Research

My research interests are geometry, foundations of mathematics, history of mathematics, and mathematics education.  I have been studying the works of Mario Pieri (1860-1913), an algebraic geometer who also made significant contributions to foundations of mathematics.

Selected Invited Talks:

2008   Engaging graduate student teaching assistants and prospective teachers in expository research. AMS-MAA Special Session on The Scholarship of Teaching and Learning in Mathematics.  Joint Mathematics Meetings.  San Diego, California.  January

2007  Evaluating the research of Mario Pieri (1860-1913) in algebraic geometry.  Workshop on Contemporary Schubert Calculus and Schubert Geometry.  Banff International Research Station, Banff, Canada.  March.

2006  Mario Pieri: standing on the shoulders of Peano.  Les mathématiques italiennes au XIXe siècle.  Le Séminaire de Philosophie des Mathématiques.  Centre d'épistémologie et d'ergologie comparatives.  Université de Provence, France.  October.

2006   Emerging from the shadows:  Mario Pieri, the man and his work. San Francisco State University Mathematics Colloquium Series, May.     

2005   The projective geometry of Mario Pieri.  Istituto Tecnico Pier Cresecnzi, Bologna,  Italy,  October.
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2005    Liberal arts mathematics:  making a connection between us and them.     Project NExT.   Albuquerque Math Fest.  Mathematical Association of America  Summer meeting.  August.        

2005   Mathematics from an in-depth perspective:  a course for secondary school teachers with content envisioned as applied mathematics.  Mathematics Colloquium Series.  Humboldt State University.  September.

2005     Teaching teachers to do proofs.  PMET (Preparing Mathematicians to Educate Teachers) Workshop, University of San Diego, June.

 2004     Mario Pieri's contributions to inversive geometry.  Fourth international Congress.  Societa Italiana Storia delle Mathematiche.  Padova, Italy.  September. 

2004     Foundations of geometry:  connections between Alfred Tarski and Mario Pieri .  International Conference on Statistics and Mathematics.  Hawaii.  June.

2004      Finite Geometries as a tool to understanding the why and how of  Doing Proofs.  PMET (Preparing Mathematicians  to Educate Teachers) Workshop, University of San Diego, June.

2003    Mario Pieri's role in the history of algebraic geometry and foundations of mathematics.  Spring Eastern Sectional  Meeting of the American Mathematical Society, Courant Institute of New York University, April.

2002    The fundamental theorem of projective geometry. Conference on the History of Modern Mathematics sponsored by  The British Society for the History of Science and the Open University.  Milton Keynes, England.  September. 

2002    Mario Pieri, rediscovered.  Conference on the History of Modern Mathematics sponsored by The British Society for the History of Science and the Open University.  Milton Keynes, England.  September.
2002    Teachers’ Mathematics  --a collection of content deserving to be a field.  National Council of Teachers of  Mathematics. Las Vegas   April.
2002    MARIO PIERI in the shadow of Peano, von Staudt, and Hilbert. Joint meetings of the American Mathematical Society  and the Mathematical Association of America, San Diego, California, January. Special AMS Session on the History of Mathematics .

Books: 

The Legacy of Mario Pieri: Geometry and Arithmetic, with a foreward by Ivor Grattan-Guinness.  Cambridge: Birkhauser Boston, 2007  (co-author: James. T. Smith).  ISBN: 9780817632106.   MR2310967 (2008b:01008).  Also reviewed by P. N. Ruane at MAA on-line http://mathdl.maa.org/mathDL/19/
 
Mathematics for High School Teachers, An Advanced Perspective.  Upper Saddle River: Prentice Hall, 2003 (co-authors:  Z. Usiskin, A. Peressini, and D. Stanley). ISBN: 0-13-044941-5.   www.prenhall.com/usiskin
The Mathematical Experience, Study Edition, with an introduction by Gian-Carlo Rota, and The Mathematical Experience Companion Guide.  New York: Birkhäuser, 1995 (co-authors: P. Davis and R. Hersh).  ISBN 0-8176-3739-7.  Reviewed by Kenneth C. Millett in the Notices of the American Mathematical Society 44, no. 10, 1997, 1361-1318;  by A. M. Coyne  in Zentralblatt für Mathematik und ihre Grenzgebiete Mathematics Abstracts, 1996,  837-41; MR1347448 (96f:00008a) and MR1355999 (96f:00008b).
 
