Alan Smith

Amartya Kumar Dutta

Professor, Stat-Math Unit

  • Indian Statistical Institute
    203, B.T. Road
    Kolkata 700 108

  • Email:
  • Phone: 91-33-2575 3427


Ph.D. in Mathematics from the University of Bombay (Institute : TIFR).

Ph.D Details

Ph.D. Awarded : December 1994
Title of Ph.D. Thesis : Problems in Algebra: On Affine Fibrations and Linear Planes over a D.V.R.
Name of the Guide : Prof. S.M. Bhatwadekar, TIFR.

Ph.D. students

Prosenjit Das, NBHM research scholar at ISI Kolkata during 2004–2010, got his Ph.D. from ISI in 2010. Thesis title “A Study on Algebras with Retractions and on Planes over a DVR”. He is now an Associate Professor in the Department of Mathematics, Indian Institute of Space Science and Technology, Trivandrum.

Neena Gupta, SPMF research scholar at ISI Kolkata during 2008–2012, got her Ph.D. from ISI in 2012. Thesis title “Some Results on Laurent Polynomial Fibrations and Quasi A? -algebras”. She is an Associate of the Indian Academy of Sciences and a recipient of the inaugural Cowsik Medal of TIFR, INSA Young Scientist Medal, inaugural A.K. Agarwal Prize of the Indian Mathematical Society, SwarnaJayanti Fellowship and B.M. Birla Award. She is currently Assistant Professor in Stat-Math Unit, Indian Statistical Institute, Kolkata.

Publications in Commutative Algebra

(with S.M. Bhatwadekar), On Residual Variables and Stably Polynomial Algebras, Communications in Algebra, 21(2) (1993), p. 635-645.

(with S.M. Bhatwadekar), Linear Planes over a Discrete Valuation Ring, Journal of Algebra, 166(2) (1994), p. 393-405.

(with S.M. Bhatwadekar), On Affine Fibrations, in Commutative Algebra (ed. A. Simis, N.V. Trung, G. Valla): Conf. Comm. Algebra ICTP (1992), World Sc., 1994, p. 1-17.

(with S.M. Bhatwadekar), On A1 -fibrations of subalgebras of polynomial algebras, Compositio Mathematica, 95(3) (1995), p. 263-285.

On A1 -bundles of Affine Morphisms, Journal of Mathematics of Kyoto University, 35(3) (1995), p. 377-385.

(with S.M. Bhatwadekar), Kernel of Locally Nilpotent R-Derivations of R[X, Y ], Transactions of the American Mathematical Society, 349(8) (1997), p. 3303-3319.

(with S.M. Bhatwadekar), Structure of A∗ -fibrations over one-dimensional seminormal semilocal domains, J Algebra, 220(2) (1999), p. 561-573.

(with S.M. Bhatwadekar), On A∗ -fibrations, Journal of Pure and Applied Algebra, 149 (2000), p. 1-14.

On Separable A1 -forms, Nagoya Math J., 159 (2000), p. 45–51.

Some Results on Affine Fibrations, Advances in Algebra and Geometry (ed. C.Musili): Conf. on Algebra and Geometry, Univ. Hyderabad (2001), HBA (2003), p. 7–24.

Some Results on Subalgebras of Polynomial Algebras, Contemporary Mathematics 390 (2005), p. 85–96.

(with N. Onoda) Some results on codimension-one A1 -fibrations, J Algebra, 313 (2007), p. 905–921.

(with N. Onoda) On finite generation of R-subalgebras of R[X], J. Algebra, 320 (2008), p. 57–80.

(with P. Das) On codimension-one A1 -fibration with retraction, J. Commutative Algebra, 3(2) (2011), p. 207–224.

(with P. Das) Planes of the form b(X, Y )Z n − a(X, Y ) over a DVR, J. Commutative Algebra, 3(4) (2011), p. 491–509.

