Abhijit Dasgupta

Teaching

Information on the Engineering PhD Math Qualifying Examination. Students planning to take the exam should follow the guidelines given in this web page.

Teaching Page (includes courses taught in earlier academic years).

Integrating Piecewise Discontinuous Bounded Functions.

Simulation Tool (in MATLAB) for Frequency and Free Response in second order vibrations.

Old post on Great Calculus Reference Texts for Students Who Want to Learn More.

Selected Publications

My primary research has been in Topology, Real Analysis, and Measure Theory, and involves classifying sets in topology and analysis (part of an area known as Descriptive Set Theory). I have also been interested in Randomness in Sequences and Non-standard Analysis.

Book


Articles (Refereed Journals)

  • Compactness and Symmetric Well-Orders, Bulletin Polish Acad. Sci. Math. 72 (2024), 67⁠–⁠80. DOI: 10.4064/ba230424-28-12. Available from journal website for Volume 72 Number 1, and also as a local Preprint published online on 17 Jan 2024, © Instytut Matematyczny PAN, 2024.

  • A Set of Axioms for Nonstandard Extensions, Math. Logic Quarterly 57, No. 5 (2011), 485⁠–⁠493. DOI: 10.1002/malq201010025.

  • Mathematical Foundations of Randomness, Philosophy of Statistics (Volume 7 of the Handbook of Philosophy of Science, ISBN 978-0-444-51862-0), North-Holland (2011), pp. 641-710. © Copyright 2011 Elsevier BV. Preprint, book (at Amazon).

  • The Riemann Integrable Functions are \(\boldsymbol{\Pi}^0_3\)-complete in the Lebesgue Integrable Functions, J. Math. Anal. Appl. 332(2007), 700-708. DOI: 10.1016/j.jmaa.2006.09.080.

  • Constructing \(\boldsymbol{\Delta}^0_3\) using topologically restrictive countable disjoint unions, Real Analysis Exchange 31(2), 2005/2006, 547-552.

  • A Universal coanalytic linear ordering, Proc. Amer. Math. Soc. 129(12), December 2001, 3715-9.

  • Borel complexity of the space of probability measures, Proc. Amer. Math. Soc. 129(8), August 2001, 2441-3.

  • (with R. Cheng and others) When does \(f^{-1} = 1/f\)?, Amer. Math. Monthly 105(8), October 1998, 704-717.

    Michael Penn has a youtube video presentation of this article.

  • Boolean operations, Borel sets, and Hausdorff's question, J. Symbolic Logic 61(4), December 1996, 1287-1304.

Talk (on Axiomatic Nonstandard Analysis)


Expository Articles

Topology Atlas was founded by Dmitri Shakhmatov and Stephen Watson in 1995 as a comprehensive online resource for topology, and ran until 2020. It went offline in 2020, but an archive seems to be available again (as of 2024 March) at the original site hosted by York University (partial content also in wayback archives).

The following appeared in Topology Atlas in 2005, under Topology Explained, notes written by Henno Brandsma (Amsterdam) and Abhijit Dasgupta (Detroit), for the Ask a Topologist forum.

  • Countable metric spaces without isolated points, in ``Topology Explained,'' June 2005. (Originally published by Topology Atlas here, local PDF copy here).

  • Limit points of discrete sets in metric spaces, in ``Topology Explained,'' July 2005. (Originally published by Topology Atlas here, local PDF copy here).

Brief Bio/CV

Employment and Education, in reverse chronological order

  • Professor, University of Detroit Mercy, Detroit, Michigan, 2015-present
  • Associate Professor, University of Detroit Mercy, Detroit, Michigan, 2009-2015
  • Assistant Professor, University of Detroit Mercy, Detroit, Michigan, 2006-2009
  • Instructor and Assistant Professor, University of Detroit Mercy, Detroit, Michigan, 2004-2006
  • Lecturer, Jadavpur University, India, 2001-2002
  • Software Engineer at Cisco Systems, Ann Arbor, Michigan, 2000-2001
  • Visiting Scientist, Indian Statistical Institute, Kolkata, Summer 2000
  • Network Engineer (Hardware and Software) at ANS, AOL, UUNet, and MCI/Worldcom, Ann Arbor, Michigan, 1995-2000
  • Visiting Assistant Professor, University of Louisville, Kentucky, 1994-1995
  • Ph.D. in Mathematics, University of California, Berkeley, 1994
  • M.A. in Mathematics, University of Rochester, New York, 1988
  • B.Sc. and M.Sc. in Mathematics, Jadavpur University, India, 1984, 1986

Other

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