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 - Books - Journal Articles - Chapters in Books - Book Reviews

Selected Invited Talks
  • 2011 - Mathematical Culture and Mathematical Life. MAA Panel Discussion. Joint Mathematics Meetings, New Orleans, Lousiana, January.
  • 2010 - Mario Pieri, the man, the scholar, the teacher. L’opera scientifica di Mario Pieri (1860-1913) a 150 anni dalla nascita. Associazione Sub. Mathesis – Seminario di Storia delle Matematiche Tullio Viola, Dipartimento di Matematica ‘Giuseppe Peano’ – Università di Torino March.
  • 2009 - (event link) Projective Geometry from Pappus to Pieri. Sonoma State University Department of Mathematics and Statistics Colloquium. April.
  • 2008 - (event link) I fondamenti della geometria nella scuola di Peano. Congresso Internazionale Giuseppe Peano e la sua Scuola, fra matematica, logica e interlingua. Accademia delle Scienze, Torino, Italy. October.
  • 2008 - Why do I need to prove this? In-Service Geometry Workshop for High School Teachers. Department of Mathematics. University of Utah. August.
  • 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.
  • 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
  • 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
  • Mario Pieri: Man, Mathematician, Mentor. La Matematica nella Società e nella Cultura - Rivista dell'Unione Matematica Italiana (ISSN 1972-7356) To appear (in Italian), December 2010.
  • 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
  • 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
  • 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
  • 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
  • To appear, December 2010: The foundations of geometry in the school of Peano. Chapter 9 in Giuseppe Peano between Mathematics and Logic edited by F. Skov. Italy: Springer-Verlag, 161-173.
  • 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
  • Califano, M. B. (ed.) Paradossi e disarmonie nelle scienze e nelle arti. History and Philosophy of Logic, 30 (3), 2009
  • Charpentier, Eric, Annick Lesne, and Nikolai Nikolski, Editors Kolmogorov’s Heritage in Mathematics. Book Review MAA online.
  • Magnani, Lorenzo . Philosophy and Geometry, Theoretical and Historical Issues. Book Review Mathesis. Series III, volume 2, no. 2, July-December, 2006, 403-404.URL
  • Polster, Burkard. A Geometrical Picture Book. Book Review MAA online, 1999
  • Wilson, Alistair Macintosh. The Infinite in the Finite. Book Review. Maa online, 1999.