. of Lectures

Detailed Syllabus

Dr. B. Sriram
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 to
11.30)

Lecturer 2

(11.30–01.00)

Lunch

(1.00
to
2.30)

Tutorial 1

(2.30-3.30)

Tea

(3.30 to
4.00)

Tutorial 2

(4.00-500)

Snacks

(5.00
to
5.30)

 

 

 

 

(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
to
1.30)

GA

Lunch

(1.00
to
2.30)

AS, NB, AKD

Tea

(3.30 to
4.00)

PS, NB, AKD

Snacks

(5.00
to
5.30)

 

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

Selected Applicants: 

 

Serial No SID Full Name Gender Affiliation Position in College/University Year of Passing M.Sc./M.A Ph.D. Degree Date
1 67498 Mr. Indra Bate Male National Institute of Technology Karnataka PhD Student 2016  
2 67499 Dr. Radhakrishnan Mohanasundaram Male SRM University AP Assistant Professor 2011 19-10-2020
3 67507 Mr. Satyaranjan Pradhan Male Govt. Model Degree College, Nabarangpur Assistant Professor 2015  
4 67514 Ms. Ronnie Kenneth Athota Female Indian Institute of Technology Madras Jurior Research Fellow 2025  
5 67561 Ms. Aanchal . Female Banasthali Vidyapith PhD 2023  
6 67596 Ms Chanchal Sharma Female Banasthali Vidyapith PhD 2024  
7 67629 Dr. Manoj Kumar Male Department of Mathematics, SR University, Warangal, India-506371 Assistant Professor 2019 27-10-2025
8 67632 Mr Gnanam Mahesh Kalakaoi Male Agurchand Manmull Jain College Assistant Professor 2013  
9 67641 Dr. Suresh Kumar M Male The Gandhigram Rural Institute-Deemed to be University Assistant Professor 2010 01-05-2018
10 67648 Ms Aishwaraya . Female MIT Art, Design, and Technology University, Pune ASSISTANT PROFESSOR 2017 26-10-2024
11 67663 Dr. Nirvin Prasath Male JEPPIAAR ENGINEERING COLLEGE Assistant Professor 2014 20-05-2022
12 67683 Dr. Mohammad Arshad Male KCC Institute of Technology and Management - Greater Noida Assistant Professor 2019 20-03-2025
13 67701 Ms Vandna Sharma Female Banasthali Vidyapith Ph.D Student 2016  
14 67707 Mr Chandru S Male SRM Institute of Science and Technology
Ph. D Research scholar (1st Year).		 Ph.D Research scholar 2023  
15 67712 Mr Pandiyaraj Elumalai Male AGURCHAND MANMULL JAIN COLLEGE Assistant Professor 2013  
16 67752 Mr Murugan M Male Agurchand Manmull Jain College Assistant professor 2012  
17 67774 Mr. Muniyasamy M Male National Institute of Technology Karnataka PhD Research Scholar 2019  
18 67789 Ms. Thinkal V Female National Institute of Technology PhD 2023  
19 67807 Dr Surjeet Kaushik Male Sreenidhi University Assistant Professor 2014 05-08-2018
20 67858 Mr. Tshering Dorjee Bhutia Male RAMAKRISHNA MISSION RESIDENTIAL COLLEGE (AUTONOMOUS) ASSISTANTPROFESSOR    
21 67961 Mr. Deepak Kumar Male Govt.,PG College Ambala Cantt Asst. professor 2006  
22 68016 Mr. Vijay R Male National Institute of Technology Puduchery PhD student 2022  
23 68019 Dr. Muthuvel K Male Guru Nanak College Assistant Professor 2007 24-09-2024
24 68131 Dr. Ajay Raj Male Parul University, Vadodara Asst. Prof. 2017 26-08-2025
25 68169 Mr. Nikhil Rai Male INDIAN INSTITUTE OF TECHNOLOGY, ROORKEE PhD 2025  
26 68222 Mr. Sureshkrishnan K Male INDIAN INSTITUTE OF TECHNOLOGY ROORKEE PhD 2020  
27 68323 Ms Manjusree Gopal Female National Institute of Technology Karnataka PhD 2019  
28 68638 Dr. Sethuraman Balaji Male Vellore Institute of Technology CHennai Campus Assistant Professor 2011 08-04-2019
29 68688 Dr Jayagopal R Male Vellore Institute of Technology, Chennai Assistant Professor 2012 28-09-2017
30 68830 Dr. Sourav Mandal Male NIT DURGAPUR CSIR RESEARCH ASSOCIATE 2018 08-08-2025
31 68966 Mr. Gaurav Aggarwal Male Jaypee Institute of Information Technology, Noida Assistant Professor 2014 15-03-2022
32 68971 Mr Lakshmanan S Male Central University of Tamil Nadu PhD Student 2020  
33 69039 Mrs. Kaleeswari P Female VYASA ARTS AND SCIENCE WOMEN'S COLLEGE ASSISTANT PROFESSOR 2013  
34 69068 Ms. Oviya R Female St. Xavier's College (Autonomous) PhD 2024  
35 69072 Mr. Amarthya A Male St.Xavier's College (Autonomous) , Palayamkottai PhD 2024  
Waitlisted Candidates:            
Serial No SID Full Name Gender Affiliation Position in College/University Year of Passing M.Sc./M.A Ph.D. Degree Date
1 67552 Mr. Thangeshwaran M Male PERIYAR UNIVERSITY CENTRE FOR POSTGRADUATE AND RESEARCH STUDIES, DHARMAPURI-635205. GUEST LECTURER 2013  
2 67999 Dr. Eknath Dnyandeo Pawar Male School of Engineering and Technology Asst. Prof. 2008 16-07-2025
3 68608 Mr. Soumyaranjan Satapathy Male BARUNESWAR MOHAVIDYALAYA Lecturer in Mathematics 2020  
4 68914 Mr. Pal Bharatbhai Patel Male B. K. M. SCIENCE COLLEGE, VALSAD ADHOC LECTURER (MATHEMATICS) 2023  
5 68258 Dr Deepa Mathew Female ST JOSEPHS UNIVERSITY BENGALURU Asst. Professor 2017 08-10-2021
6 68060 Ms Sumaiya Parveen Female Aligarh Muslim University PhD 2018  

How to Reach: 

TBA

School Short Name: 

raaaalt

Last Date Application: 

Sunday, May 28, 2023

School Type: 

IST

Separate faculty form: 

0