| Formatted contents note |
Numbers, Sets, and Operations -- Counting Methods -- Fingers and Sticks -- Roman Numerals -- Hindu-Arabic Numerals -- The Counting Base -- The Language of Sets -- The Concept of a Set -- How Sets Relate -- Set Intersection -- Set Union -- Natural Numbers and Integers -- How Natural Numbers are Made -- Special Natural Numbers -- Natural Number Nontrivia -- The Integers -- Addition and Subtraction -- Moving Up and Down -- Identity, Grouping, and Signs -- The Commutative Law for Addition -- The Associative Law for Addition -- Multiplication and Division -- Moving Out and In -- Identity, Grouping, and Signs -- The Commutative Law for Multiplication -- The Associative Law for Multiplication -- The Distributive Laws -- Fractions Built of Integers -- "Messy" Quotients -- "Reducing" a Fraction or Ratio -- Multiplying and Dividing Fractions -- Adding and Subtracting Fractions -- Decimal Fractions -- Powers of 10 -- Terminating Decimals -- Endless Decimals -- Conversions -- Powers and Roots -- Integer Powers -- Reciprocal-of-Integer Powers -- Multiplying and Dividing with Exponents -- Multiple Powers -- Irrational and Real Numbers -- The Number Hierarchy -- More About Irrationals and Reals -- How Real Variables Behave -- More Rules for Real Variables -- Review Questions and Answers -- Linear Equations and Relations -- Equations and Inequalities -- Equation Morphing Revisited -- Inequalities -- How Inequalities Behave -- Inequality Morphing -- First-Degree Equations in One Variable -- Constants, Sums, and Differences -- Products and Ratios -- Combinations of Operations -- Word Problems -- Mappings, Relations, and Functions -- Mapping "Territories" -- Types of Mappings -- Examples of Relations -- Examples of Functions -- The Cartesian Plane -- Two Number Lines -- Three Relations -- Three Functions -- Graphs of Linear Relations -- Slope-Intercept Form -- Point-Slope Form -- Equations from Graphs -- Two-by-Two Linear Systems -- Morph and Mix -- Double Elimination -- Rename and Replace -- 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 -- Larger Linear Systems -- Eliminate One Variable -- Solve the Two-by-Two -- Substitute Back -- General Linear Systems -- The Matrix Morphing Game -- How to Build a Matrix -- Matrix Operations -- A Sample Problem -- Review Questions and Answers -- Nonlinear Equations and Relations -- Imaginary and Complex Numbers -- The Square Root of -1 -- The Imaginary Number Line -- Real + Imaginary = Complex -- Quadratic Equations with Real Roots -- Second-Degree Polynomials -- Binomial Factor Form -- Completing the Square -- The Quadratic Formula -- Quadratic Equations with Complex Roots -- Complex Roots by Formula -- Imaginary Roots in Factors -- Conjugate Roots in Factors -- Graphs of Quadratic Functions -- Two Real Zeros -- One Real Zero -- No Real Zeros -- Cubic Equations in Real Numbers -- Cube of Binomial -- Three Binomial Factors -- Binomial Times Trinomial -- Polynomial Equation of Third Degree -- Polynomial Equations in Real Numbers -- Binomial to the nth Power -- Binomial Factors -- Polynomial Standard Form -- Digging for Real Roots -- More Two-by-Two Systems -- Linear and Quadratic -- Two Quadratics -- Enter the Cubic -- More Two-by-Two Graphs -- Linear and Quadratic -- Two Quadratics -- Enter the Cubic -- Logarithms and Exponentials -- What Is a Logarithm? -- How Logarithms Work -- What Is an Exponential? -- How Exponentials Work -- Final Exam -- Worked-Out Solutions to Exercises: Chapters 1 to 9 -- Worked-Out Solutions to Exercises: Chapters 11 to 19 -- Worked-Out Solutions to Exercises: Chapters 21 to 29 -- Answers to Final Exam Questions -- Special Characters in Order of Appearance |
CSU-Carig