Number Theory

[Peter Murphy]

Well, since a fair amount of people have been asking for Number Theory
books (including myself, I must admit), I decided to get off my butt, 
and see the major number theorist in this department, Dr. Keith Matthews.
He is a really nice guy, and is always interested in writing and/or
distributing programs for number theory calculations. He even showed me
one of his newest programs, and demostrated it by factoring 2^71 -1 for
me.
	Anyway, I asked him if he had any bibliographies for the subjects
he teaches, and could I post it to the list. Voila! Not only did he have
it printed out on paper, but he also mailed me the relevant LATEX files.
I have decided to remove the LATEX symbols, course codes, class times, etc.,
from the files and just strip it down to the textbook list. Of course, this
is only for a 2nd level subject, but the Library of Congress catalog codes
included should help you look for new books. There are, of course, other 
books on this subject. I hope people find it useful. (If anyone wants the 
original LATEX files, well. . . I've got those too.) So, with Dr. Matthews
kind permission, I present the following refernces:

(Peter Murphy. <pkm at maths.uq.oz.au>)


{Textbooks: Number Theory}

G. Andrews, "Number theory",  QA 241.A5 1971,

D. M. Bressoud, "Factorization and primality testing", QA161.F3B731989,

T.H. Cormen, C.E. Leiserson, R.L. Rivest, "Algorithms", MIT Press, 1989,
 QA76.6.C6621990.

H. Davenport, "The higher arithmetic", QA 241.D2 1952;

G. H. Hardy and E. M. Wright, "Introduction to the theory of numbers",
 QA 241.H3 1945,

T. H. Jackson, "Number theory", QA 241.J3 1975,

N. Koblitz, "A course in number theory and cryptography", QA3.G7NO.114,

W. J. LeVeque, "Fundamentals of number theory",  QA 241.L57219771,

I. Niven, H.S. Zuckermann, H.L. Montgomery, "An introduction to the theory 
 of numbers", QA 241.N561991,

O. Ore, "Invitation to number theory", QA 241.O68 1967,

H. Riesel, "Prime numbers and computer methods for factorization", 
 QA 246.R54 1985,

K. Rosen, "Elementary number theory and its applications",  QA 241.R67 1984,

H. Shapiro, "Introduction to number theory",  QA 241.S445 1983,

M. Schroeder, "Number theory in science and communication",  QA 241.S318 1984,

W. Sierpinski, "Elementary theory of numbers",  QA 241.S477 1964,

H. Stark, "Introduction to the theory of numbers",  QA 241.S72 1970,

R. F. C. Walters, "Number theory -- an introduction",  QA 241.W32 1987,

N.L. Biggs, "Discrete Mathematics", QA 76.9.M35B541989,

P. Giblin, "Primes and Programming", Cambridge University Press 1993.


The following books are also of interest:

[(a)] H. Flanders, "Scientific Pascal", QA76.73P2F551984,

[(b)] R.K. Guy, "Unsolved problems in number theory", QA141.G891981.

[(c)] P. Ribenboim, "The book of prime number records", QA246.R471988.

{Textbooks: Cryptography}

N. Koblitz, "A course in number theory and cryptography", QA3.G7NO.114,

D. Welsh, "Codes and Cryptography", Oxford Science Publications, 1988,
 Z103.W461988

H.C.A. van Tilborg, "An Introduction to Cryptology", Kluwer Academic
 Publishers, 1988, Z103.T541988

W. Patterson, "Mathematical Cryptology for Computer Scientists and
 Mathematicians", Rowman and Littlefield, 1987, Z103.P351987

C. Pomerance, "Cryptology and Computational Nunber Theory",

Proceedings of Symposia in Applied Mathematics, Volume 42, AMS, 
  QA76.9.A25C841990

D.E.R. Denning, "Cryptography and Data Security", Addison-Wesley, 1982,
 QA76.9.A25D461982

G. Brassard, "Modern Cryptology: a tutorial", Lecture Notes in Computer 
 Science 325, Springer 1988, QA76.L4V.325

G.J. Simmons,"Contemporary Cryptology", IEEE Press, 1992, QA76.9.A25C66781992

{ Textbooks: Error--Correcting Codes}

S. Roman,"Coding and Information Theory", GTM 134, 1992, QA3.G7NO.134
 
S.A. Vanstone and P.C. van Ooorschot, "An Introduction to Error Correcting 
Codes", Kluwer Academic Publishers,1989, TK5102.5.V321989
 
R. Hill, "A First Course in Coding Theory", Oxford Applied Mathematics and
Computing Science Series, 1986, QA268.H551986

V. Pless, "Introduction to the Theory of Error-Correcting Codes", Wiley 1982,
QA268.P551982

D.G. Hoffman et al, "Coding Theory", Marcel Dekker, 1991, QA268.C691991

O. Pretzel, "Error--Correcting Codes and Finite Fields"", Oxford Applied 
Mathematics and Computing Science Series, Clarendon Press 1992.