Project III (MATH3382) 2014-15


Exploring the Number Jungle

Norbert Peyerimhoff

Description

At the beginning of this project is E. Burger's book ''Exploring the Number Jungle'', which is a very good introduction into problems in number theory and diophantine approximation. The book has plenty of challenging problems and questions while it gives first insights into many interesting special topics in this area. The book is an ideal platform to start and then to branch out into many different specialised topics like, e.g., ''History of irrational and transcendental numbers'', ''Connections between diophantine approximation and hyperbolic geometry'', ''Minkowski's and Pick's theorem and applications'', etc...

Corequisite

There is no explicit corequisite. Useful courses to be taken simultaneously are here, however, Geometry III , Number Theory III or Elliptic Functions III.

Resources

Some recommendable Books covering the general theory are
  • Edward B. Burger: Exploring the Number Jungle , Student Mathematical Library 8, American Mathematical Society, 2000

  • G. H. Hardy, E. M. Wright: An Introduction to the Theory of Numbers , Fifth Edition, Oxford Science Publications, Clarendon Press, 1979

  • J. W. S. Cassels: An Introduction to Diophantine Approximation, Cambridge Tracts in Mathematics and Mathematical Physics 45, Hafner Publishing Company, 1972

email: N Peyerimhoff