## Algebra: abstract and concreteAddresses the needs of those who often have weak analytic ability, little idea of strategies of problem solving, and less of the patience and confidence needed to work proofs. It introduces readers to the "active" practice of mathematics -- luring them away from the view of mathematics as a system of rules and procedures and helping them learn to think things through for themselves and to explain accurately what they have understood. Uses linear algebra and complex numbers throughout. Highlights all theorems (propositions, lemmas, corollaries) and definitions in boxes. Features an abundance of high-quality exercises. |

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### Contents

Symmetry | 3 |

A First Look at Groups | 22 |

Basic Theory of Groups | 53 |

Copyright | |

13 other sections not shown

### Common terms and phrases

2-cycles abelian group algebraic Autjf automorphism axes axis bijection coefficients complex numbers compute conjugacy conjugate Consider contains Corollary cosets crystal cube cycle cyclic group defined Definition denote divides dodecahedron equation equivalence relation Example Exercises Exercise field extension Figure fixed follows functions g e G Galois group GL(n greatest common divisor group G group of order ideal identity induction integers intermediate fields inverse isometry isomorphism kernel lattice left cosets Lemma Let G linear mathematics matrix minimal polynomial modulo monic multiplication table natural number non-zero elements normal subgroup orbits orthogonal permutation phism point group prime numbers Proof Proposition quotient real numbers reflection relatively prime ring homomorphism root of unity roots of f(x rotation group Show solvable splitting field square subfield subgroup of G subring subset Suppose surjective symmetry group tetrahedron Theorem transitive subgroups unique variables Verify vertices