Thinking Mathematically

Cover......Page 1
Table of Contents......Page 4
1.Problem Solving and Critical Thinking......Page 8
 1.Inductive and Deductive Reasoning......Page 9
 2.Estimation, Graphs, and Mathematical Models......Page 20
 3.Problem Solving......Page 33
 4.Chapter Summary, Review, and Test......Page 44
2.Set Theory......Page 54
 1.Basic Set Concepts......Page 55
 2.Subsets......Page 67
 3.Venn Diagrams and Set Operations......Page 76
 4.Set Operations and Venn Diagrams with Three Sets......Page 88
 5.Survey Problems......Page 99
 Chapter Summary, Review, and Test......Page 109
3.Logic......Page 118
 1.Statements, Negations, and Quantified Statements......Page 119
 2.Compound Statements and Connectives......Page 126
 3.Truth Tables for Negation, Conjunction, and Disjunction......Page 138
 4.Truth Tables for the Conditional and the Biconditional......Page 153
 5.Equivalent Statements and Variations of Conditional Statements......Page 163
 6.Negations of Conditional Statements and De Morgan’s Laws......Page 172
 7.Arguments and Truth Tables......Page 179
 8.Arguments and Euler Diagrams......Page 193
 Chapter Summary, Review, and Test......Page 202
4.Number Representation and Calculation......Page 222
 1.Our Hindu-Arabic System and Early Positional Systems......Page 223
 2.Number Bases in Positional Systems......Page 230
 3.Computation in Positional Systems......Page 236
 4.Looking Back at Early Numeration Systems......Page 244
 Chapter Summary, Review, and Test......Page 251
5.Number Theory and the Real Number System......Page 258
 1.Number Theory: Prime and Composite Numbers......Page 259
 2.The Integers; Order of Operations......Page 269
 3.The Rational Numbers......Page 281
 4.The Irrational Numbers......Page 295
 5.Real Numbers and Their Properties......Page 306
 6.Exponents and Scientific Notation......Page 313
 7.Arithmetic and Geometric Sequences......Page 323
 Chapter Summary, Review, and Test......Page 333
6.Algebra: Equations and Inequalities......Page 342
 1.Algebraic Expressions and Formulas......Page 343
 2.Linear Equations in One Variable and Proportions......Page 352
 3.Applications of Linear Equations......Page 366
 4.Linear Inequalities in One Variable......Page 377
 5.Quadratic Equations......Page 385
 Chapter Summary, Review, and Test......Page 399
7.Algebra: Graphs, Functions, and Linear Systems......Page 408
 1.Graphing and Functions......Page 409
 2.Linear Functions and Their Graphs......Page 422
 3.Systems of Linear Equations in Two Variables......Page 433
 4.Linear Inequalities in Two Variables......Page 447
 5.Linear Programming......Page 455
 6.Modeling Data: Exponential, Logarithmic, and Quadratic Functions......Page 461
 Chapter Summary, Review, and Test......Page 475
8.Consumer Mathematics and Financial Management......Page 490
 1.Percent, Sales Tax, and Income Tax......Page 491
 2.Simple Interest......Page 501
 3.Compound Interest......Page 507
 4.Annuities, Stocks, and Bonds......Page 515
 5.Installment Loans, Amortization, and Credit Cards......Page 528
 Chapter Summary, Review, and Test......Page 541
9.Measurement......Page 552
 1.Measuring Length; The Metric System......Page 553
 2.Measuring Area and Volume......Page 562
 3.Measuring Weight and Temperature......Page 570
 Chapter Summary, Review, and Test......Page 578
10.Geometry......Page 584
 1.Points, Lines, Planes, and Angles......Page 585
 2.Triangles......Page 593
 3.Polygons, Perimeter, and Tessellations......Page 603
 4.Area and Circumference......Page 611
 5.Volume......Page 621
 6.Right Triangle Trigonometry......Page 629
 7.Beyond Euclidean Geometry......Page 637
 Chapter Summary, Review, and Test......Page 647
11.Counting Methods and Probability Theory......Page 656
 1.The Fundamental Counting Principle......Page 657
 2.Permutations......Page 663
 3.Combinations......Page 670
 4.Fundamentals of Probability......Page 676
 5.Probability with the Fundamental Counting Principle, Permutations, and Combinations......Page 685
 6.Events Involving Not and Or; Odds......Page 691
 7.Events Involving And; Conditional Probability......Page 703
 8.Expected Value......Page 714
 Chapter Summary, Review, and Test......Page 721
12.Statistics......Page 732
 1.Sampling, Frequency Distributions, and Graphs......Page 733
 2.Measures of Central Tendency......Page 746
 3.Measures of Dispersion......Page 758
 4.The Normal Distribution......Page 766
 5.Problem Solving with the Normal Distribution......Page 779
 6.Scatter Plots, Correlation, and Regression Lines......Page 784
 Chapter Summary, Review, and Test......Page 795
13.Mathematical Systems......Page 808
 1.Mathematical Systems......Page 809
 2.Rotational Symmetry, Groups, and Clock Arithmetic......Page 818
 Chapter Summary, Review, and Test......Page 829
14.Voting and Apportionment......Page 834
 1.Voting Methods......Page 835
 2.Flaws of Voting Methods......Page 847
 3.Apportionment Methods......Page 858
 4.Flaws of Apportionment Methods......Page 871
 Chapter Summary, Review, and Test......Page 881
 C......Page 888
 F......Page 889
 L......Page 890
 P......Page 891
 R......Page 892
 T......Page 893
 Z......Page 894