What is included with this book?
Preface | p. xiii |
Acknowledgment | p. xiv |
Numbers, Sets, and Operations | |
Counting Methods | p. 3 |
Fingers and Sticks | p. 3 |
Roman Numerals | p. 6 |
Hindu-Arabic Numerals | p. 8 |
The Counting Base | p. 11 |
Practice Exercises | p. 17 |
The Language of Sets | p. 19 |
The Concept of a Set | p. 19 |
How Sets Relate | p. 22 |
Set Intersection | p. 27 |
Set Union | p. 30 |
Practice Exercises | p. 33 |
Natural Numbers and Integers | p. 35 |
How Natural Numbers are Made | p. 35 |
Special Natural Numbers | p. 38 |
Natural Number Nontrivia | p. 42 |
The Integers | p. 45 |
Practice Exercises | p. 49 |
Addition and Subtraction | p. 51 |
Moving Up and Down | p. 51 |
Identity, Grouping, and Signs | p. 55 |
The Commutative Law for Addition | p. 57 |
The Associative Law for Addition | p. 59 |
Practice Exercises | p. 63 |
Multiplication and Division | p. 65 |
Moving Out and In | p. 65 |
Identity, Grouping, and Signs | p. 70 |
The Commutative Law for Multiplication | p. 73 |
The Associative Law for Multiplication | p. 75 |
The Distributive Laws | p. 78 |
Practice Exercises | p. 81 |
Fractions Built of Integers | p. 83 |
"Messy" Quotients | p. 83 |
"Reducing" a Fraction or Ratio | p. 87 |
Multiplying and Dividing Fractions | p. 89 |
Adding and Subtracting Fractions | p. 91 |
Practice Exercises | p. 94 |
Decimal Fractions | p. 95 |
Powers of 10 | p. 95 |
Terminating Decimals | p. 99 |
Endless Decimals | p. 101 |
Conversions | p. 104 |
Practice Exercises | p. 107 |
Powers and Roots | p. 109 |
Integer Powers | p. 109 |
Reciprocal-of-Integer Powers | p. 112 |
Multiplying and Dividing with Exponents | p. 117 |
Multiple Powers | p. 119 |
Practice Exercises | p. 123 |
Irrational and Real Numbers | p. 124 |
The Number Hierarchy | p. 124 |
More About Irrationals and Reals | p. 129 |
How Real Variables Behave | p. 133 |
More Rules for Real Variables | p. 136 |
Practice Exercises | p. 140 |
Review Questions and Answers | p. 142 |
Linear Equations and Relations | |
Equations and Inequalities | p. 173 |
Equation Morphing Revisited | p. 173 |
Inequalities | p. 176 |
How Inequalities Behave | p. 179 |
Inequality Morphing | p. 183 |
Practice Exercises | p. 190 |
First-Degree Equations in One Variable | p. 192 |
Constants, Sums, and Differences | p. 192 |
Products and Ratios | p. 196 |
Combinations of Operations | p. 198 |
Word Problems | p. 203 |
Practice Exercises | p. 207 |
Mappings, Relations, and Functions | p. 208 |
Mapping "Territories" | p. 208 |
Types of Mappings | p. 211 |
Examples of Relations | p. 215 |
Examples of Functions | p. 218 |
Practice Exercises | p. 221 |
The Cartesian Plane | p. 223 |
Two Number Lines | p. 223 |
Three Relations | p. 226 |
Three Functions | p. 232 |
Practice Exercises | p. 234 |
Graphs of Linear Relations | p. 236 |
Slope-Intercept Form | p. 236 |
Point-Slope Form | p. 242 |
Equations from Graphs | p. 244 |
Practice Exercises | p. 249 |
Two-by-Two Linear Systems | p. 251 |
Morph and Mix | p. 251 |
Double Elimination | p. 255 |
Rename and Replace | p. 258 |
Practice Exercises | p. 262 |
Two-by-Two Linear Graphs | p. 264 |
We Morphed, We Mixed, We Can Graph | p. 264 |
We Added, We Eliminated, We Can Graph | p. 267 |
We Renamed, We Replaced, We Can Graph | p. 271 |
We Couldn't Solve, but We Can Graph | p. 275 |
Practice Exercises | p. 278 |
Larger Linear Systems | p. 281 |
Eliminate One Variable | p. 281 |
Solve the Two-by-Two | p. 285 |
Substitute Back | p. 288 |
General Linear Systems | p. 290 |
Practice Exercises | p. 294 |
The Matrix Morphing Game | p. 296 |
How to Build a Matrix | p. 296 |
Matrix Operations | p. 298 |
A Sample Problem | p. 300 |
Practice Exercises | p. 306 |
Review Questions and Answers | p. 308 |
Nonlinear Equations and Relations | |
Imaginary and Complex Numbers | p. 349 |
The Square Root of -1 | p. 349 |
The Imaginary Number Line | p. 351 |
Real + Imaginary = Complex | p. 355 |
Practice Exercises | p. 361 |
Quadratic Equations with Real Roots | p. 363 |
Second-Degree Polynomials | p. 363 |
Binomial Factor Form | p. 367 |
Completing the Square | p. 371 |
The Quadratic Formula | p. 375 |
Practice Exercises | p. 379 |
Quadratic Equations with Complex Roots | p. 381 |
Complex Roots by Formula | p. 381 |
Imaginary Roots in Factors | p. 387 |
Conjugate Roots in Factors | p. 391 |
Practice Exercises | p. 395 |
Graphs of Quadratic Functions | p. 396 |
Two Real Zeros | p. 396 |
One Real Zero | p. 402 |
No Real Zeros | p. 407 |
Practice Exercises | p. 412 |
Cubic Equations in Real Numbers | p. 413 |
Cube of Binomial | p. 413 |
Three Binomial Factors | p. 415 |
Binomial Times Trinomial | p. 419 |
Polynomial Equation of Third Degree | p. 422 |
Practice Exercises | p. 430 |
Polynomial Equations in Real Numbers | p. 432 |
Binomial to the nth Power | p. 432 |
Binomial Factors | p. 435 |
Polynomial Standard Form | p. 438 |
Digging for Real Roots | p. 439 |
Practice Exercises | p. 445 |
More Two-by-Two Systems | p. 447 |
Linear and Quadratic | p. 447 |
Two Quadratics | p. 451 |
Enter the Cubic | p. 456 |
Practice Exercises | p. 461 |
More Two-by-Two Graphs | p. 463 |
Linear and Quadratic | p. 463 |
Two Quadratics | p. 466 |
Enter the Cubic | p. 471 |
Practice Exercises | p. 475 |
Logarithms and Exponentials | p. 479 |
What Is a Logarithm? | p. 479 |
How Logarithms Work | p. 482 |
What Is an Exponential? | p. 487 |
How Exponentials Work | p. 491 |
Practice Exercises | p. 496 |
Review Questions and Answers | p. 498 |
Final Exam | p. 545 |
Worked-Out Solutions to Exercises: Chapters 1 to 9 | p. 587 |
Worked-Out Solutions to Exercises: Chapters 11 to 19 | p. 619 |
Worked-Out Solutions to Exercises: Chapters 21 to 29 | p. 663 |
Answers to Final Exam Questions | p. 716 |
Special Characters in Order of Appearance | p. 717 |
Suggested Additional Reading | p. 719 |
Index | p. 721 |
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