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**About this book :- **
**Abstract Algebra (2nd Edition) ** written by
** Justin R. Smith **.

This book arose out of courses in Abstract Algebra, Galois Theory, Algebraic Geometry, and Manifold Theory the author taught at Drexel University. It is useful for self-study or as a course textbook. The first four chapters are suitable for the first of a two semester undergraduate course in Abstract Algebra and chapters five through seven are suitable for the second semester.

**Book Detail :- **
** Title: ** Abstract Algebra
** Edition: ** Second Edition
** Author(s): ** Justin R. Smith
** Publisher: **
** Series: **
** Year: **
** Pages: ** 462
** Type: ** PDF
** Language: ** Englsih
** ISBN: **
** Country: ** US

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**Book Contents :- **
**Abstract Algebra (2nd Edition) ** written by
** Justin R. Smith **.
cover the following topics.

Foreword

List of Figures
**1. Introduction**
**2. Preliminaries**

2.1. Set theory

2.2. Operations on sets

2.3. The Power Set
**3. A glimpse of number theory**

3.1. Prime numbers and unique factorization

3.2. Modular arithmetic

3.3. The Euler f-function

3.4. Applications to cryptography
**4. Group Theory**

4.1. Introduction

4.2. Homomorphisms

4.3. Cyclic groups

4.4. Subgroups and cosets

4.5. Symmetric Groups

4.6. Abelian Groups

4.7. Group-actions

4.8. The Sylow Theorems

4.9. Subnormal series

4.10. Free Groups

4.11. Groups of small order
**5. The Theory of Rings**

5.1. Basic concepts

5.2. Homomorphisms and ideals

5.3. Integral domains and Euclidean Rings

5.4. Noetherian rings

5.5. Polynomial rings

5.6. Unique factorization domains
**6. Modules and Vector Spaces**

6.1. Introduction

6.2. Vector spaces

6.3. Modules

6.4. Rings and modules of fractions
**7. Fields**

7.1. Definitions

7.2. Algebraic extensions of fields

7.3. Computing Minimal polynomials

7.4. Algebraically closed fields

7.5. Finite fields

7.6. Transcendental extensions
**8. Further topics in ring theory**

8.1. Artinian rings

8.2. Integral extensions of rings

8.3. The Jacobson radical and Jacobson rings

8.4. Discrete valuation rings

8.5. Graded rings and modules
**9. Galois Theory**

9.1. Before Galois

9.2. Galois

9.3. Isomorphisms of fields

9.4. Roots of Unity

9.5. Cyclotomic Polynomials

9.6. Group characters

9.7. Galois Extensions

9.8. Solvability by radicals

9.9. Galois’s Great Theorem

9.10. The fundamental theorem of algebra
**10. Division Algebras over R**

10.1. The Cayley-Dickson Construction

10.2. Quaternions

10.3. Octonions and beyond
**11. A taste of category theory**

11.1. Introduction

11.2. Functors

11.3. Adjoint functors

11.4. Limits

11.5. Abelian categories

11.6. Tensor products

11.7. Tensor Algebras and variants
**12. A little algebraic geometry**

12.1. Introduction

12.2. Hilbert’s Nullstellensatz
**13. Cohomology**

13.1. Chain complexes and cohomology

13.2. Rings and modules

13.3. Cohomology of groups
**Appendix**

A. Axiomatic Set Theory

A.1. Introduction

A.2. Zermelo-Fraenkel Axioms

B. Solutions to Selected Exercises

Glossary

Index

Bibliography

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Divison related shortcut Tricks

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Prime Number related shortcut Tricks

- Find the prime number from 1 to 100 just in 5 second (MATH PRIME NUMBER SHORTCUT TRICK from 1 to 100 number) ?
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- Find the composite number from 1 to 100 just in 5 second (MATH COMPOSITE NUMBER SHORTCUT TRICK from 1 to 100 number) ?