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:

  • MA5450 Functional Analysis Assignments
  • MA2010: Complex Variables and Transform Techniques Assignments
  • 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:
    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

  • "Some Thoughts, articles and poems".
  • General articles of interest by P.R. Halmos:

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


    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


    1. Spectral Approximation.
    2. Approximate Solution of Integral and Operator Equations of the Second Kind.
    3. Regularization of Inverse and Ill-Posed Problems.
    4. Linear Algebra and Analysis

    Research Experience Before Ph.D:

    1. Research Scholar: TIFR Bombay (August 1980 - July 1981).
    2. Junior/Senior Research Fellow: IIT Bombay (July 1981 - September 1984).

    Research and Teaching Experience After Ph.D.:

    1. Post-Doctoral Fellow: University of Grenoble, France (December 1984 - December 1985)
    2. Research Scientist: IIT Bombay (February 3, 1986 - February 2, 1987)
    3. Lecturer: Goa University (February 3, 1987 - November 30, 1989)
    4. Reader: Goa University (December 1, 1989 - December 10, 1995)
    5. Assistant Professor: IIT Madras (December 11, 1995 - December 17, 1996)
    6. Associate Professor: IIT Madras (December 18, 1996 - January 11, 2004)
    7. Professor : IIT Madras (January 12, 2004 onwards)

    Foreign Assignments:

    1. Post-Doctoral Fellow: University of Grenoble (FRANCE), December 1984 - November 1985.
    2. Visiting Fellow: Australian National University (AUSTRALIA), March-June, 1989.
    3. Visiting Professor: University of Kaiserslautern (GERMANY), October-November, 1992.
    4. Visiting Fellow: Australian National University (AUSTRALIA), June-December 1993.
    5. Visitng Professor: University of Kasiserslautern (GERMANY), May-June 1996.
    6. Visiting Professor: University of Kasiserslautern (GERMANY), June-July 1999.
    7. Visiting Guest Professor (DAAD): University of Kaiserslautern (GERMANY), April-July 2002.
    8. Visiting Mathematician: Sun Yat-sen University, Guangzhou (CHINA), May 20 - June 17, 2011.


    1. French Goverment Scholarship to do Post-Doctoral Research in France (December 1984 - November 1985).
    2. Visiting Guest Professor under DAAD to teach a course in University of Kaiserslautern (GERMANY) (April-July, 2002).
    3. C.L.Chandna Award for Distinguished and Outstanding Contributions to Mathematics Research and Teaching in India for the year 2003.


    1. Books:
      (i) Functional Analysis: A First Course , Prentice-Hall of India, New Delhi, 2002.

      (ii) Linear Operator Equations: Approximation and Regulrization , World Scientific, Singapore, May 2009.
      (iii) Calculus of One Variable , Ane Books Pvt. Ltd. (For typos, see )

    2. Research Papers in Refereed Journals: 67 ( See Reviews by AMS)

    3. Papers in Proceedings of Conferences: 12

    4. Research Reports of Australian National University and University of Kasiserslautern: 12

    Member, Editorial Board:

    1. Journal of Analysis and Number Theory (Natural Sciences Publishers, USA)
    2. Inverse Problems in Science and Engineering (IPSE)
    3. Journal of Matheamtical Analysis (ISSN 2217-3412)

    Some Educative Articles (Linear Algebra and Analysis):

    ·  Linear equations, matrices and determinants (pdf)

    ·  Example of a nonseparable inner product space with all its orthonormal sets countable (pdf)

    ·  How many? (pdf)

    ·  Eigenvalues of self adjoint operators: Spectral theorem and singular value decomposition , (pdf).

    ·  Existence of eigenvalues for self adjoint operators: A simple proof (pdf) .

    ·  Linear equations and matrices (pdf) .

