## Abhijit Dasgupta

Professor

Mathematics and Computer Science

University of Detroit Mercy

Official University Web Entry## 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).

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 MATH, by Werner Kleinert (Berlin), Vol.1286(2), 2014 (PDF).Book review at Choice (from IMSA Library), by D. P. Turner, Vol.52(6), Feb 2015 (©American Library Association, restricted access reviews).Errata list.- Browse more MAA BLL set theory books.

## 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

Topology Atlaswas founded by Dmitri Shakhmatov and Stephen Watson in 1995 as a comprehensive online resource for topology. It seems to have gone offline permanently in 2020 (partial content may be available via archives at Wayback Machine). The following appeared in Topology Atlas in 2005.

## 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
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Perl Script to Convert UTF-8 Bangla into bangtexASCII format

(Also hosted here.)