Integers, polynomials, and rings: a course in algebra/ (Record no. 179839)
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| 000 -LEADER | |
|---|---|
| fixed length control field | 00379nam a2200145Ia 4500 |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| International Standard Book Number | 0387201726 |
| 040 ## - CATALOGING SOURCE | |
| Transcribing agency | CUS |
| 082 ## - DEWEY DECIMAL CLASSIFICATION NUMBER | |
| Classification number | 512 |
| Item number | IRV/I |
| 100 ## - MAIN ENTRY--PERSONAL NAME | |
| Personal name | Irving, Ronald S. |
| 245 #0 - TITLE STATEMENT | |
| Title | Integers, polynomials, and rings: a course in algebra/ |
| Statement of responsibility, etc. | Ronald S. Irving |
| 250 ## - EDITION STATEMENT | |
| Edition statement | 2004 |
| 260 ## - PUBLICATION, DISTRIBUTION, ETC. (IMPRINT) | |
| Place of publication, distribution, etc. | New York: |
| Name of publisher, distributor, etc. | Springer, |
| Date of publication, distribution, etc. | 2004. |
| 300 ## - PHYSICAL DESCRIPTION | |
| Extent | 284p. |
| 505 ## - FORMATTED CONTENTS NOTE | |
| Formatted contents note | 1 Introduction: The McNugget Problem 1<br/>Part I Integers<br/>2 Induction and the Division Theorem 9<br/>2.1 The Method of Induction 9<br/>2.2 The Tower of Hanoi 15<br/>2.3 The Division Theorem 17<br/>3 The Euclidean Algorithm 23<br/>3.1 Greatest Common Divisors 23<br/>3.2 The Euclidean Algorithm 27<br/>3.3 Bezout's Theorem 31<br/>3.4 An Application of Bezout's Theorem 34<br/>3.5 Diophantine Equations 36<br/>4 Congruences 41<br/>4.1 Congruences 41<br/>4.2 Solving Congruences 46<br/>4.3 Congruence Classes and McNuggets 50<br/>5 Prime Numbers 57<br/>5.1 Prime Numbers and Generalized Induction 57<br/>5.2 Uniqueness of Prime Factorizations 61<br/>5.3 Greatest Common Divisors Revisited 63<br/>6.4 Modular Arithmetic Rings gg<br/>6.5 Congruence Rings gj<br/>7 Euler's Theorem g5<br/>7.1 Units g5<br/>7.2 Roots of Unity gg<br/>7.3 The Theorems of Fermat and Euler 101<br/>7.4 Tlie Euler 0-Function 105<br/>7.5 RSA Encryption HO<br/>8 Binomial Coefficients<br/>8.1 Pascal's Triangle<br/>8.2 The Binomial Theorem 120<br/>Part II Polynomials<br/>9 Polynomials and Roots 127<br/>9.1 Polynomial Equations 127<br/>9.2 Rings of Polynomials 128<br/>9.3 Factoring a Polynomial 130<br/>9.4 The Roots of a Polynomial 133<br/>9.5 Minimal Polynomials 136<br/>10 Polynomials with Real Coefficients 141<br/>10.1<br/>Quadratic Polynomials 141<br/>10.2<br/>Cubic Polynomials 146<br/>10.3 The Discriminant of a Cubic Polynomial 153<br/>10.4 Quartic Polynomials 159<br/>10.5 A Closer Look at Quartic Polynomials 164<br/>10.6 The Discriminant of a Quartic Polynomial 167<br/>10.7 The Fundamental Theorem of Algebra 171<br/>11 Polynomials with Rational Coefficients 177<br/>11.1 Polynomials over Q 177<br/>11.2 Gauss's Lemma 181<br/>11.3 Eisenstein's Criterion 184<br/>11.4 Polynomials with Coefficients in Fp 187<br/>Contents xv<br/>12 Polynomial Rings 193<br/>12.1 Unique Factorization for Integers Revisited 193<br/>12.2 The Finchdean Algorithm 196<br/>12.3 Bezout's Theorem 198<br/>12.4 Unique Factorization for Polynomials 199<br/>13 Quadratic Polynomials 201<br/>13.1 Square Roots 201<br/>13.2<br/>The Quadratic Formula 204<br/>13.3 Square Roots in Finite Fields 209<br/>13.4 Quadratic Field Constructions 214<br/>14 Polynomial Congruence Rings 221<br/>14.1 A Construction of New Rings 221<br/>14.2 Polynomial Congruences 226<br/>14.3 Polynomial Congruence Rings 230<br/>14.4 Equations and Congruences with Polynomial Unknowns 233<br/>14.5 Polynomial Congruence Fields 236<br/>Part III All Together Now<br/>15 Euclidean Rings 241<br/>15.1 Factoring Elements in Rings 241<br/>15.2 Euclidean Rings 245<br/>15.3 Unique Factorization 249<br/>16<br/>The Ring of Gaussian Integers 255<br/>16.1 The Irreducible Gaussian Integers 255<br/>16.2 Gaussian Congruence Rings 259<br/>16.3 Fermat's Theorem 262<br/>17 Finite Fields 267<br/>17.1 Primitive Roots 267<br/>17.2 Quadratic Reciprocity 271<br/>17.3 Classification 277<br/> |
| 942 ## - ADDED ENTRY ELEMENTS (KOHA) | |
| Koha item type | General Books |
| Withdrawn status | Lost status | Damaged status | Not for loan | Home library | Current library | Shelving location | Date acquired | Full call number | Accession number | Date last seen | Koha item type |
|---|---|---|---|---|---|---|---|---|---|---|---|
| Central Library, Sikkim University | Central Library, Sikkim University | General Book Section | 29/08/2016 | 512 IRV/I | P34850 | 29/08/2016 | General Books |