620-113 Continued Fractions

 

Course Outline

  • Outline,PDF (20 K)
  • Links

  • An informative and in depth introduction, but no proofs Eric Weistein's site
  • Similar to the above J.D. Barrow's site
  • The best introduction with examples, but cuts out early R. Knott's site
  • Brief introduction with some proofs A. Van Tuyl's site
  • Similar to the aboveAlexander Bogomolny's site
  • Short introduction, good on the motivation but no proofs Yury Grabovsky's site
  • Very cursory Clark Kimberling's site
  • Number theory lecture notes, Chapter 16 is relevant MP313
  • Number theory lectures William Stein's site
  • Descriptions of areas/courses in number theory, lecture notes NTW
  • Pianos and Continued Fractions Edward G. Dunne's site
  • continued fractions and chaos Robert Corless's article
  • Constants associated with continued fractions Steve Finch's site
  • Continued Fraction Arithmetic Bill Gosper's site
  • D.H. Bailey and R.E. Crandall's papers on normal numbers baicran, bcnormal
  • Bibliography

  • Bibliography,PDF ( K)
  • Lecture Notes

  • Introduction,PS (36 K)
  • Definitions,PDF (47 K)
  • Identities,PDF (31 K)
  • Some applications,PDF (32 K)
  • Rational Numbers, Euclid's GCD algorithm,PDF (55 K)
  • Recurrence relations,PDF (50 K)
  • Quadratic irrational numbers,PDF (57 K)
  • Bounds on and Convergence of continued fractions,PDF (67 K)
  • Algebraic and transcendental numbers,PDF ( K)
  • Klein model,PDF (13 K)
  • Assignment

    Given out at 3rd Lecture, 21-8-2003, and due two weeks later, 4-9-2003. Place assignments in the 620-113 box (no's 5 and 6) in the North corridor of the Richard Berry Building.
  • Assignment,PS (54 K)
  • Maple worksheets and PS files

  • Maple worksheet of simple examples,mws (15 K)
  • PS output of simple examples,PS (157 K)
  • Maple worksheet of CF for Pi,mws (36 K)
  • PS output of CF for Pi,PS (227 K)
  • Historical notes

  • Leonhard Euler,PS (844 K)
  • Carl Friederich Gauss,PS (1092 K)
  • Srinivasa Ramanujan,PS (545 K)
  • Aleksander Khinchin,PS (578 K)
  • Created: 22 January 2003
    Last modified:  2 February 2005
    Authorised by: Head, Department of Mathematics and Statistics.
    
    Maintained by: Nicholas Witte, Department of Mathematics and Statistics.
    Email: N.Witte@ms.unimelb.edu.au