Introduction to Modern Algebra and Its Applications
Auteur : Gubareni Nadiya
The book provides an introduction to modern abstract algebra and its applications. It covers all major topics of classical theory of numbers, groups, rings, fields and finite dimensional algebras. The book also provides interesting and important modern applications in such subjects as Cryptography, Coding Theory, Computer Science and Physics. In particular, it considers algorithm RSA, secret sharing algorithms, Diffie-Hellman Scheme and ElGamal cryptosystem based on discrete logarithm problem. It also presents Buchberger?s algorithm which is one of the important algorithms for constructing Gröbner basis.
Key Features:
- Covers all major topics of classical theory of modern abstract algebra such as groups, rings and fields and their applications. In addition it provides the introduction to the number theory, theory of finite fields, finite dimensional algebras and their applications.
- Provides interesting and important modern applications in such subjects as Cryptography, Coding Theory, Computer Science and Physics.
- Presents numerous examples illustrating the theory and applications. It is also filled with a number of exercises of various difficulty.
- Describes in detail the construction of the Cayley-Dickson construction for finite dimensional algebras, in particular, algebras of quaternions and octonions and gives their applications in the number theory and computer graphics.
Date de parution : 05-2022
15.6x23.4 cm
Date de parution : 11-2020
15.6x23.4 cm
Thèmes d’Introduction to Modern Algebra and Its Applications :
Mots-clés :
Modular arithmetic; Classical number theory; Division algorithm; Division with remainder; Euclidean algorithm; Extended Euclidean algorithm; Irreducible Polynomial; Integral Domain; Greatest Common Divisor; Residue Classes Modulo; Quotient Ring; Principal Ideal Domain; Associative Commutative Ring; Gauss Integers; Splitting Field; Minimal Polynomial; Normal Subgroups; Mod 13; Commutative Group; Invertible Elements; Linear Congruence; Primitive Root Modulo; BCH Code; Cyclic Code; Composition Algebra; Commutative Ring; Associative Algebra; Algebraically Closed; Proper Principal Ideals; Division Algebra