# 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).

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

## 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.

#### 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.

#### Expository Articles

Topology Atlas was 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.
• Countable metric spaces without isolated points, in Topology Explained,'' June 2005. PDF

• Limit points of discrete sets in metric spaces, in Topology Explained,'' July 2005, PDF

## 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