عنوان
پدید آورنده
موضوع
رده
QA241
QA241
کتابخانه
محل استقرار
INTERNATIONAL STANDARD BOOK NUMBER
(Number (ISBN
1470446847
(Number (ISBN
9781470446840
Erroneous ISBN
1470443481
Erroneous ISBN
9781470443481
TITLE AND STATEMENT OF RESPONSIBILITY
Title Proper
An open door to number theory /
General Material Designation
[Book]
First Statement of Responsibility
Duff Campbell.
.PUBLICATION, DISTRIBUTION, ETC
Place of Publication, Distribution, etc.
Providence, Rhode Island :
Name of Publisher, Distributor, etc.
MAA Press, an imprint of the American Mathematical Society,
Date of Publication, Distribution, etc.
[2018]
PHYSICAL DESCRIPTION
Specific Material Designation and Extent of Item
1 online resource
SERIES
Series Title
AMS/MAA textbooks ;
Volume Designation
vol. 39
INTERNAL BIBLIOGRAPHIES/INDEXES NOTE
Text of Note
Includes bibliographical references and index.
CONTENTS NOTE
Text of Note
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/ \Z.
Text of Note
18. The integers mod , \Z/ \Z19. Congruences; 20. Units and zero-divisors in \Z/ \Z; 21. Cancellation law in \Z/ \Z; 22. Solving linear equations in \Z/ \Z; 23. Solving polynomial equations in \Z/ \Z; 24. Solving systems of linear equations in \Z/ \Z; 25. Lifting roots in \Z/ ⁿ\Z; 26. Wilson's theorem and its converse; 27. Calculating ( ); 28. Euler's and Fermat's theorems; 29. The order of an integer modulo; 30. Divisibility tests; 3. Quadratic Extensions of the Integers, \Z[√ ]; 31. Divisibility in \Z[ ]; 32. The Euclidean algorithm in \Z[ ]
Text of Note
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)
Text of Note
48. The Jacobi symbol6. Further Topics; 49. When \Z/ \Z has a primitive root; 50. Minkowski's theorem (geometry in the aid of algebra); Appendix A. Tables; Appendix B. Projects; Bibliography; Index; Back Cover.
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8
8
8
SUMMARY OR ABSTRACT
Text of Note
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 cou.
OTHER EDITION IN ANOTHER MEDIUM
International Standard Book Number
1470443481
TOPICAL NAME USED AS SUBJECT
Number theory, Textbooks.
MATHEMATICS-- Algebra-- Intermediate.
Number theory-- Elementary number theory-- Congruences; primitive roots; residue systems.
Number theory-- Elementary number theory-- Continued fractions.
Number theory-- Elementary number theory-- Factorization; primality.
Number theory-- Elementary number theory-- Multiplicative structure; Euclidean algorithm; greatest common divisors.
Number theory-- Elementary number theory-- Power residues, reciprocity.
Number theory-- Elementary number theory-- Primes.
Number theory-- Instructional exposition (textbooks, tutorial papers, etc.)
Number theory.
(SUBJECT CATEGORY (Provisional
MAT-- 002040
DEWEY DECIMAL CLASSIFICATION
Number
512
.
72
Edition
23
LIBRARY OF CONGRESS CLASSIFICATION
Class number
QA241
OTHER CLASS NUMBERS
Class number
11A55
System Code
msc
PERSONAL NAME - PRIMARY RESPONSIBILITY
Campbell, Duff,1959-
ORIGINATING SOURCE
Date of Transaction
20200823025836.0
Cataloguing Rules (Descriptive Conventions))
pn
ELECTRONIC LOCATION AND ACCESS
Electronic name
مطالعه متن کتاب [Book]
Y
