Algebra know-it-all : beginner to advanced, and everything in between

Algebra know-it-all Beginner to advanced, and everything in between

Stan Gibilisco

Book - 2008

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Subjects
Algebra.
Published
New York : McGraw-Hill [2008]
Language
English
Main Author
Stan Gibilisco (-)
Physical Description
xiv, 730 pages : illustrations ; 24 cm
Bibliography
Includes bibliographical references (page 719) and index.
ISBN
9780071546171
  • Preface
  • Acknowledgment
  • Part 1. Numbers, Sets, and Operations
  • 1. Counting Methods
  • Fingers and Sticks
  • Roman Numerals
  • Hindu-Arabic Numerals
  • The Counting Base
  • Practice Exercises
  • 2. The Language of Sets
  • The Concept of a Set
  • How Sets Relate
  • Set Intersection
  • Set Union
  • Practice Exercises
  • 3. Natural Numbers and Integers
  • How Natural Numbers are Made
  • Special Natural Numbers
  • Natural Number Nontrivia
  • The Integers
  • Practice Exercises
  • 4. Addition and Subtraction
  • Moving Up and Down
  • Identity, Grouping, and Signs
  • The Commutative Law for Addition
  • The Associative Law for Addition
  • Practice Exercises
  • 5. Multiplication and Division
  • Moving Out and In
  • Identity, Grouping, and Signs
  • The Commutative Law for Multiplication
  • The Associative Law for Multiplication
  • The Distributive Laws
  • Practice Exercises
  • 6. Fractions Built of Integers
  • "Messy" Quotients
  • "Reducing" a Fraction or Ratio
  • Multiplying and Dividing Fractions
  • Adding and Subtracting Fractions
  • Practice Exercises
  • 7. Decimal Fractions
  • Powers of 10
  • Terminating Decimals
  • Endless Decimals
  • Conversions
  • Practice Exercises
  • 8. Powers and Roots
  • Integer Powers
  • Reciprocal-of-Integer Powers
  • Multiplying and Dividing with Exponents
  • Multiple Powers
  • Practice Exercises
  • 9. Irrational and Real Numbers
  • The Number Hierarchy
  • More About Irrationals and Reals
  • How Real Variables Behave
  • More Rules for Real Variables
  • Practice Exercises
  • 10. Review Questions and Answers
  • Part 2. Linear Equations and Relations
  • 11. Equations and Inequalities
  • Equation Morphing Revisited
  • Inequalities
  • How Inequalities Behave
  • Inequality Morphing
  • Practice Exercises
  • 12. First-Degree Equations in One Variable
  • Constants, Sums, and Differences
  • Products and Ratios
  • Combinations of Operations
  • Word Problems
  • Practice Exercises
  • 13. Mappings, Relations, and Functions
  • Mapping "Territories"
  • Types of Mappings
  • Examples of Relations
  • Examples of Functions
  • Practice Exercises
  • 14. The Cartesian Plane
  • Two Number Lines
  • Three Relations
  • Three Functions
  • Practice Exercises
  • 15. Graphs of Linear Relations
  • Slope-Intercept Form
  • Point-Slope Form
  • Equations from Graphs
  • Practice Exercises
  • 16. Two-by-Two Linear Systems
  • Morph and Mix
  • Double Elimination
  • Rename and Replace
  • Practice Exercises
  • 17. Two-by-Two Linear Graphs
  • We Morphed, We Mixed, We Can Graph
  • We Added, We Eliminated, We Can Graph
  • We Renamed, We Replaced, We Can Graph
  • We Couldn't Solve, but We Can Graph
  • Practice Exercises
  • 18. Larger Linear Systems
  • Eliminate One Variable
  • Solve the Two-by-Two
  • Substitute Back
  • General Linear Systems
  • Practice Exercises
  • 19. The Matrix Morphing Game
  • How to Build a Matrix
  • Matrix Operations
  • A Sample Problem
  • Practice Exercises
  • 20. Review Questions and Answers
  • Part 3. Nonlinear Equations and Relations
  • 21. Imaginary and Complex Numbers
  • The Square Root of -1
  • The Imaginary Number Line
  • Real + Imaginary = Complex
  • Practice Exercises
  • 22. Quadratic Equations with Real Roots
  • Second-Degree Polynomials
  • Binomial Factor Form
  • Completing the Square
  • The Quadratic Formula
  • Practice Exercises
  • 23. Quadratic Equations with Complex Roots
  • Complex Roots by Formula
  • Imaginary Roots in Factors
  • Conjugate Roots in Factors
  • Practice Exercises
  • 24. Graphs of Quadratic Functions
  • Two Real Zeros
  • One Real Zero
  • No Real Zeros
  • Practice Exercises
  • 25. Cubic Equations in Real Numbers
  • Cube of Binomial
  • Three Binomial Factors
  • Binomial Times Trinomial
  • Polynomial Equation of Third Degree
  • Practice Exercises
  • 26. Polynomial Equations in Real Numbers
  • Binomial to the nth Power
  • Binomial Factors
  • Polynomial Standard Form
  • Digging for Real Roots
  • Practice Exercises
  • 27. More Two-by-Two Systems
  • Linear and Quadratic
  • Two Quadratics
  • Enter the Cubic
  • Practice Exercises
  • 28. More Two-by-Two Graphs
  • Linear and Quadratic
  • Two Quadratics
  • Enter the Cubic
  • Practice Exercises
  • 29. Logarithms and Exponentials
  • What Is a Logarithm?
  • How Logarithms Work
  • What Is an Exponential?
  • How Exponentials Work
  • Practice Exercises
  • 30. Review Questions and Answers
  • Final Exam
  • Appendix A. Worked-Out Solutions to Exercises: Chapters 1 to 9
  • Appendix B. Worked-Out Solutions to Exercises: Chapters 11 to 19
  • Appendix C. Worked-Out Solutions to Exercises: Chapters 21 to 29
  • Appendix D. Answers to Final Exam Questions
  • Appendix E. Special Characters in Order of Appearance
  • Suggested Additional Reading
  • Index

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