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15 reviews(Ebook) An Introduction to Abstract Algebra 1st Edition by Derek JS Robinson - Ebook PDF Instant Download/Delivery: 9783110198164, 3110198169
Full download (Ebook) An Introduction to Abstract Algebra 1st Edition after payment
Product details:
ISBN 10: 3110198169
ISBN 13: 9783110198164
Author: Derek JS Robinson
(Ebook) An Introduction to Abstract Algebra 1st Edition Table of contents:
1 Sets, relations and functions
1.1 Sets and subsets
1.2 Relations, equivalence relations and partial orders
1.3 Functions
1.4 Cardinality
2 The integers
2.1 Well-ordering and mathematical induction
2.2 Division in the integers
2.3 Congruences
3 Introduction to groups
3.1 Permutations of a set
3.2 Binary operations: semigroups, monoids and groups
3.3 Groups and subgroups
4 Cosets, quotient groups and homomorphisms
4.1 Cosets and Lagrange’s Theorem
4.2 Normal subgroups and quotient groups
4.3 Homomorphisms of groups
5 Groups acting on sets
5.1 Group actions and permutation representations
5.2 Orbits and stabilizers
5.3 Applications to the structure of groups
5.4 Applications to combinatorics – counting labellings and graphs
6 Introduction to rings
6.1 Definition and elementary properties of rings
6.2 Subrings and ideals
6.3 Integral domains, division rings and fields
7 Division in rings
7.1 Euclidean domains
7.2 Principal ideal domains
7.3 Unique factorization in integral domains
7.4 Roots of polynomials and splitting fields
8 Vector spaces
8.1 Vector spaces and subspaces
8.2 Linear independence, basis and dimension
8.3 Linear mappings
8.4 Orthogonality in vector spaces
9 The structure of groups
9.1 The Jordan-Holder Theorem
9.2 Solvable and nilpotent groups
9.3 Theorems on finite solvable groups
10 Introduction to the theory of fields
10.1 Field extensions
10.2 Constructions with ruler and compass
10.3 Finite fields
10.4 Applications to latin squares and Steiner triple systems
11 Galois theory
11.1 Normal and separable extensions
11.2 Automorphisms of field extensions
11.3 The Fundamental Theorem of Galois Theory
11.4 Solvability of equations by radicals
12 Further topics
12.1 Zorn’s Lemma and its applications
12.2 More on roots of polynomials
12.3 Generators and relations for groups
12.4 An introduction to error correcting codes
Bibliography
Index of notation
Index
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Tags: Derek JS Robinson, Introduction, Abstract Algebra
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