MSRI

Suggested readings in Algorithmic number theory

This list was provided by the organizers of the Fall 2000 program in Algorithmic number theory.

Editor: Adleman, Leonard M. / Huang, Ming-Deh A. 
Title:  Algorithmic number theory : first international symposium,
        ANTS-I, Ithaca, NY, USA, May 6-9, 1994 : proceedings 
Publ:   Springer-Verlag
Year:   c1994
Series: Lecture notes in computer science
SerNo:  877 
Status: HERE

Author: Bach, Eric / Shallit, Jeffrey Outlaw.
Title:  Algorithmic number theory, v. 1: Efficient algorithms 
Publ:   MIT Press
Year:   c1996
Series: Foundations of computing 
Status: HERE

Author: Brassard, Gilles
Title:  Modern cryptology : a tutorial
Publ:   Springer-Verlag
Year:   1988.
Series: Lecture notes in computer science 
SerNo:  325
Status: OP

Editor: Bosma, Wieb
Title:  Algorithmic number theory : 4th international symposium, ANTS-IV,
        Leiden, the Netherlands, July 2-7, 2000 : proceedings 
Publ:   Springer
Year:   2000
Series: Lecture notes in computer science 
SerNo:  1838
Status: ORDERED 000923

Editor: Buhler, Joe P., 1950- 
Title:  Algorithmic number theory : third international symposium,
        ANTS-III, Portland, Oregon, USA, June 21-25, 1998 : proceedings  
Publ:   Springer
Year:   c1998
Series: Lecture notes in computer science
SerNo:  1423 
Status: HERE

Editor: Cassels, J. W. S. (John William Scott) ed. / Frölich, Albrecht ed. 
Title:  Algebraic number theory; proceedings of an instructional conference
Publ:   Academic Press
Year:   1967
Status: HERE

Author: Cassels, J. W. S. (John William Scott) / Flynn, E. V.
Title:  Prolegomena to a middlebrow arithmetic of curves of genus 2 
Publ:   Cambridge University Press
Year:   1996
Series: London Mathematical Society lecture note series
SerNo:  230 
Status: HERE

Author: Cohen, Henri
Title:  A course in computational algebraic number theory 
Publ:   Springer-Verlag
Year:   c1993
Series: Graduate texts in mathematics
SerNo:  138
Status: HERE

Author: Cohen, Henri.
Title:  Advanced topics in computational number theory 
Publ:   Springer
Year:   1999
Series: Graduate texts in mathematics
SerNo:  193
Status: HERE

Editor: Cohen, Henri. 
Title:  Algorithmic number theory : second internati[o]nal symposium,
        ANTS-II, Talence, France, May 18-23, 1996 : proceedings  
Publ:   Springer
Year:   c1996
Series: Lecture notes in computer science
SerNo:  1122 
Status: HERE

Editor: Cornell, Gary / Silverman, Joseph H., 1955- / Stevens, Glenn, 1953-
Title:  Modular forms and Fermat's last theorem 
Publ:   Springer
Year:   c1997
Status: HERE

Editor: Cornell, Gary / Silverman, Joseph H., 1955- 
Title:  Arithmetic geometry 
Publ:   Springer-Verlag
Year:   c1986
Status: HERE

Author: Ding, C. (Cunsheng), 1962- / P°ei, Ting-i. / Salomaa, Arto.
Title:  Chinese remainder theorem : applications in computing, coding,
        cryptography  
Publ:   World Scientific
Year:   c1996
Status: HERE

Author: von zur Gathen, J. / Gerhard, J.  
Title:  Modern computer Algebra
Publ:   Cambridge University Press
Year:   1999
ISBN:   0521641764 
Status: ORDERED 000923

Author: Goss, David, 1952-
Title:  Basic structures of function field arithmetic 
Publ:   Springer
Year:   1998
Series: Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge
SerNo:  35
Status: HERE

Author: Hartshorne, Robin
Title:  Algebraic geometry / Robin Hartshorne.
Publ:   Springer-Verlag
Year:   c1977
Series: Graduate texts in mathematics
SerNo:  52
Status: HERE

Author: Koblitz, Neal, 1948-
Title:  A course in number theory and cryptography 
Publ:   Springer-Verlag
Year:   c1987
Series: Graduate texts in mathematics
SerNo:  114
Status: HERE

