620-113CF

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 above Alexander 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)