Contemporary Abstract Algebra is a math book written by Joseph Gallian. The book is mainly focused on abstract algebra and along with explaining the rules of the topic, it also tells the readers about the use of abstract algebra in daily life. It was originally published in 1974 and the latest edition was published by Brooks in the July of 2012.
Contemporary Abstract Algebra Pdf Review:
The book focuses on the use of algebra in daily life. In our daily life, math is extensively used although most people are not aware of it. Algebra is used by mathematicians, chemists, and physicians around the world. This is what the author tries to tell the readers in the book, while also teaching the way algebra is used. It is a great book for students since it is filled with illustrations and also has a section dedicated to further reads. This section lets the readers know of the other books that they can read to get more information on the subject.
Contemporary Abstract Algebra Pdf Features:
- There are many photographs and charts in the book to display the information in the best way possible and to make the text easy for the readers to understand.
- Moreover, the author has also included computer exercises in the book to get the interest of the readers boosted up.
- There are also biographies of the mathematicians that lived and people who were involved in the explanation and use of abstract algebra.
Table of Contents:
PART I: INTEGERS AND EQUIVALENCE RELATIONS.
Preliminaries. Properties of Integers. Complex Numbers. Modular Arithmetic. Mathematical Induction. Equivalence Relations. Functions (Mappings). Exercises.
PART I!: GROUPS.
- Introduction to Groups.
Symmetries of a Square. The Dihedral Groups. Exercises. Biography of Neils Abel
Definition and Examples of Groups. Elementary Properties of Groups. Historical Note. Exercises.
- Finite Groups; Subgroups.
Terminology and Notation. Subgroup Tests. Examples of Subgroups. Exercises.
- Cyclic Groups.
Properties of Cyclic Groups. Classification of Subgroups of Cyclic Groups. Exercises. Biography of J. J. Sylvester. Supplementary Exercises for Chapters 1-4.
- Permutation Groups.
Definition and Notation. Cycle Notation. Properties of Permutations. A Check-Digit Scheme Based on D5. Exercises. Biography of Augustin Cauchy.
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