Ten Chapters of the Algebraical Art by Peter J. Cameron
About this book :-
This text is a set of lecture notes designed to introduce students to fundamental algebraic concepts. The text is intended as a first introduction to the ideas of proof and abstraction in mathematics, as well as to the concepts of abstract algebra (groups and rings). This module is an introduction to the basic notion of algebra, such as sets, numbers, matrices, polynomials and permutations. It not only introduces the topics, but shows how they form examples of abstract mathematical structures such as groups, rings, and fields and how algebra can be developed on an axiomatic foundation.
It also providing clear definitions, examples, and exercises to reinforce understanding. This resource is particularly useful for students seeking a focused and accessible approach to learning abstract algebra.
Book Detail :-
Title:
Ten Chapters of the Algebraical Art by Peter J. Cameron
Publisher:
Queen Mary, University of London
Year:
2007
Pages:
108
Type:
PDF
Language:
English
ISBN-10 #:
0198569130
ISBN-13 #:
978-0198569138
License:
Linked Content Owned by Author
Amazon:
Amazon
About Author :-
The author
Peter J. Cameron
is Emeritus Professor of Mathematics at Queen Mary, University of London, having been a Professor of Mathematics in the School of Mathematical Sciences from 1987 to 2012. He is famous for his notes for Introduction to Algebra, Linear Algebra, Algebraic Structures, Number Theory, Combinatorics, Probability, Cryptography, and Complexity. There are also graduate notes on Classical Groups, Polynomial Aspects of Codes etc., Enumerative Combinatorics, Primitive Lambda-Roots (with Donald Preece), Projective and Polar Spaces, and Finite Geometry and Coding Theory, as well as LTCC notes on Synchronization and (with R. A. Bailey) on Laplace eigenvalues and optimality.
Book Contents :-
1. What is mathematics about?
1.1 Some examples of proofs
1.2 Some proof techniques
1.3 Proof by induction
1.4 Some more mathematical terms
2. Numbers
2.1 The natural numbers
2.2 The integers
2.3 The rational numbers
2.4 The real numbers
2.5 The complex numbers
2.6 The complex plane, or Argand diagram
3. Other algebraic systems
3.1 Vectors
3.2 Matrices
3.3 Polynomials
3.4 Sets
4. Relations and functions
4.1 Ordered pairs and Cartesian product
4.2 Relations
4.3 Equivalence relations and partitions
4.4 Functions
4.5 Operations
4.6 Appendix: Relations and functions
5. Division and Euclid’s algorithm
5.1 The division rule
5.2 Greatest common divisor and least common multiple
5.3 Euclid’s algorithm
5.4 Euclid’s algorithm extended
5.5 Polynomials
6. Modular arithmetic
6.1 Congruence mod m
6.2 Operations on congruence classes
6.3 Inverses
6.4 Fermat’s Little Theorem
7. Polynomials revisited
7.1 Polynomials over other systems
7.2 Division and factorisation
7.3 “Modular arithmetic” for polynomials
7.4 Finite fields
7.5 Appendix: Laws for polynomials
8. Rings
8.1 Rings
8.2 Examples of rings
8.3 Properties of rings
8.4 Units
8.5 Appendix: The associative law
9. Groups
9.1 Definition
9.2 Elementary properties
9.3 Examples of groups
9.4 Cayley tables
9.5 Subgroups
9.6 Cosets and Lagrange’s Theorem
9.7 Orders of elements
9.8 Cyclic groups
10. Permutations
10.1 Definition and representation
10.2 The symmetric group
10.3 Cycles
10.4 Transpositions
10.5 Even and odd permutations
Similar
Abstract Algebra (Introduction)
Books