## 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 asDescriptive Set Theory). Recently, I have also been interested inRandomness in SequencesandNon-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 MAAby Tom Schulte (also at goodreads).Book review at Zentralblatt MATHVol.1286(2), 2014 (PDF) by Werner Kleinert (Berlin).Book review at Choice(excerpt) Vol.52(6), Feb 2015, by D. P. Turner. Full Text (restricted access).Errata list.

## Articles (Refereed Journals)

A Set of Axioms for Nonstandard Extensions,Math. Logic Quarterly57, No. 5 (2011), 485-493.doi:10.1002/malq201010025.

Mathematical Foundations of Randomness,Philosophy of Statistics (Volume 7 of theHandbook 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 Exchange31(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. Monthly105(8), October 1998, 704-717.

Boolean operations, Borel sets, and Hausdorff's question,J. Symbolic Logic61(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 TopologistandAsk an AnalystForum posts (200+ 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 unicodeintobangtex'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 bangtexASCII format

(Also hosted here and here.)