R. Sivaramakrishnan
Certain Number-Theoretic Episodes In Algebra, Second Edition
R. Sivaramakrishnan
Certain Number-Theoretic Episodes In Algebra, Second Edition
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The book attempts to point out the interconnections between number theory and algebra with a view to making a student understand certain basic concepts in the two areas forming the subject-matter of the book.
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The book attempts to point out the interconnections between number theory and algebra with a view to making a student understand certain basic concepts in the two areas forming the subject-matter of the book.
Produktdetails
- Produktdetails
- Verlag: Bsp Books Pvt. Ltd.
- 2nd edition
- Seitenzahl: 412
- Erscheinungstermin: 26. März 2019
- Englisch
- Abmessung: 234mm x 156mm x 25mm
- Gewicht: 798g
- ISBN-13: 9781138495784
- ISBN-10: 1138495786
- Artikelnr.: 55116389
- Verlag: Bsp Books Pvt. Ltd.
- 2nd edition
- Seitenzahl: 412
- Erscheinungstermin: 26. März 2019
- Englisch
- Abmessung: 234mm x 156mm x 25mm
- Gewicht: 798g
- ISBN-13: 9781138495784
- ISBN-10: 1138495786
- Artikelnr.: 55116389
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.
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.
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.
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.