Certain Number-Theoretic Episodes In Algebra, Second Edition
CRC Press (Verlag)
978-1-138-49578-4 (ISBN)
Sivaramakrishnan Ramakrishna Ayyar has served a few educational institutions in Kerala as a math-teacher. In particular, he has served the university of Calicut, Kerala-673635 during the years 1977-1996. A monograph entitled: ‘Classical Theory of Arithmetic Functions’ (Marcel Dekker (1989)) was published during his visitorship (1987-88) at the University of Kansas, Lawrence, KS66045, U.S.A. He has also visited Mangalore University (1996-1997), Mangalagangotri, Mangalore-574199. He holds an Emeritus membership of American Mathematical Society, since 2008. His e-mail address is: rsjreeg@gmail.com. The first edition of this book was published in the year 2006 (Chapman & Hall/CRC (Tayor & Francis Group)) when he could receive a Government of India Grant under ‘Utilization of Services of Retired Scientists’ (USERS) scheme to work at the University of Calicut during the two-year period April, 2000–March, 2002.
Section A - ELEMENTS OF THE THEORY OF NUMBERS. From Euclid to Lucas: Elementary theorems revisited. Solutions of Congruences, Primitive Roots. The Chinese Remainder Theorem. M¨obius inversion. Quadratic Residues. Decomposition of a number as a sum of two or four squares. Dirichlet Algebra of Arithmetical Functions. Modular arithmetical functions. A generalization of Ramanujan sums. Ramanujan expansions of multiplicative arithmetic functions. Section B - SELECTED TOPICS IN ALGEBRA. On the uniqueness of a group of order r (r > 1). Quadratic Reciprocity in a finite group. Commutative rings with unity. Noetherian and Artinian rings. Section C - GLIMPSES OF THE THEORY OF ALGEBRAIC NUMBERS. Dedekind domains. Algebraic number fields. Section D - SOME ADDITIONAL TOPICS. Vaidyanathaswamy’s class-division of integers modulo r. Burnside’s lemma and a few of its applications. On cyclic codes of length n over Fq. An Analogue of the Goldbach problem. Appendix A. Appendix B. Appendix C. Index.
| Erscheinungsdatum | 05.02.2019 |
|---|---|
| Zusatzinfo | 3 Tables, black and white; 47 Illustrations, black and white |
| Verlagsort | London |
| Sprache | englisch |
| Maße | 156 x 234 mm |
| Gewicht | 748 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Algebra |
| Mathematik / Informatik ► Mathematik ► Angewandte Mathematik | |
| Mathematik / Informatik ► Mathematik ► Arithmetik / Zahlentheorie | |
| ISBN-10 | 1-138-49578-6 / 1138495786 |
| ISBN-13 | 978-1-138-49578-4 / 9781138495784 |
| Zustand | Neuware |
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