    ·  Truncations of Fourier series as best approximants (pdf)

    ·  Ill-posedness of backward heat conduction problem (pdf)

    ·  Spectral characterization of closed range operators (pdf)

    ·  Use of Functional Analysis in Solving Equations (pdf)

    Invited Talks Invited Talks at Various Conferences

    Some Useful Links:

    ·  MathSciNet

    ·  Zentralblatt MATH

    ·  Math on the Web

    Series of Lectures:

    ·  Linear System Theory, IIT Bombay, 1986

    ·  Inverse Problems , University of Kaiserslautern, 2002.

    Talks at Various Institutes/Universities in India and Abroad:

    In India:

    1. Indian Statistical Institute, Delhi .
      Talk: Spectral approximation (July 1984).
    2. University of Calicut, Kerala.
      Talk: Spectral approximation and numerical approximation, (May 14 & 15, 1987).
      Talk: Projection methods for equations of the second kind, (May 7, 1990).
    3. Indian Institute of Technology Bombay, Mumbai.
      Talk: Projection methods for equations of the second kind (May 1998).
    4. Indian Institute of Science, Bangalore.
      Talk: Regularization and approximation of ill-posed problems (August 18, 2000).
      Talk: On optimal order results for Tikhonov regularization,
      "C.L.Chandna Award Lecture" (25 June 2004). (ps-file)
    5. Tata Institute of Fundamental Research, Bangalore.
      talk: Projection methods for integral equations of the second kind (May 25, 1991).
    6. Institute of Mathematical Sciences, Chennai.
      Talk: Ill-posed problems and their regularization (November 11, 1998).
      (Under UNESCO programme for college and university teachers of ASEAN countries.)
    7. Bharatiar University, Coimbatore.
      Talk: Perturbation of eigen-pairs of matrices (March 26, 2004).
      "C.L.Chandna Award Lecture" (March 26, 2004).
    8. Cochin University of Science and Technology, Kochi.
      Talk: Operator equations and ill-posed problems (June 4, 1997).
    9. Anna University, Chennai.
      Talk: What makes a matrix non-diagonalizable? (March 6, 2002).

    Outside India:

    1. Centre for Mathematical Analysis, Australian University, Canberra (Host: Prof.Dr. R.S.Anderssen).
    2. University of New South Wales, Sydney (Host: Prof.Dr. I.Sloan).
    3. University of Kaserslautern (Host: Prof.Dr. E.Schock).
    4. Technical Unversity of Berlin (Host: Prof. R.Plato).
    5. University of Karlsruhe (Host: Prof.Dr. A.Rieder).
    6. University of Mainz (Host: Prof.Dr. M.Hanke).
    7. Sun Yat-sen University, Guangzhou, China (Host: Prof.Dr. Y. Xu ).
    8. Insitute of Geology and Geophysics, Chinese Academy of Sciences, Beijing (Host: Prof.Dr. Yanfei Wang ).

    Lectures at Refesher Courses for College Teachers

    Research Collaborators (Other than Ph.D. students):

    1. Prof. B.V.Limaye (IIT Bombay).
    2. Prof. R.S.Anderssen (Austrtalian National University).
    3. Prof. E.Schock (University of Kaiserslautern, Germany).
    4. Prof. M.Hegland (Austrtalian National University).
    5. Prof. U.Tautenhahn (University of Zittau, Germany).
    6. Prof. S.Pereverzyev ( RICAM, Linz, Austria ).
    7. Prof. S.H.Kulkarni (IIT Madras).
    8. Prof. M.N.N.Namboodiri( Cochin University).



    1. Santhosh George (1991-1995): Approximation methods for Ill-Posed Operator Equations
    2. M.P.Rajan (1997-2001): On Regularizaion and Approximation of Linear Ill-Posed Problems
    3. Shine Lal (2000-2005): A General Mollifier-Type Method for Ill-Posed Operator Equations
    4. Pallavi (2003-2008): Regularization of Nonlinear Ill-Posed Problems under General Souce Conditions
    5. Ravi Shankar (2004-2010): Regularized Continuous newton Type Methods for Solving Nonlinear Ill-Posed Operator Equations
    6. K.P. Deepesh (2006-2011) A Study on Approximation Numbers of Operators


