Introduction to Modern Algebra and Its Applications
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A01=Nadiya Gubareni
advanced algebra for computer science
algebraic structures
Algebraically Closed
Associative Algebra
Associative Commutative Ring
Author_Nadiya Gubareni
BCH Code
Category=PB
Category=PBF
Category=PBW
Classical number theory
Commutative Group
Commutative Ring
Composition Algebra
cryptographic algorithms
Cyclic Code
discrete logarithm applications
Division Algebra
Division algorithm
Division with remainder
eq_isMigrated=1
eq_isMigrated=2
eq_nobargain
Euclidean algorithm
Extended Euclidean Algorithm
finite field theory
Gauss Integers
Greatest Common Divisor
group homomorphisms
Integral Domain
Invertible Elements
Irreducible Polynomial
Linear Congruence
Minimal Polynomial
Mod 13
Modular arithmetic
Normal Subgroups
polynomial factorization
Primitive Root Modulo
Principal Ideal Domain
Proper Principal Ideals
Quotient Ring
Residue Classes Modulo
Splitting Field
Product details
- ISBN 9780367820916
- Weight: 890g
- Dimensions: 156 x 234mm
- Publication Date: 15 Nov 2020
- Publisher: Taylor & Francis Ltd
- Publication City/Country: GB
- Product Form: Hardback
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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.
Nadiya Gubareni, Associate Professor of Silesian University of Technology, Poland
