MAT 465 -- Number Theory
References By Topic
- Prime Number Theory:
- A. E. Ingham, The Distribution of Prime Numbers, Cambridge University Press, 1990.
- Gérald Tenenbaum and Michel Mendes France, The Prime Numbers and Their Distribution, American Mathematical Society, 2000.
- Analytic Number Theory:
- Tom M. Apostol, Introduction to Analytic Number Theory, Springer-Verlag, 1986.
- Donald J. Newman, Analytic Number Theory, Springer-Verlag Graduate Texts in Mathematics #177, New York, 1998.
- A. G. Postnikov, Introduction to Analytic Number Theory, American
Mathematical Society, Translations of Mathematical Monographs Vol. 68, 1988.
- K. Chandrasekharan, Arithmetical Functions, Springer-Verlag,
1970.
- Probabilistic Number Theory:
- Gérald Tenenbaum, Introduction to Analytic and Probabilistic
Number Theory, Cambridge University Press, 1995.
- J. Kubilius, Probabilistic Methods in the Theory of Numbers,
American Mathematical Society, Translations of Mathematical Monographs Vol. 11, Providence, Rhode Island, 1978.
- Algebraic Number Theory:
- Harry Pollard and Harold G. Diamond, The Theory of Algebraic Numbers (2nd edition), Mathematical Association of America, Carus Mathematical Monographs, 1975.
- Pierre Samuel, Algebraic Theory of Numbers, Kershaw Publishing, London, 1971.
- Additive Number Theory:
- L. K. Hua, Additive Theory of Prime Numbers, American Mathematical
Society, Translations of Mathematical Monographs Vol. 13, Providence, Rhode Island, 1966.
- George E. Andrews, The Theory of Partitions, Cambridge University Press, 1984.
- Transcendental Number Theory:
- Ivan Niven, Irrational Numbers, Mathematical Association of America, Carus Mathematical Monographs, 1967.
- Lennart Berggren, Jonathan Borwein, Peter Borwein, Pi: A Source Book, Springer-Verlag, 1997.
- Alan Baker, Transcendental Number Theory, Cambridge University
Press, Cambridge, 1994.
- Computational Number Theory:
- Eric Bach and Jeffrey Shallit, Algorithmic Number Theory, MIT
Press, 1996.
- Henri Cohen, A Course in Computational Algebraic Number Theory,
Springer-Verlag, 1993.
- Applications to Cryptography:
- Neal Koblitz, A Course in Number Theory and Cryptography,
Springer-Verlag Graduate Texts in Mathematics #114, 1994.
- Carl Pomerance, ed. Cryptology and Computational Number Theory
Proceedings of Symposia in Applied Mathematics Vol. 42, American Mathematical Society, Providence, 1990.
- Additional References
- Joseph H. Silverman, A Friendly Introduction to Number Theory (2nd edition), Prentice-Hall, 2001.
- Edmund Landau, Elementary Number Theory, American Mathematical Society, 1999.
- H. Davenport, The Higher Arithmetic (7th edition), Cambridge University Press, 1999.
- Richard Dedekind, Essays on the Theory of Numbers, Dover, New York, 1963.
- A. Y. Khinchin, Three Pearls of Number Theory, Dover Publications, New York, 1998.
- Leonard Eugene Dickson, History of the Theory of Numbers,
Vols. 1,2,3, AMS Chelsea Publishing, Providence, 1992.
- Stefan A. Burr, ed. The Unreasonable Effectiveness of Number Theory, Proceedings of Symposia in Applied Mathematics Vol. 46, American Mathematical Society, 1991.
- Jonathan M. Borwein and Peter B. Borwein, Pi and the AGM,
John Wiley and Sons, 1998.
- Godfrey Harold Hardy, Ramanujan, American Mathematical Society,
1999.