"Introduction To Modern Algebra And Its Applications | Science Publishers

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 El Gamal 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. |Introduction to Modern Algebra and Its Applications | Science Publishers