Publications
First, a list of my scientific publications:
- Unidades de Anéis de Grupo e o Problema do
Isomorfismo, M.A. dissertation, IME-USP, October 1981
- "Diophantine Equations and Geometry," Bowdoin Prize expository
essay on the Natural Sciences, 1987
- Arithmetic of p-adic Modular Forms, Ph.D. thesis,
Harvard University, June 1987
- Arithmetic of p-adic Modular Forms, Lecture Notes in
Mathematics vol. 1304, Springer-Verlag, 1988
- Review of Mathenauts, ed. by Rudy Rucker, Mathematical
Intelligencer, 10 (1988), no. 4, p. 70
- Primeiros Passos p-ádicos, notes for a
mini-course given at the 17^{o} Colóquio Brasileiro de
Matemática, IMPA, 1989
- "Pontos Racionais em Curvas Algébricas", expository article,
in Atas do 17^{o} Colóquio Brasileiro de
Matemática, 1989
- "Deforming Galois Representations: Controlling the Conductor,"
Journal of Number Theory, 34 (1990), 95--113
- Introdução às Formas Modulares,
notes for a mini-course given at the X Escola de Álgebra,
February 1989, IMPA, 1990
- "Curvas Elípticas e o `Teorema' de Fermat", expository
article, in Atas da X Escola de Álgebra, SBM/IMPA,
1990.
- "Em Busca da Demonstração Maravilhosa," expository
article for high school teachers, in Revista do Professor de
Matemática, 1990
- "The Square-free Sieve and the Rank of Elliptic Curves," with Barry
Mazur, Journal of the A.M.S., 4 (1991), 1--23
- "On the Ordinary Hecke Algebra", Journal of Number Theory,
41 (1992), 178--198
- "Families of Modular Eigenforms," with Barry Mazur,
Mathematics of Computation, 58 (1992), 793--805
- "The Square-free Sieve over Number Fields," Journal of
Number Theory, 43 (1993), 109--122
- Advances in Number Theory: the proceedings of the third
conference of the Canadian Number Theory Association, editor,
with Noriko Yui; Oxford University Press, 1993.
- "On the Characteristic Power Series of the U operator," with
Barry Mazur, Annales de L'Institut Fourier, 42
(1993), 301--312.
- p-adic Numbers: an introduction, Springer-Verlag,
Berlin, 1993. A second edition has appeared, see
below.
- "Continuity Properties of p-adic Modular Forms," in
Elliptic Curves and Related Topics, ed. by H. Kisilevsky
and M. R. Murty, American Mathematical Society, 1994.
- "A Marvelous Proof," American Mathematical
Monthly, 101(1994), 203--222.
- "E_{2}, Theta, and Overconvergence" with Robert Coleman and
Naomi Jochnowitz, International Mathematics Research
Notices, 1995, Number 1, 23--41.
- Arithmetic of Diagonal Hypersurfaces over Finite Fields,
with Noriko Yui, London Mathematical Society Lecture Note
Series, Cambridge University Press, 1995.
- "Deforming Galois Representations: a survey," in Seminar of
Fermat's Last Theorem, CMS Conference Proceedings, vol. 17,
AMS, 1995, pp. 179--207.
- "Searching for p-adic eigenforms," with Barry Mazur,
Mathematics Research Letters, 2(1995), 515--536.
- "Uma Demonstração Maravilhosa,"
Matemática Universitária, 19
(December, 1995), 16--43.
- "Brauer Numbers of Twisted Fermat Motives," with Noriko Yui,
in Number Theory: New York Seminar, 1991--1995, ed. by
D. V. Chudnosvsky, G. V. Chudnovsky, and M. B. Nathanson,
Springer-Verlag, 1996.
- p-adic Numbers: an introduction, second edition,
Springer-Verlag, Berlin, 1997.
- "On the Density of Modular Representations," with Barry Mazur, in
Computational Perspectives on Number Theory (Chicago, Illinois
1995), AMS/IP Studies in Advanced Mathematics, vol. 7 (1998),
127--142.
- "Non-ordinary forms: a story," Experimental Mathematics,
6 (1997), 195--205.
- "Observations on Fermat Motives of K3-Type", with Noriko Yui,
Journal of Number Theory 71 (1998), 203--226.
- p-adic Numbers: an introduction, second
edition, corrected second printing, Springer-Verlag, Berlin, 2000.
- "Where the Slopes Are," Journal of the Ramanujan Mathematical
Society, 16 (2001), 75--99.
- "Deformations of Galois Representations," in Arithmetic Algebraic
Geometry, ed. by Brian Conrad and Karl Rubin, American
Mathematical Society, 2001, pp. 235--406. (With appendices by Mark
Dickinson, Tom Weston, and Matthew Emerton.)
