Search Results - "RINGS"

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    Abstract Algebra Theory and Applications by Judson, Thomas W.

    Published 2016
    Table of Contents: “…Preliminaries -- The Integers -- Groups -- Cyclic Groups -- Permutation Groups -- Cosets and Lagrange's Theorem -- Introduction to Cryptography -- Algebraic Coding Theory -- Isomorphisms -- Normal Subgroups and Factor Groups -- Homomorphisms -- Matrix Groups and Symmetry -- The Structure of Groups -- Group Actions -- The Sylow Theorems -- Rings -- Polynomials -- Integral Domains -- Lattices and Boolean Algebras -- Vector Spaces -- Fields -- Finite Fields -- Galois Theory…”
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    A Computational Introduction to Number Theory and Algebra by Shoup, Victor

    Published 2009
    Table of Contents: “…1 Basic properties of the integers -- 2 Congruences -- 3 Computing with large integers -- 4 Euclid's algorithm -- 5 The distribution of primes -- 6 Abelian groups -- 7 Rings -- 8 Finite and discrete probability distributions -- 9 Probabilistic algorithms -- 10 Probabilistic primality testing -- 11 Finding generators and discrete logarithms in Z∗p -- 12 Quadratic reciprocity and computing modular square roots -- 13 Modules and vector spaces -- 14 Matrices -- 15 Subexponential-time discrete logarithms and factoring -- 16 More rings -- 17 Polynomial arithmetic and applications -- 18 Finite Fields -- 19 Linearly generated sequences and applications -- 20 Algorithms for finite fields -- 21 Deterministic primality testing…”
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