First, a reader - especially one interested in teaching, one interested in introducing non-trivial ideas in a motivated way - may find suitable material in various corners of my web site, especially in the Courses I Teach or Talented Youth sections.
I only reference books that I have in my own personal library.
Aigner, M. & Ziegler, G., Proofs from the BOOK (3rd edition), Springer-Verlag (2003), 94-97.
Baker, A., Transcendental Number Theory, Cambridge University Press, 1975
Baker, A. & Masser, D., Transcendence Theory: Advanced and Applications, Proceedings of a conference held in Cambridge in 1976, Academic Press, 1977
Baker, A. & Wüstholz, G., Number Theory, transcendence and Diophantine geometry in the next millennium (in MATHEMATICS: FRONTIERS AND PERSPECTIVES, V. Arnold, M. Atiyah, P. Lax and B. Mazur (Editors), American Mathematical Society, (2000), 1-12)
Berggren, L., Borwein, J. and P., Pi : A Source Book, Springer, 1997
Borel, A., Chowla, S., Herz, C.S., Iwasawa, K., Serre, J-P., Seminar on Complex Multiplication, Springer Lecture Notes on Mathematics, Number 21, 1966
Browder, F. (Editor), Mathematical Developments Arising From Hilbert Problems, American Mathematical Society, 1976
Brown, Dan, The Da Vinci Code, Corgi Books, 2003
Calkin, N. and H. Wilf, H. Recounting the rationals , American Mathematical Monthly, 107 (2000), 360-363.
Cassels, J. W. S., An Introduction to Diophantine Approximation (Cambridge Tracts N0. 45), Cambridge University Press, (First printed 1957, reprinted 1965)
Conway, J. H., & Guy, R. K., The Book of Numbers, COPERNICUS (An Imprint of Springer-Verlag), 1996
Devaney, R. L., Chaos, Fractals, and Dynamics ( COMPUTER EXPERIMENTS IN MATHEMATICS ), Addison-Wesley, (1990) (I have a signed copy from the AMS Centenary Meeting, Cincinnati, January 1994.)
Fel'dman, N. I., and A. B. Shidlovskii, A. B., The development and present state of the theory of transcendental numbers . (London Mathematical Society Translations) Russian Mathematical Surveys (1967), Vol. 22, 1-79.
Gelfond, A. O., Algebraic and Transcendental Numbers. Dover, 1960
Gelfond, A. O. and Yu. V. Linnik, Yu. V., Elementary Methods in Analytic Number Theory, George Allen & Unwin, 1966
Goldfeld, D., Gauss' class number problem for imaginary quadratic fields , Bulletin American Mathematical Society, July 1985, Vol. 13, Number 1, 23-37.
Gowers, W. T., THE IMPORTANCE OF MATHEMATICS , available form his Cambridge University web site at
Granville, A. and Tucker, T. J., It's As Easy As abc . Notices American Mathematical Society, November 2002 (available on-line from www.ams.org).
Kline, M., Mathematical Thought from Ancient to Modern Times. Oxford University Press, 1972
Lang, S., Introduction to Transcendental Numbers, Addison-Wesley, 1966
Le Veque, W. J., Topics in Number Theory (Vol. 2), Addison-Wesley, (Second printing 1961)
Mahler, K. Lectures on Diophantine Approximations (Part 1: g-adic anumbers and Roth's theorem), University of Notre Dame, 1961
Masser, D., Elliptic Functions and Transcendence, Springer Lecture Notes in Mathematics, Number 437, 1975
Mordell, L. J., Diophantine Equations, Academic Press, (1969). I have a signed 1st edition dated 21st August 1969, the day of the Oxford 1969 photo. See the Oxford 1969 corner of my web site.
Nasar, S., A Beautiful Mind . faber and faber, 1998
Niven, I., Irrational Numbers, Carus Mathematical Monographs , MAA, 1967
Reid, C., Hilbert (includes an appreciation of Hilbert's mathematical work by Hermann Weyl), George Allen & Unwim Ltd, 1970
Schmidt, W., Review of Selected mathematical papers of Axel Thue , Bulletin of the American Mathematical Society, Vol. 84, Number 5, September 1978, 919-925.
Siegel, C. L., Transcendental Numbers, Princeton University Press, 1949 (recently reissued)
Stollarsky, K. B., Algebraic Numbers and Diophantine Approximation, Marcel Dekker Inc., 1974
Stollarsky, K. B. Review of books by Baker, Mahler, and Waldschmidt, Bulletin of the American Mathematical Society, Vol. 84, Number 6, November 1978, 1370-1378.
Waldschmidt, M., Nombres transcendants, Springer Lecture Notes in Mathematics, Number 402, 1975
Whittaker and Watson. Modern Analysis. Cambridge University Press (4th edition, 1935). (My own copy, which I bought in 1990, was the personal copy of the late Cornelius Lanczos. It is stamped as follows: PROF. C. LANCZOS PURDUE UNIVERSITY LAFAYETTE, IND., and is signed: C. Lanczos 1938)
Wüstholz, G., A Panorama of Number Theory (or The View from Baker's Garden), Cambridge University Press, 2002
The MacTutor History of Mathematics archive at http://www-groups.dcs.st-andrews.ac.uk/~history/ is a famous
resource (though I have noted frequent errors of mathematical detail) and some quite bizzare ommisions (e.g. there are - as yet - no entries for Wolfgang Schmidt or Theodore Schneider).
After August 31st 2007 please use the following Gmail address: jbcosgrave at gmail.com
This page was last updated 18 February 2005 15:10:01 -0000