Algebra.  New York:  John Wiley & Sons, 1986.


Journal Articles:


The Projective Geometry of Mario Pieri -- A Legacy of Georg Karl Christian von Staudt.   On-line version published October, 2005: ScienceDirect (www.sciencedirect.com).  Print version: Historia Mathematica, 33/3, August 2006, 277-314.   III, volume 2, no. 2, July-December, 2006, 277-314.   MR2233594 (2007b:01018)  Zbl. (1101.51002).
 
The Theorem of Pappus:  A Bridge between Algebra and Geometry.  The American Mathematical Monthly 109, no. 6, June/July 2002, 497-516. MR1908005 (2003c:51001), Zbl (1028.51001).  Cited in Zbl (1052.20016).    Stable URL: http://links.jstor.org/sici?sici=0002-9890%28200206%2F07%29109%3A6%3C497%3ATTOPAB%3E2.0.CO%3B2-Q

The Next Step: Extended Group Projects for Introductory Mathematics Classes.  Primus, June 1996, 167-172 (co-author: R.Vakilian).

In the Shadows of Giants: The Work of Mario Pieri in Foundations of Mathematics.  History and Philosophy of Logic 16, no. 1, 1995, 107-119.  MR1468603 (98e:03001), Zbl (0844.01007).  Cited in MR1936800 (2300h:01022) and MR1918541 (2003g:01028).


An Invitation to Integration in Finite Terms.  The College Mathematics Journal 25, September 1994,  295-308 (co-author: A. Zakeri).
Stable URL: http://links.jstor.org/sici?sici=0746-8342%28199409%2925%3A4%3C295%3AAITIIF%3E2.0.CO%3B2-H . 

Connections in Mathematics: An Introduction to Fibonacci via Pythagoras.  Fibonacci Quarterly 31, no. 1,  February, 1993, 21-27. . MR1202338 (94g:01003)

Mario Pieri and his Contributions to Geometry and Foundations of Mathematics.  Historia Mathematica 20, no. 3, August 1993, 285-303..  MR1238180 (94d:01074)  doi:10.1006/hmat.1993.1024

The Work of Mario Pieri in the Foundations and Philosophy of Mathematics.  History and Philosophy of Logic 14, 1993, 215-220 (co-author: F. Rodriguez-Consuegra).

Lines without order.  The America Mathematical Monthly 99, no. 8,  October, 1992, 738-745. MR1186458 (93j:51010)
Stable URL: http://links.jstor.org/sici?sici=0002-9890%28199210%2999%3A8%3C738%3ALWO%3E2.0.CO%3B2-W

Mathematics as a Humanistic Discipline.  Humanistic Mathematics Network Journal. April, 1992, 69-76.

Small Steps to a Student Centered Classroom.  Primus, September, 1991, 253-274 (co-authors: J. Castro, J. Gold, M. Schilling, J. Zeitlin).

Mario Pieri: His Contributions to the Foundations and Teaching of Geometry.  Historia Mathematica 16 (3), 1989, 287-288.

Mathematics 095, Review of Pre-College Mathematics: A Modular, Multi-Media Course.  International Journal of Mathematics, Education, Science and Technology 15, 1984, 221-230.


Chapters in Books:

The Graduate Student as Teacher, Faculty Meetings as a Catalyst for Teacher Development.  In Mathematics Education:  An Encyclopedia.  Taylor & Francis Group, Farmer Press Publisher, 2001, 195-197.

Teaching Mathematics Humanistically: A New Look at an Old Friend.  In Essays in Humanistic Mathematics: Mathematical Association of America (MAA) Notes Series, 1993, 183-190.


Book Reviews

<>Charpentier, Eric, Annick Lesne, and Nikolai Nikolski, Editors Kolmogorov’s Heritage in Mathematics.  Book Review MAA online. http://mathdl.maa.org/mathDL/19/<>

Magnani, Lorenzo . Philosophy and Geometry, Theoretical and Historical Issues. Book Review  Mathesis.  Series III, volume 2, no. 2, July-December, 2006, 403-404.  (www.comoydondecomprar.com/mathesis/actual.htm)

Polster, Burkard.  A Geometrical Picture Book.  Book Review MAA online, 1999 http://mathdl.maa.org/mathDL/19/

Wilson, Alistair Macintosh.  The Infinite in the Finite.  Book Review.  Maa online,  1999. http://mathdl.maa.org/mathDL/19/