Lecture Notes

Number Theory, Algebraic Geometry and Cryptography

"Beauty is the first test: there is no permanent place in the world for ugly mathematics."
- G. H. Hardy

  • Lecture Notes

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  • Problem Sets

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  • References and Further Reading

    • Elementary Number Theory

    • G. H. Hardy and E. M. Wright, An Introduction to the Theory of Numbers, Fourth Edition, Oxford at the Clarendon Press, 1975
      Neal Koblitz, A Course in Number Theory and Cryptogtraphy, Graduate Texts in Mathematics 114, Springer-Verlag, 1994
      Franz Lemmermeyer, Numbers and Curves, Springer-Verlag, 2001
      Manfred Schroeder, Number Theory in Science and Communication with Applications in Cryptography, Physics, Digital Information, Computing, and Self-Similarity, Fifth Edition, Springer-Verlag, 2009
      Simon Singh, Fermat's Last Theorem, The Story of a Riddle that Confounded the World's Greatest Minds for 358 Years, Fourth Estate
      André Weil, Number Theory for Beginners, Springer-Verlag, 1979

    • Cryptography

    • Neal Koblitz, A Course in Number Theory and Cryptogtraphy, Graduate Texts in Mathematics 114, Springer-Verlag, 1994
      Bruce Schneier, Applied Cryptography, Protocols, Algorithms, and Source Code in C, Second Edition, John Wiley & Sons, Inc., 1996

    • Analytic Number Theory

    • Tom M. Apostol, Introduction to Analytic Number Theory, Undergraduate Texts in Mathematics, Springer-Verlag, 1976
      Tom M. Apostol, Modular Functions and Dirichlet Series in Number Theory, Graduate Texts in Mathematics 41, Springer-Verlag, 1976

      This is the second volume of a 2-volume textbook along with the preceding book.

      Peter Borwein, Stephen Choi, Brendan Rooney, and Andrea Weirathmueller, The Riemann Hypothesis, A Resource for the Afficionado and Virtuoso Alike, Springer-Verlag, 2007
      Igor Dolgachev, Lectures on Modular Forms, Lecture Notes, Fall 1997/98
      Neal Koblitz, p-adic Numbers, p-adic Analysis, and Zeta-Functions, Graduate Texts in Mathematics 58, Second Edition, Spriner-Verlag, 1984
      Donald J. Newman, Analytic Number Theory, Graduate Texts in Mathematics 177, Springer-Verlag, 1997
      S.J. Patterson, An introduction to the theory of the Riemann Zeta-Function, Cambridge University Press, 1987
      Dan Rockmore, Stalking the Riemann Hypothesis, The Quest to Find the Hidden Law of Prime Numbers, Pantheon Books, 2005
      E. C. Titchmarsh, The Theory of the Riemann Zeta-Function, Oxford University Press, 1986
      Don Zagier, Modular Forms of One Variable, Lecture Notes, 1991

    • Elliptic Curves

    • J.W.S. Cassels, Lectures on Elliptic Curves, Cambridge University Press, 1991
      Dale Husemöller, Elliptic Curves, Graduate Texts in Mathematics 111, Springer, 2002
      Neal Koblitz, Introduction to Elliptic Curves and Modular Forms, Graduate Texts in Mathematics 97, Springer-Verlag, 1984
      J.S. Milne, Elliptic curves, 1996
      Bjorn Poonen, Elliptic Curves, 2001
      Joseph H. Silverman, The Arithmetic of Elliptic Curves, Springer-Verlag, 1985

    • Random Matrices

    • Pavel Bleher and Alexander Its (eds.), Random Matrix Models and Their Applications, Cambridge University University Press, 2001
      Madan Lal Mehta, Random Matrices, Elsevier Academic Press, 2004
      M. L. Mehta, Random Matrices and the Statistical Theory of Energy Levels, Academic Press, 1967
      Leonid Pastur and Mariya Shcherbina, Eigenvalue Distribution of Large Random Matrices, Mathematical Surveys and Monographs Volume 171, American Mathematical Society, 2010