(with N. Gupta and N. Onoda) Some patching results on algebras over two-dimensional factorial domains, J. Pure and Applied Algebra, 216 (2012), p. 1667–1679.

(with S.M. Bhatwadekar and N. Onoda) On algebras which are locally A1 in codimension-one, Transactions of the American Mathematical Society, 365 (9), (2013), p. 4497–4537.

On A1 -patch by a regular sequence, in Proceedings of the Commutative Algebra and Algebraic Geometry (CAAG 2010) conference (ed. H. Flenner and D.P. Patil), Ramanujan Mathematical Society Lecture Note Series 17 (2013), p. 69–76.

(with P. Das) A note on residual variables of an affine fibration, J. Pure and Applied Algebra, 218 (2014), p 1792–1799.

(with N. Gupta) The Epimorphism Theorem and its generalisations, Journal of Algebra and its applications 14 (9) (2015), Special Issue In Honor of Shreeram S. Abhyankar, pp. 1540010- 1–1540010-30.

Publications in Journals of Science/Math Education, Cultural Journals, Books

  1. Turning Points in Mathematics — Historical Perspectives I, Srinvantu XLVXIV(1), February 2002, pp. 38–46.

  2. Mathematics in Ancient India: An Overview, Resonance 7(4), April 2002, pp. 4-19.

  3. Turning Points in Mathematics — Historical Perspectives II, Srinvantu XLVXIV(2), August 2002, pp. 49–64.

  4. Diophantine Equations: The Kuttaka, Resonance 7(10), October 2002, pp. 6–22.

  5. Turning Points in Mathematics — Historical Perspectives III, Srinvantu, 125th Birth Anniversary of the Mother and Golden Jubilee Special Number, pp. 178–192.

  6. Diophantine Equations: The Samasabhavana, Resonance 8(11), November 2003, pp. 10–24 and 9(1), January 2004, pp. 61–63.

  7. Medhatithi, Pingala, Aryabhata and Brahmagupta, Shraddha 2, Feb–Apr 2005, pp. 16–28.

  8. Brahmagupta’s Bhavana: Some Reflections, Contributions to the History of Indian Mathematics (ed. G.G. Emch, R. Sridharan, M.D. Srinivas), Hindustan Book Agency: Culture and History of Mathematics (CHOM) 3, 2005, pp. 77–114.

  9. Aryabhata and Axial Rotation of Earth: Khagola (The Celestial Sphere), Resonance 11(3), March 2006, pp. 51–68.

  10. Mathematics in Ancient India, Mother India LIX(4), April 2006, pp. 270–283.

  11. Aryabhata and Axial Rotation of Earth: Naks.atra Dina (The Sidereal Day), Resonance 11(4), April 2006, pp. 56–69.

  12. Aryabhata’s Alphabetical Coding of Large Numbers, Resonance 11(4),April 2006, pp. 69– 74.

  13. Aryabhata and Axial Rotation of Earth: A Brief History, Resonance 11(5), May 2006, pp. 58–72.

  14. Bijaganita of Bhaskaracharya, Prabuddha Bharata 112(9), September 2007, pp. 51–52.

  15. The Abel Laureate Srinivasa Varadhan, Shraddha 4(3), November 2007, pp. 8–12. 2

  16. Powers of Ten: Genesis and Mystic Significance, Srinvantu 58(2), August 2008, pp. 44–52; reprinted in Mother India LXII(11), November 2009, pp. 957–967 & Vedic Venues 2, 2013, pp. 43–56.

  17. Kuttaka, Bhavana and Cakravala, in Studies in the History of Indian Mathematics (ed. C.S. Seshadri), Hindustan Book Agency: Culture and History of Mathematics (CHOM) 5, 2010, pp. 145–199.

