Normale Ansicht MARC-Ansicht ISBD

An open door to number theory / Duff Campbell

Von:

Campbell, Duff, 1959- [VerfasserIn]

Resource type: Ressourcentyp: Buch (Online)Buch (Online)Sprache: Englisch Reihen: AMS/MAA textbooks ; vol 39Verlag: Providence, Rhode Island : MAA Press, an imprint of the American Mathematical Society, 2018Beschreibung: 1 Online-RessourceSchlagwörter:

Number theory

Andere physische Formen: 1470443481 | 9781470443481 | 1470446847. | 9781470446840. | Erscheint auch als: Kein Titel Druck-Ausgabe | Print version: Kein Titel MSC: MSC: *11-01 | 00A05 | 11Axx | 97F60LOC-Klassifikation:

QA241

Online-Ressourcen:

Zugang im Netz des KIT

Zusammenfassung: A well-written, inviting textbook designed for a one-semester, junior-level course in elementary number theory. The intended audience will have had exposure to proof writing, but not necessarily to abstract algebra. That audience will be well prepared by this text for a second-semester course focusing on algebraic number theory. The approach throughout is geometric and intuitive; there are over 400 carefully designed exercises, which include a balance of calculations, conjectures, and proofs. There are also nine substantial student projects on topics not usually covered in a first-semester couZusammenfassung: 33. Unique factorization in \Z[ ]34. The structure of \Z[√2]; 35. The Euclidean algorithm in \Z[√ ]; 36. Factoring in \Z[ ]; 37. The primes in \Z[ ]; 4. An Interlude of Analytic Number Theory; 38. The distribution of primes in \Z; 5. Quadratic Residues; 39. Perfect squares; 40. Quadratic residues; 41. Calculating the Legendre symbol (hard way); 42. The arithmetic of \Z[√-2] and the Legendre symbol \Leg{-2}; 43. Gauss's lemma; 44. Calculating the Legendre symbol (easier way); 45. The arithmetic of \Z[√-3]; 46. The arithmetic of \Z[ ]; 47. Calculating the Legendre symbol (easiest way)Zusammenfassung: 33. Unique factorization in \Z[ ]34. The structure of \Z[√2]; 35. The Euclidean algorithm in \Z[√ ]; 36. Factoring in \Z[ ]; 37. The primes in \Z[ ]; 4. An Interlude of Analytic Number Theory; 38. The distribution of primes in \Z; 5. Quadratic Residues; 39. Perfect squares; 40. Quadratic residues; 41. Calculating the Legendre symbol (hard way); 42. The arithmetic of \Z[√-2] and the Legendre symbol \Leg{-2}; 43. Gauss's lemma; 44. Calculating the Legendre symbol (easier way); 45. The arithmetic of \Z[√-3]; 46. The arithmetic of \Z[ ]; 47. Calculating the Legendre symbol (easiest way)Zusammenfassung: Cover; Title page; 1. The Integers, \Z; 1. Number systems; 2. Rings and fields; 3. Some fundamental facts about \Z and \N; 4. Proofs by induction; 5. The binomial theorem; 6. The fundamental theorem of arithmetic (foreshadowing); 7. Divisibility; 8. Greatest common divisors; 9. The Euclidean algorithm; 10. The amazing array; 11. Convergents; 12. The amazing super-array; 13. The modified division algorithm; 14. Why does the amazing array work?; 15. Primes; 16. The proof of the fundamental theorem of arithmetic; 17. Unique factorization in other rings; 2. Modular Arithmetic in \Z/ \ZZusammenfassung: A well-written, inviting textbook designed for a one-semester, junior-level course in elementary number theory. The intended audience will have had exposure to proof writing, but not necessarily to abstract algebra. That audience will be well prepared by this text for a second-semester course focusing on algebraic number theory. The approach throughout is geometric and intuitive; there are over 400 carefully designed exercises, which include a balance of calculations, conjectures, and proofs. There are also nine substantial student projects on topics not usually covered in a first-semester couPPN: PPN: 1026518245Package identifier: Produktsigel: ZDB-4-NLEBK

Exemplare ( 0 )

Dieser Titel hat keine Exemplare