Abhijit Dasgupta

Professor
Department of Mathematics and Computer Science
University of Detroit Mercy
Official UDM Web Entry

Teaching

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

Teaching Page (includes courses taught at UDM at earlier academic years).

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

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). Recently, I have also been interested in Randomness in Sequences and Non-standard Analysis.

Book

• 
  Set Theory: With an Introduction to Real Point Sets. Birkhauser / Springer, 2014. xv, 444 pages. ISBN 978-1-4614-8853-8 (hardcover), 978-1-4614-8854-5 (ebook).
  • Publisher Product Flyer.
  • Get the book at Springer or Amazon.
  • Book review at MAA by Tom Schulte (also at goodreads).
  • Book review at Zentralblatt MATH, by Werner Kleinert (Berlin), Vol.1286(2), 2014 (PDF).
  • Book review at Choice (restricted access), by D. P. Turner, Vol.52(6), Feb 2015.
  • Errata list.
  • Browse more MAA BLL set theory books.

Articles (Refereed Journals)

• 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.

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

Talk (on Axiomatic Nonstandard Analysis)

• Logicless Nonstandard Analysis: An Axiom System (Abstract, Slides), presented in UltraMath 2008: Applications of Ultrafilters and Ultraproducts in Mathematics, Pisa, Italy, June 1--7, 2008.

Expository Articles (in Topology Atlas)

• Countable metric spaces without isolated points, in ``Topology Explained,'' June 2005, online at http://at.yorku.ca/p/a/c/a/25.htm.

• Limit points of discrete sets in metric spaces, in ``Topology Explained,'' July 2005, online at http://at.yorku.ca/p/a/c/a/26.htm.

• Ask a Topologist and Ask an Analyst Forum posts (mostly in summer 2005; use Google search http://www.google.com/search?q=abhijit+dasgupta+site:at.yorku.ca).

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

Orthographic Lexical Analysis of Bangla Unicode

• This perl program, developed for converting Bangla unicode into bangtex's transliterated ASCII format, performs a full Lexical Analysis of Bangla Unicode into orthographic tokens. See details at:
  Perl Script to Convert UTF-8 Bangla into bangtex ASCII format
  (Also hosted here and here.)