
Algebra (Classic Version), 2nd edition
Your access includes:
- Search, highlight, and take notes
- Easily create flashcards
- Use the app for access anywhere
- 14-day refund guarantee
$10.99per month
4-month term, pay monthly or pay $43.96
Learn more, spend less
-
Special partners and offers
Enjoy perks from special partners and offers for students
-
Find it fast
Quickly navigate your eTextbook with search
-
Stay organized
Access all your eTextbooks in one place
-
Easily continue access
Keep learning with auto-renew
Overview
Hallmark features of this title
- High emphasis on concrete topics such as symmetry, linear groups, quadratic number fields, and lattices prepares students to learn more abstract concepts. This focus also allows some abstractions to be treated more concisely.
- The chapter organization emphasizes the connections between algebra and geometry at the start, with the beginning chapters containing the content most important for students in other fields. To counter the fact that arithmetic receives less initial emphasis, the later chapters have a strong arithmetic slant.
- Treatment beyond the basics sets this book apart. Students with a reasonably mature mathematical background will benefit from the relatively informal treatments the author gives to the more advanced topics.
- Content notes in the preface include teaching tips from the author’s own classroom experience.
- Challenging exercises are indicated with an asterisk, allowing instructors to easily create the right assignments for their class.
Published by Pearson (June 1st 2023) - Copyright © 2023
ISBN-13: 9780137980994
Subject: Advanced Math
Category: Abstract Algebra
Table of contents
1. Matrices
- 1.1 The Basic Operations
- 1.2 Row Reduction
- 1.3 The Matrix Transpose
- 1.4 Determinants
- 1.5 Permutations
- 1.6 Other Formulas for the Determinant
- 1.7 Exercises
2. Groups
- 2.1 Laws of Composition
- 2.2 Groups and Subgroups
- 2.3 Subgroups of the Additive Group of Integers
- 2.4 Cyclic Groups
- 2.5 Homomorphisms
- 2.6 Isomorphisms
- 2.7 Equivalence Relations and Partitions
- 2.8 Cosets
- 2.9 Modular Arithmetic
- 2.10 The Correspondence Theorem
- 2.11 Product Groups
- 2.12 Quotient Groups
- 2.13 Exercises
3. Vector Spaces
- 3.1 Subspaces of Rn
- 3.2 Fields
- 3.3 Vector Spaces
- 3.4 Bases and Dimension
- 3.5 Computing with Bases
- 3.6 Direct Sums
- 3.7 Infinite-Dimensional Spaces
- 3.8 Exercises
4. Linear Operators
- 4.1 The Dimension Formula
- 4.2 The Matrix of a Linear Transformation
- 4.3 Linear Operators
- 4.4 Eigenvectors
- 4.5 The Characteristic Polynomial
- 4.6 Triangular and Diagonal Forms
- 4.7 Jordan Form
- 4.8 Exercises
5. Applications of Linear Operators
- 5.1 Orthogonal Matrices and Rotations
- 5.2 Using Continuity
- 5.3 Systems of Differential Equations
- 5.4 The Matrix Exponential
- 5.5 Exercises
6. Symmetry
- 6.1 Symmetry of Plane Figures
- 6.2 Isometries
- 6.3 Isometries of the Plane
- 6.4 Finite Groups of Orthogonal Operators on the Plane
- 6.5 Discrete Groups of Isometries
- 6.6 Plane Crystallographic Groups
- 6.7 Abstract Symmetry: Group Operations
- 6.8 The Operation on Cosets
- 6.9 The Counting Formula
- 6.10 Operations on Subsets
- 6.11 Permutation Representation
- 6.12 Finite Subgroups of the Rotation Group
- 6.13 Exercises
7. More Group Theory
- 7.1 Cayley's Theorem
- 7.2 The Class Equation
- 7.3 r-groups
- 7.4 The Class Equation of the Icosahedral Group
- 7.5 Conjugation in the Symmetric Group
- 7.6 Normalizers
- 7.7 The Sylow Theorems
- 7.8 Groups of Order 12
- 7.9 The Free Group
- 7.10 Generators and Relations
- 7.11 The Todd-Coxeter Algorithm
- 7.12 Exercises
8. Bilinear Forms
- 8.1 Bilinear Forms
- 8.2 Symmetric Forms
- 8.3 Hermitian Forms
- 8.4 Orthogonality
- 8.5 Euclidean spaces and Hermitian spaces
- 8.6 The Spectral Theorem
- 8.7 Conics and Quadrics
- 8.8 Skew-Symmetric Forms
- 8.9 Summary
- 8.10 Exercises
9. Linear Groups
- 9.1 The Classical Groups
- 9.2 Interlude: Spheres
- 9.3 The Special Unitary Group SU2
- 9.4 The Rotation Group SO3
- 9.5 One-Parameter Groups
- 9.6 The Lie Algebra
- 9.7 Translation in a Group
- 9.8 Normal Subgroups of SL2
- 9.9 Exercises
10. Group Representations
- 10.1 Definitions
- 10.2 Irreducible Representations
- 10.3 Unitary Representations
- 10.4 Characters
- 10.5 One-Dimensional Characters
- 10.6 The Regular Representations
- 10.7 Schur's Lemma
- 10.8 Proof of the Orthogonality Relations
