Includes 2-weeks free access to

step-by-step solutions for this book.

# Elements Of Modern Algebra

**by**Gilbert, Linda

7th

### 9780495561361

0495561363

Hardcover

10/20/2008

Cengage Learning

Step-by-Step solutions are actual worked out problems to the questions at the end of each chapter that help you understand your homework and study for your exams. Chegg and eCampus are providing you two weeks absolutely free. 81% of students said using Step-by-Step solutions prepared them for their exams.

List Price: ~~$263.66~~

Term

Due

Price

$25.00

**Hurry!**

Only one copy

in stock at this price.

In Stock Usually Ships in 24 Hours.

$31.52

Usually Ships in 2-3 Business Days

$237.29

Downloadable Offline Access

Duration

Price

$52.99

More New and Used

from Private Sellers

from Private Sellers

Starting at $18.08

## Questions About This Book?

Why should I rent this book?

Renting is easy, fast, and cheap! Renting from eCampus.com can save you hundreds of dollars compared to the cost of new or used books each semester. At the end of the semester, simply ship the book back to us with a free UPS shipping label! No need to worry about selling it back.

How do rental returns work?

Returning books is as easy as possible. As your rental due date approaches, we will email you several courtesy reminders. When you are ready to return, you can print a free UPS shipping label from our website at any time. Then, just return the book to your UPS driver or any staffed UPS location. You can even use the same box we shipped it in!

What version or edition is this?

This is the 7th edition with a publication date of 10/20/2008.

What is included with this book?

- The
**New**copy of this book will include any supplemental materials advertised. Please check the title of the book to determine if it should include any CDs, lab manuals, study guides, etc. - The
**Used**copy of this book is not guaranteed to include any supplemental materials. Typically, only the book itself is included. - The
**Rental**copy of this book is not guaranteed to include any supplemental materials. You may receive a brand new copy, but typically, only the book itself.

## Related Products

## Summary

ELEMENTS OF MODERN ALGEBRA 7e, with its user-friendly format, provides you with the tools you need to get succeed in abstract algebra and develop mathematical maturity as a bridge to higher-level mathematics courses.. Strategy boxes give you guidance and explanations about techniques and enable you to become more proficient at constructing proofs. A summary of key words and phrases at the end of each chapter help you master the material. A reference section, symbolic marginal notes, an appendix, and numerous examples help you develop your problem solving skills.

## Table of Contents

Preface | p. xi |

Fundamentals | p. 1 |

Sets | p. 1 |

Mappings | p. 12 |

Properties of Composite Mappings (Optional) | p. 25 |

Binary Operations | p. 30 |

Permutations and Inverses | p. 37 |

Matrices | p. 42 |

Relations | p. 55 |

Key Words and Phrases | p. 62 |

A Pioneer in Mathematics: Arthur Cayley | p. 62 |

The Integers | p. 65 |

Postulates for the Integers (Optional) | p. 65 |

Mathematical Induction | p. 71 |

Divisibility | p. 81 |

Prime Factors and Greatest Common Divisor | p. 86 |

Congruence of Integers | p. 95 |

Congruence Classes | p. 107 |

Introduction to Coding Theory (Optional) | p. 114 |

Introduction to Cryptography (Optional) | p. 123 |

Key Words and Phrases | p. 134 |

A Pioneer in Mathematics: Blaise Pascal | p. 135 |

Groups | p. 137 |

Definition of a Group | p. 137 |

Properties of Group Elements | p. 145 |

Subgroups | p. 152 |

Cyclic Groups | p. 163 |

Isomorphisms | p. 174 |

Homomorphisms | p. 183 |

Key Words and Phrases | p. 188 |

A Pioneer in Mathematics: Niels Henrik Abel | p. 189 |

More on Groups | p. 191 |

Finite Permutation Groups | p. 191 |

Cayley's Theorem | p. 205 |

Permutation Groups in Science and Art (Optional) | p. 208 |

Cosets of a Subgroup | p. 215 |

Normal Subgroups | p. 223 |

Quotient Groups | p. 230 |

Direct Sums (Optional) | p. 239 |

Some Results on Finite Abelian Groups (Optional) | p. 246 |

Key Words and Phrases | p. 255 |

A Pioneer in Mathematics: Augustin Louis Cauchy | p. 256 |

Rings, Integral Domains, and Fields | p. 257 |

Definition of a Ring | p. 257 |

Integral Domains and Fields | p. 270 |

The Field of Quotients of an Integral Domain | p. 276 |

Ordered Integral Domains | p. 284 |

Key Words and Phrases | p. 291 |

A Pioneer in Mathematics: Richard Dedekind | p. 292 |

More on Rings | p. 293 |

Ideals and Quotient Rings | p. 293 |

Ring Homomorphisms | p. 303 |

The Characteristic of a Ring | p. 313 |

Maximal Ideals (Optional) | p. 319 |

Key Words and Phrases | p. 324 |

A Pioneer in Mathematics: Amalie Emmy Noether | p. 324 |

Real and Complex Numbers | p. 325 |

The Field of Real Numbers | p. 325 |

Complex Numbers and Quaternions | p. 333 |

De Moivre's Theorem and Roots of Complex Numbers | p. 343 |

Key Words and Phrases | p. 352 |

A Pioneer in Mathematics: William Rowan Hamilton | p. 353 |

Polynomials | p. 355 |

Polynomials over a Ring | p. 355 |

Divisibility and Greatest Common Divisor | p. 367 |

Factorization in F[x] | p. 375 |

Zeros of a Polynomial | p. 384 |

Solution of Cubic and Quartic Equations by Formulas (Optional) | p. 397 |

Algebraic Extensions of a Field | p. 409 |

Key Words and Phrases | p. 421 |

A Pioneer in Mathematics: Carl Friedrich Gauss | p. 422 |

The Basics of Logic | p. 423 |

Answers to True/False and Selected Computational Exercises | p. 435 |

Bibliography | p. 499 |

Index | p. 503 |

Table of Contents provided by Ingram. All Rights Reserved. |