- Review of Cohomology of Number Fields, by Jürgen
Neukirch, Alexander Schmidt, and Kay Wingberg. Bulletin of the
American Mathematical Society, 39 (2001), 101--107.
- Math through the Ages: A Gentle History for Teachers and
Others, with William P. Berlinghoff.
Oxton House Publishers,
2002.
- Review of The Honors Class, by Benjamin Yandell.
Science, 296 (May 3, 2002), pp. 853-854.
- p-adic Numbers: an introduction, second
edition, corrected third printing, Springer-Verlag, Berlin, 2003.
- Math through the Ages, Expanded Edition: A Gentle History for
Teachers and Others, with William P. Berlinghoff. Mathematical Association of America and
Oxton House Publishers,
2004.
- "As Others See Us: Four Science-Fictional Mathematicians," Math
Horizons, April 2004.
- History of Mathematics, chapter 2 in Using the Mathematics
Literature, ed. by Kristine Fowler, Marcel Dekker, 2004.
- Review of János Bolyai, Non-Euclidean Geometry, and the
Nature of Space, by Jeremy J. Gray, Science, 306
(December 10, 2004), pp. 1893–1894.
- Review of Sherlock Holmes in Babylon and Other Tales of
Mathematical History, ed. by Marlow Anderson, Victor Katz, and
Robin Wilson,
Aestimatio
2 (2005), 68–70.
- Review of Letters to a Young Mathematician, by Ian Stewart,
Science and Spirit, September-October 2006
- "Euler's Convincing Non-Proofs,"
FOCUS, January 2007
- Review of A First Course in Modular Forms, by Fred Diamond and
Jerry Shurman, American Mathematical Monthly, January 2007
- Review of Equations from God, by Daniel Cohen, First
Things, December 2007
- "Local and Global in Number Theory," in the Princeton
Companion to Mathematics (Princeton University Press, 2008)
- "Numbers and Number Systems," in the Princeton
Companion to Mathematics (Princeton University Press, 2008)
- Review of Is God a Mathematician?, by Mario Livio. First
Things, February 2009
- Review
of Plato's Ghost, by Jeremy Gray,
Aestimatio,
6 (2009). (Actually posted July 2010.)
- "How to Read Mathematics", with Shai Simonson, Hacker Monthly,
October 2010, pp. 4–8. This is a shorter version of an article
posted online
here.
- Pathways from the Past I: Using History to Teach Numbers,
Numerals, & Arithmetic, with William P. Berlinghoff. Oxton House,
2010.
- "Rigid
Calabi-Yau Threefolds over Q are Modular" with Noriko
Yui, Expositiones Mathematicae 29(2011), 142-149.
- "Was Cantor Surprised?", American Mathematical
Monthly 118, March 2011, 198-209.
- "Learning to Move with Dedekind," to appear in Mathematical Time
Capsules, to be published by the MAA.
I've also published a few other things...
- Many reviews of books related in some way to mathematics, most of
them in either MAA
Reviews. I've
listed other reviews above, but the MAA ones are too many to list
here.
- The liner notes for the video/DVD of
Fermat's
Last Tango, a
musical play about the proof of Fermat's Last Theorem. I was a
consultant for the authors while they
were writing the play, and ended up writing most of the booklet that
comes with the video/DVD which is distributed by the
Clay Mathematics Institute.
- I was one of the "steering advisors" for Mathematics
Illuminated, a series of videos and other resources for
mathematics teachers and others interested in mathematics.
- Many reviews of science fiction and fantasy literature, appearing
in Science Fiction Review, Fantasy Review, and
The New York Review of Science Fiction, among others. These
were mostly some time ago, when I had more free time.
- Five short articles in The Evangelical Dictionary of
Theology, ed. by Walter Elwell, Baker Book House, 1984.
- One trimester of curriculum material for Sunday School, Presbyterian
Church of Brazil.
- Software Reviews:
- "A Look at PARI and GP," Notices of the
American Mathematical Society, 38 (1991),
903--904
- "Mathematica 2.0 for Windows," Notices of the
American Mathematical Society, 39 (1992),
435--437
- "MathType for Windows," Notices of the American
Mathematical Society, 39 (1992), 1069--1075
I've been editor of FOCUS, the newsletter of the Mathematical
Association of America, since November 1999. My term will end after the
Joint Mathematics Meetings in January 2011.
And finally there's MAA
Reviews, the MAA's online book review and database, which aims to cover
everything that's published in the field. I'm the editor, and also
contribute (mostly brief) reviews. You need to be a member of MAA to get to
the reviews here, but the current reviews are always accessible through the
MAA web site.
Fernando Q. Gouvêa ---- fqgouvea@colby.edu
Last modified: Mon Sep 06 10:11:16 -0400 2010