Introduction to Modern Algebra and Its Applications

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 Gr?obner basis. The Cayley-Dickson construction for finite dimensional algebras is described. The structure and properties of quaternions and octonions are studied indetails and their applications in the number theory and computer graphics are presented--