Author: Lang, Serge, 1927-
Title:  Introduction to modular forms 
Publ:   Springer-Verlag
Year:   1976
Series: Grundlehren der mathematischen Wissenschaften
SerNo:  222
Status: HERE

Editor: Lenstra, H. W. / Tijdeman, R.
Title:  Computational methods in number theory 
Publ:   Mathematisch Centrum (Amsterdam)
Year:   1982
Series: Mathematical Centre tracts 
SerNo:  154-155
Status: HERE

Author: Lenstra, A. K. (Arlen K.), 1956- / Lenstra, H. W.
Title:  The development of the number field sieve 
Publ:   Springer-Verlag
Year:   c1993
Series: Lecture notes in mathematics
SerNo:  1554
Status: HERE

Author: Lidl, Rudolf / Niederreiter, Harald, 1944-
Title:  Finite fields / Rudolf Lidl, Harald Niederreiter 
Publ:   Addison-Wesley 
Year:   1983
Series: Encyclopedia of mathematics and its applications 
SerNo:  20
Status: HERE

Editor: van Lint, J. H. / Tijdeman, R.
Title:  Cryptography & Data Protection
Series: Verhandelingen der Koninklijke Nederland
SerNo:  38 
ISBN:   044485746X 
Status: Out of print

Author: Menezes, A. J. 
Title:  Elliptic curve public key cryptosystems
ISBN:   0792393686
Publ:   Kluwer 
Status: ORDERED 000923

Author: Menezes, A. J. / P.C. van Oorschot / S.A. Vanstone
Title:  Handbook of applied cryptography
Publ:   CRC Press
Year:   1997
ISBN:   0849385237
Status: ORDERED 000923

Editor: Menezes, A. J. (Alfred J.), 1965- 
Title:  Applications of finite fields 
Publ:   Kluwer Academic Publishers
Year:   c1993
Series: The Kluwer international series in engineering and computer science: Communications and information theory 
SerNo:  SECS199
Status: HERE

Editor: Loxton, J. H.
Title:  Number theory and cryptography 
Publ:   Cambridge University Press
Year:   1990
Series: London Mathematical Society lecture note series
SerNo:  154
Status: OP (SEARCHING)

Author: Pohst, Michael E.  
Title:  Computational algebraic number theory
Publ:   Birkhäuser 
Year:   1993
ISBN:   0817629130
Status: ORDERED 000923

Author: Pohst, M. / Zassenhaus, Hans
Title:  Algorithmic algebraic number theory / M. Pohst, H. Zassenhaus.
Publ:   Cambridge University Press
Year:   1989
Series: Encyclopedia of mathematics and its applications 
Status: HERE

Editor: Pomerance, Carl / Goldwasser, S. (Shafi), 1958-
Title:  Cryptology and computational number theory 
Publ:   American Mathematical Society
Year:   c1990
Series: Proceedings of symposia in applied mathematics
SerNo:  42
Status: HERE

Author: Riesel, Hans, 1929-
Title:  Prime numbers and computer methods for factorization 
Publ:   Birkhäuser
Year:   1985
Series: Progress in mathematics
SerNo:  57
Status: HERE

Author: Silverman, Joseph H., 1955- / Tate, John Torrence, 1925-
Title:  Rational points on elliptic curves 
Publ:   Springer-Verlag
Year:   c1992
Series: Undergraduate texts in mathematics 
Status: HERE

Author: Silverman, Joseph H., 1955-
Title:  Advanced topics in the arithmetic of elliptic curves 
Publ:   Springer-Verlag
Year:   c1994
Series: Graduate texts in mathematics
SerNo:  151
Status: HERE

Author: Silverman, Joseph H., 1955-
Title:  The arithmetic of elliptic curves 
Publ:   Springer-Verlag
Year:   c1986
Series: Graduate texts in mathematics
SerNo:  106
Status: HERE

Author: Smart, Nigel P. (Nigel Paul), 1967-
Title:  The algorithmic resolution of diophantine equations 
Publ:   Cambridge University Press
Year:   1998
Series: London Mathematical Society student texts
SerNo:  41 
Status: HERE

Author: Zimmer, Horst G.
Title:  Computational problems, methods, and results in algebraic number theory
Publ:   Springer-Verlag
Year:   1972
Series: Lecture notes in mathematics
SerNo:  262 
Status: HERE

Everything by Diophantus, Fermat (there is a new edition of his
        number theory!! in French, strongly recommended), Euler
        (his Algebra!!), Grothendieck, Serre, Weil.