    ·  Lucas Miranda (1991): On Projection Methods for Operator equations of the Second Kind


    1. L.Bharath (1997): On perturbation results for eigenelements
    2. A. Arthi (1998): An introduction to orthonormal wavelets
    3. R.Sudharsana (1998): On Discrete ill-posed problems
    4. R.Tara (1999): On functions of several complex variables
    5. R.Prabha (1999): Interpolation and numerical integration
    6. G.Swaminathan (2000): Perturbation analysis of singular subspaces
    7. N.V.Nirmala (2001): On a Generalized Riemann integral
    8. S.R.Varadharaj (2002): Perturbation of eigenvalues and invarianbt subspaces
    9. Aneesa Zeenath (2003): Differentiability Theorems: A simple approach based on Caratheodary's definition of differentiability
    10. Srividya (2004): On Linear preservers
    11. Anoop, T.V. (2005): Stability of invariant subspaces
    12. Maulik Shah, (2008): A study of approximate invariant subspaces
    13. Harsha, Kelkar Narasimha (2008): On fundamental theorem of calculus and algebra
    14. Banhita Maitra (2010): On a geometric approach to saddle points of surfaces
    15. Arghya Partha Chattopadhyay (2011): A study on several complex variables
    16. Samprita Das Roy (2014): Weak solutions of elliptic partial differential equations

    Courses Taught:

    At Goa University:

    For M.Sc.:

    1. Real Analysis
    2. Complex Analysis
    3. Functional Analysis
    4. Topics in Advanced Analysis (Distribution Theory and Fourier Transforms)
    5. Topology

    For M.Phil.:

    ·  Numerical Functional Analysis

    At IIT Madras:

    For M.Sc.:

    1. Linear Algebra
    2. Real Analysis
    3. Toplology
    4. Complex Analysis
    5. Measure and Integration
    6. Advanced Analysis ( Advanced Topics in Measure and Integration)
    7. Functional Analysis
    8. Operator Theory

    For B.Tech.:

    1. MA 101 (Sequences and Series, Integration, Functions of Several Variables )
    2. MA 102 (Multiple Integrals, Matrics, Differential Equations)
    3. MA 103 ( Complex Variables, Partial differential Equations, Special Functions)
    4. Linear Algebra
    5. MA 1010: Calculus-I ( Functions of single variable )
    6. MA 1020: Calculus-II ( Functions of several variables )
    7. MA2030: Linear Algebra and Numerical Analysis
    8. MA2010: Complex Variables and Transform Techniques
    9. MA 2020: Differential Equations

    For M.Tech.:

    ·  Numerical Linear Algebra

    For Ph.D.:

    ·  Topics in Advanced Analysis and differential Equations

    At University of Kaiserslautern:

    For M.Sc./M.Tech./Diplom/Ph.D.:

    ·  Inverse Problems

    Some Useful Links

    ·  Math-Archives

    Other Details:

    ·  Life Member, Indian Mathematical Society.

    ·  Life Member, Ramanujan Mathematical Society.

    ·  Member, American Mathematical Society (1988-2003).

    ·  Coordinator and a Teacher for MTTS (2000).

    ·  Member, Board of Studies of Mathematics, Goa University (1987-1992).

    ·  Member, Board of Studies of Mathematics, Pondicherry Central University (2003-).

    ·   Member, Board of Studies of Mathematics, University of Calicut (2003-).

    ·   Member, Board of Academic Courses, IIT Madras (2003-2004).

    ·  Warden, Sarayu Hostel, IIT Madras (July 2002-August 2005).

    ·  Vice-Chairman, JAM- 2004 .

    ·  Secretary, GATE-2006

    ·  Vice-Chairman, JAM- 2006

    ·  Vice-Chairman, GATE/JAM/JMET-2007

    ·  M.Tech. Admission Chairman-2007

    ·  Chairman, GATE/JAM/JMET-2008

    ·   Member, Board of Studies of Mathematics, Cochin University of Science and Technology (Kochi) (2013-).

    Last Updated: March, 2013.