  18. Brahmagupta’s Contributions to Algebra, The Mathematics Teacher, 47, 2011, pp. 147–168.

  19. Glimpses from Ancient Indian Mathematics, Mirror of Tomorrow, 15 Janunary 2012,−archives/2012/1/15/4973560.html

  20. Narayana’s treatment of varga-prakr. ti, Indian Journal of History of Science 47.4, 2012, pp. 633–677.

  21. Acharya Prafulla Chandra Ray I, Mother India LXVI(11), November 2013, pp. 953–962.

  22. Acharya Prafulla Chandra Ray II, Mother India LXVI(12), December 2013, pp. 1038–1951.

  23. Acharya Prafulla Chandra Ray III, Mother India LXVII(1), January 2014, pp. 43–55.

  24. Acharya Prafulla Chandra Ray IV, Mother India LXVII(3), March 2014, pp. 233–243.

  25. Acharya Prafulla Chandra Ray V, Mother India LXVII(4), April 2014, pp. 309–321.

  26. Acharya Prafulla Chandra Ray VI, Mother India LXVII(5), May 2014, pp. 408–417.

  27. Bıjagan. ita of Bhaskaracarya, At Right Angles 3(3), November 2014, pp. 9–12.

  28. Decimal System in India, Encyclopaedia of the History of Science, Technology, and Medicine in Non-Western Cultures (ed. H. Selin), Springer, 2016, pp. 1492-1504; online version in DOI 10.1007/978-94-007-3934-5 10321-1

  29. " Was there Sophisticated Mathematics during Vedic Age? in An anthology of disparate technical thoughts at a popular level (ed. A. Chaudhuri), ISIREA, 2016, pp. 91–132. Reprinted in Platinum Jubilee Memorial Volume, Ramakrishna Mission Vidyamandira, Belur Math, 2016, pp. 361–385.

  30. The bhavana in Mathematics, Bhavana 1(1), January 2017, pp. 13–19.

  31. The Concept of Arithmetic Mean in Ancient India, to appear in 25 Years Gone By (ed. A. Chaudhuri), ISIREA, 2017.

  32. Weighted Arithmetic Mean in Ancient India, to appear in Bh¯avan¯a.

  33. (with M.S. Sriram) Mathematics and Astronomy in India before 300 BCE, Preprint.

Lecture Notes

  1. Introduction to Commutative Rings, Refresher Course in University of Calcutta, February 1998.

  2. Mathematics in Ancient India: Some Diophantine Equations, for the NBHM World Mathematical Year Lectures at Presidency College, Calcutta, and the Ramakrishna Mission Residential College, Narendrapur, in December 2000.

  3. History of Algebra, for the Refresher Course in Mathematics at the University of Calcutta, August 2001.

  4. Rings and Ideals: Stray Remarks, National Seminar on Perspectives in Mathematics at RKM Vidyamandira, Belur, February 2006.

  5. Brahmagupta’s Contributions to Algebra, for the R.C. Gupta Endowment Lecture organised by the Association for Mathematics Teachers of India (AMTI) in December 2010.

  6. Mathematics in Ancient India: Some Glimpses, for the Indology course of the Ramakrishna Mission Institute of Culture, Kolkata.

  7. Science in Modern India: Some Notes, for the Indology course of the Ramakrishna Mission Institute of Culture, Kolkata.

Book Reviews on History of Indian Mathematics

  1. “Indian Mathematics and Astronomy, Some Landmarks” by S. Balachandra Rao, in The Vedanta Kesari 94(9), September 2007, pp. 363–364.

  2. “Bhaskaracharya’s Bijaganitham” by V.B. Panicker, in Prabuddha Bharata 112(9), September 2007, p. 551.

Articles for Students’ Magazines

  1. Roots of Some Mathematical Terms, Canvas (2005), pp. 11–21.

Other cultural publications

  1. Goethe’s Epigram on “Shakuntala”, Canvas (2007), pp. 5–6.

  2. Prof. Nadkarni, We Do Hear You, Mother India LXI(7), July 2008, pp. 632–635.