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Exploring the number jungle : [electronic resource] a journey into diophantine analysis / Edward B. Burger.

Author/Creator:
Burger, Edward B., 1963-, author.
Publication:
Providence, RI : American Mathematical Society, c2000.
Format/Description:
Book
1 online resource (vi, 151 pages) : illustrations.
Series:
The Student Mathematical Library, v. 8
Status/Location:
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Other Title:
Student Mathematical Library.
Subjects:
Diophantine analysis.
Contents:
Opening thoughts: Welcome to the jungle Chapter 1. A bit of foreshadowing and some rational rationale Chapter 2. Building the rationals via Farey sequences Chapter 3. Discoveries of Dirichlet and Hurwitz Chapter 4. The theory of continued fractions Chapter 5. Enforcing the law of best approximates Chapter 6. Markoff's spectrum and numbers Chapter 7. Badly approximable numbers and quadratics Chapter 8. Solving the alleged "Pell" equation Chapter 9. Liouville's work on numbers algebraic and not Chapter 10. Roth's stunning result and its consequences Chapter 11. Pythagorean triples through Diophantine geometry Chapter 12. A quick tour through elliptic curves Chapter 13. The geometry of numbers Chapter 14. Simultaneous diophantine approximation Chapter 15. Using geometry to sum some squares Chapter 16. Spinning around irrationally and uniformly Chapter 17. A whole new world of $p$-adic numbers Chapter 18. A glimpse into $p$-adic analysis Chapter 19. A new twist on Newton's method Chapter 20. The power of acting locally while thinking globally Appendix 1. Selected big picture question commentaries Appendix 2. Hints and remarks Appendix 3. Further reading
Notes:
Includes bibliographical references (pages 145-146) and index.
Electronic reproduction. Providence, Rhode Island : American Mathematical Society. 2012
Description based on print version record.
Other format:
Print version: Burger, Edward B., 1963- Exploring the number jungle :
ISBN:
9781470421267 (online)
Access Restriction:
Restricted for use by site license.