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- catalog abstract ""This book brings to life the fundamental ideas and theorems from diophantine approximation and equations, geometry of numbers, diophantine geometry, and p-adic analysis. Through his engaging style, the author creates an inviting atmosphere where readers actively build intuition, develop ideas, and prove results as they journey through some beautiful areas of number theory. The minimal background requirements and the author's fresh approach make this book enjoyable and accessible to a wide range of students, mathematicians, and fans of number theory."--Jacket.".
- catalog contributor b11774515.
- catalog created "2000.".
- catalog date "2000".
- catalog date "2000.".
- catalog dateCopyrighted "2000.".
- catalog description ""This book brings to life the fundamental ideas and theorems from diophantine approximation and equations, geometry of numbers, diophantine geometry, and p-adic analysis. Through his engaging style, the author creates an inviting atmosphere where readers actively build intuition, develop ideas, and prove results as they journey through some beautiful areas of number theory. The minimal background requirements and the author's fresh approach make this book enjoyable and accessible to a wide range of students, mathematicians, and fans of number theory."--Jacket.".
- catalog description "Includes bibliographical references and index.".
- catalog description "Opening thoughts: Welcome to the jungle -- 1. A bit of foreshadowing and some rational rationale -- 2. Building the rationals via Farey Sequences -- 3. Discoveries of Dirichlet and Hurwitz -- 4. The theory of continued fractions -- 5. Enforcing the law of best approximates -- 6. Markoff's spectrum and numbers -- 7. Badly approximable numbers and quadratics -- 8. Solving the alleged "Pell" equation -- 9. Liouville's work on numbers algebraic and not -- 10. Roth's stunning result and its consequences -- 11. Pythagorean triples through diophantine geometry -- 12. A quick tour through elliptic curves -- 13. The geometry of numbers -- 14. Simultaneous diophantine approximation -- 15. Using geometry to sum some squares -- 16. Spinning around irrationally and uniformly -- 17. A whole new world of p-adic numbers -- 18. A glimpse into p-adic analysis -- 19. A new twist on Newton's method -- 20. The power of acting locally while thinking globally -- App. 1. Selected Big Picture Question commentaries.".
- catalog extent "vi, 151 p. ;".
- catalog identifier "0821826409 (alk. paper)".
- catalog isPartOf "Student mathematical library, 1520-9121 ; v. 8".
- catalog issued "2000".
- catalog issued "2000.".
- catalog language "eng".
- catalog publisher "Providence, RI : American Mathematical Society,".
- catalog subject "512/.74 21".
- catalog subject "Diophantine analysis.".
- catalog subject "QA242 .B96 2000".
- catalog tableOfContents "Opening thoughts: Welcome to the jungle -- 1. A bit of foreshadowing and some rational rationale -- 2. Building the rationals via Farey Sequences -- 3. Discoveries of Dirichlet and Hurwitz -- 4. The theory of continued fractions -- 5. Enforcing the law of best approximates -- 6. Markoff's spectrum and numbers -- 7. Badly approximable numbers and quadratics -- 8. Solving the alleged "Pell" equation -- 9. Liouville's work on numbers algebraic and not -- 10. Roth's stunning result and its consequences -- 11. Pythagorean triples through diophantine geometry -- 12. A quick tour through elliptic curves -- 13. The geometry of numbers -- 14. Simultaneous diophantine approximation -- 15. Using geometry to sum some squares -- 16. Spinning around irrationally and uniformly -- 17. A whole new world of p-adic numbers -- 18. A glimpse into p-adic analysis -- 19. A new twist on Newton's method -- 20. The power of acting locally while thinking globally -- App. 1. Selected Big Picture Question commentaries.".
- catalog title "Exploring the number jungle : a journey into diophantine analysis / Edward B. Burger.".
- catalog type "text".