- 10.9 Representationsof SU2
- 10.10 Exercises
11. Rings
- 11.1 Definition of a Ring
- 11.2 Polynomial Rings
- 11.3 Homomorphisms and Ideals
- 11.4 Quotient Rings
- 11.5 Adjoining Elements
- 11.6 Product Rings
- 11.7 Fraction Fields
- 11.8 Maximal Ideals
- 11.9 Algebraic Geometry
- 11.10 Exercises
12. Factoring
- 12.1 Factoring Integers
- 12.2 Unique Factorization Domains
- 12.3 Gauss's Lemma
- 12.4 Factoring Integer Polynomial
- 12.5 Gauss Primes
- 12.6 Exercises
13. Quadratic Number Fields
- 13.1 Algebraic Integers
- 13.2 Factoring Algebraic Integers
- 13.3 Ideals in Z √(-5)
- 13.4 Ideal Multiplication
- 13.5 Factoring Ideals
- 13.6 Prime Ideals and Prime Integers
- 13.7 Ideal Classes
- 13.8 Computing the Class Group
- 13.9 Real Quadratic Fields
- 13.10 About Lattices
- 13.11 Exercises
14. Linear Algebra in a Ring
- 14.1 Modules
- 14.2 Free Modules
- 14.3 Identities
- 14.4 Diagonalizing Integer Matrices
- 14.5 Generators and Relations
- 14.6 Noetherian Rings
- 14.7 Structure to Abelian Groups
- 14.8 Application to Linear Operators
- 14.9 Polynomial Rings in Several Variables
- 14.10 Exercises
15. Fields
- 15.1 Examples of Fields
- 15.2 Algebraic and Transcendental Elements
- 15.3 The Degree of a Field Extension
- 15.4 Finding the Irreducible Polynomial
- 15.5 Ruler and Compass Constructions
- 15.6 Adjoining Roots
- 15.7 Finite Fields
- 15.8 Primitive Elements
- 15.9 Function Fields
- 15.10 The Fundamental Theorem of Algebra
- 15.11 Exercises
16. Galois Theory
- 16.1 Symmetric Functions
- 16.2 The Discriminant
- 16.3 Splitting Fields
- 16.4 Isomorphisms of Field Extensions
- 16.5 Fixed Fields
- 16.6 Galois Extensions
- 16.7 The Main Theorem
- 16.8 Cubic Equations
- 16.9 Quartic Equations
- 16.10 Roots of Unity
- 16.11 Kummer Extensions
- 16.12 Quintic Equations
- 16.13 Exercises
Appendix A. Background Material
- A.1 About Proofs
- A.2 The Integers
- A.3 Zorn's Lemma
- A.4 The Implicit Function Theorem
- A.5 Exercises
Your questions answered
Pearson+ is your one-stop shop, with eTextbooks and study videos designed to help students get better grades in college.
A Pearson eTextbook is an easy‑to‑use digital version of the book. You'll get upgraded study tools, including enhanced search, highlights and notes, flashcards and audio. Plus learn on the go with the Pearson+ app.
Your eTextbook subscription gives you access for 4 months. You can make a one‑time payment for the initial 4‑month term or pay monthly. If you opt for monthly payments, we will charge your payment method each month until your 4‑month term ends. You can turn on auto‑renew in My account at any time to continue your subscription before your 4‑month term ends.
When you purchase an eTextbook subscription, it will last 4 months. You can renew your subscription by selecting Extend subscription on the Manage subscription page in My account before your initial term ends.
If you extend your subscription, we'll automatically charge you every month. If you made a one‑time payment for your initial 4‑month term, you'll now pay monthly. To make sure your learning is uninterrupted, please check your card details.
To avoid the next payment charge, select Cancel subscription on the Manage subscription page in My account before the renewal date. You can subscribe again in the future by purchasing another eTextbook subscription.
Channels is a video platform with thousands of explanations, solutions and practice problems to help you do homework and prep for exams. Videos are personalized to your course, and tutors walk you through solutions. Plus, interactive AI‑powered summaries and a social community help you better understand lessons from class.
Channels is an additional tool to help you with your studies. This means you can use Channels even if your course uses a non‑Pearson textbook.
When you choose a Channels subscription, you're signing up for a 1‑month, 3‑month or 12‑month term and you make an upfront payment for your subscription. By default, these subscriptions auto‑renew at the frequency you select during checkout.
When you purchase a Channels subscription it will last 1 month, 3 months or 12 months, depending on the plan you chose. Your subscription will automatically renew at the end of your term unless you cancel it.
We use your credit card to renew your subscription automatically. To make sure your learning is uninterrupted, please check your card details.