Welcome to the Home Page of
Prof.Dr.M.Thamban Nair

Department of Mathematics
Indian Institute of Technology Madras

Chennai - 600 036, INDIA
E:mail: mtnair@iitm.ac.in
URL: http://mat.iitm.ac.in/home/mtnair/public_html/index.html
Phone: (Office) 044-2257 4610
Phone: (Residence) 044-2257 6610/2257 0474

Dr. M. T. Nair (Brief-CV)

(Mathematical Reviews - Papers and Books: MathSciNet and zbMATH )

Some Links:

  • Entrance Examinations: GATE, JAM , JEE

  • M.Sc. Courses:
    1. Linear Algebra
    2. Measure and Integration
    3. Complex Analysis
    4. Topics in Advanced Analysis
    5. Functional Analysis
    6. Operator Theory
    7. Fourier Analysis

  • Ph.D Course:
    1. Advanced Mathematical Analysis & Differential Equations
    2. Analysis


  • B.Tech. Courses:

  • MA2010: Complex Variables and Transform Techniques Assignments
    1. MA1010: Calculus-I: Assignments & Notes
    2. MA1020: Calculus-II: Assignments & Notes
    3. MA2010: Complex Variables and Transform Techniques Assignments
    4. MA2030: Linear Algebra and Numerical Analysis: Moodle [ Assignments & Notes ]
    5. MA2020: Differential Equations: Assignments & Notes

  • Notes (based on some series of lectures):
    1. Advanced Analysis: A Crash Course
    2. Measure and Integration: A Crash Course
    3. Some Topics in Advanced Functional Analysis: A Crash Course
    4. On Controllability of Linear Systems

  • Some questions and anwwers Q-A

    General articles of interest by P.R. Halmos:

    1. How to Talk Mathematics
    2. How to Write Mathematics

    News!


    1. Took Charge as Head of the Department of Mathematics, IIT Madras, on December 5, 2014.

    2. New BOOK (2014): Calculus of One Variable , Ane Books Pvt. Ltd. (For typos, see )

    3. Fourth Print (2014) of the Book (with corrections incorporated): Functional Analysis: A First Course , PHI-Learning (Formerly: Prentice-Hall of India), New Delhi, 2002. (Review: zbMATH )

    4. Member, Editorial Boaard : Journal of Analysis and Number Theory (Natural Sciences Publishers, USA).

    5. A new paper: Approximation numbers for relatively bounded operators (With K.P. Deepesh and S.H. Kulkarni), Functional Analysis, Approximation and Computation, 5:2 (2013), 35-42.

    6. Member, International Scientific Committee for the Symposium on Inverse Problems, Design and Optimization (IPDO-2013), Albi (France), June 26-28, 2013.

    7. Article: Generalized inverses and approximation numbers (With K.P. Deepesh and S.H. Kulkarni), Pages 143-158,
      In: Combinatorial Matrix Theory and Generalized Inverses of Matrices , Springer, 2013, Editors: R.B. Bapat, S.J. Kirkland, M.M. Prasad and S. Putenen.

    8. Contributed: Chapter 3: Regularization of Fredholm integral equations of the first kind using Nystrom approximation, Pages 65-82,
      In: Computeational Methods for Applied Inverse Problems, De Gruyter, 2012, Editors: Y. Wang, A.G. Yagola and C. Yang.

    9. NPTEL-Web-Course: Functional Analysis , Aughust 2012.

    10. Associate Editor: Inverse Problems in Science and Engineering (IPSE)

    11. Member, Editorial Boaard : Journal of Matheamtical Analysis (ISSN 2217-3412)

    12. New BOOK (2009): Linear Operator Equations: Approximation and Regulrization , World Scientific, 2009 (Review: zbMATH).

    13. An iterative method considered by me in the paper: An iterative procedure for solving Riccati equation A_2 R - R A_1 = A_3 + R A_4 R (pdf), Studia Mathematica, Vol. 147 (2001) 15-26,
      has been named as "M.T.Nair Method" by N.B.Uskova in a paper titled "On M.T.Nair Method for Linear Operator Invariant Subspace Construction" , presented to the 12th International Conference of the EWM Association.
      Full paper (in Russian) appeared in the Journal ``Vestnik" Vol. 1, 2005 (see the paper by Uskova in Mathematics Section).



    Family Profile:

  • I am from a small village called Udma (Udayamangalam) in North Malabar region ( Kasaragod District) of Kerala state. I had my school education in Government High School Udma, and college education (Pre-Degree and B.Sc.) at Goverment College Kasaragod, about 15 kilometers from my village. My interests, other than Mathematics, include philosophy and spirituality.

    I lost my father (Chandu Nair) when I was barely 13 years old. My mother (Meloth Parvathi Amma) is now 90 years old and living in the village. I have four sisters (Padmavathi, Parvathi, Karthiayani, Lakshmi) and a brother (Chandra Sekharan). Sisters are all married and settled in the nearby villages, and brother and his family are living in Dubai.

    I live in the IIT Campus along with my wife Sunita, and daughters Priya and Sneha. My wife is a Professor of Chemistry at SSN College of Engineering (Kalavakkam) about 35 kilometers from IIT Campus. Priya is doing her Ph.D in Bio-Medical Engineering at Arizona State University USA and Sneha is doing BE in Bio-Medical Engineering at SSN College of Engineering.

    Academic Background:

    1. B.Sc. (1978): Government College Kasaragod (University of Calicut)
      [ First Class, & College Topper]
    2. M.Sc. (1980): Department of Mathematics, University of Calicut
      [ First Class & First Rank].
    3. Ph.D.: Indian Institute of Technology Bombay.
      Thesis Submission: June 1984
      Thesis Defence: January 1986
      Title of the Thesis: Approximation and Localization of Eigenlements
      Supervisor: Prof. B.V.Limaye (IIT Bombay)
    4. P.D.F. (Post Doctoral Fellow): (November 1984 - December 1985),
      Institute IMAG, University of Grenoble (FRANCE).

    Research Interests:

    Broad Area: Functional Analysis and Operator Theory
    Specialization: Applicable Functional Analysis

    Specifically:

    1. Spectral Approximation.
    2. A