Outline of Beginning Finite Mathematics

Terms of Use......Page 5
Want to learn more?......Page 6
Preface......Page 7
Contents......Page 9
 Introduction; Real Line R......Page 13
 Cartesian Plane R2......Page 15
 Linear Equations in One Unknown......Page 17
 Linear Equations in Two Unknowns and Their Graphs......Page 18
 Slope of a Line......Page 19
 Linear Functions and Linear Growth......Page 21
 Lines and Their Equations; Point-Slope Formula......Page 23
 General Equations and Curves; Functions......Page 24
 Introduction: Linear vs. Exponential Change......Page 42
 Logarithms......Page 43
 Doubling Time......Page 44
 Exponential Decay......Page 45
 Growth and Decay in Terms of Natural Base......Page 46
 Summary......Page 48
 Comment on Exact Equations, Approximate Mathematical Models, and Numerical Accuracy......Page 49
 Simple Interest......Page 59
 Simple Discount......Page 60
 Compound Interest......Page 61
 Continuous Interest......Page 63
 Effective Rate of Interest......Page 64
 Sinking Funds and Future Value......Page 65
 Amortization and Present Value......Page 66
 Sets and Elements; Subsets......Page 82
 Set Operations......Page 84
 Finite Sets; Counting Principle......Page 87
 Product Sets......Page 88
 Classes of Sets; Power Sets and Partitions......Page 89
 Mathematical Induction (Optional)......Page 90
 Arguments and Venn Diagrams (Optional)......Page 91
 Basic Counting Principles......Page 105
 Mathematical Functions......Page 106
 Permutations......Page 108
 Combinations......Page 109
 Tree Diagrams......Page 110
 Sample Space and Events......Page 122
 Finite Probability Spaces......Page 123
 Conditional Probability......Page 125
 Independent Events......Page 128
 Independent Repeated Trials; Binomial Distribution......Page 129
 Random Variables......Page 131
 Normal Distribution......Page 135
 Normal Approximation of the Binomial Distribution......Page 139
 Gathering Data; Random Samples......Page 166
 Displaying Data; Frequency Histograms......Page 168
 Measures of Central Tendency; Sample Mean and Median......Page 172
 Measures of Dispersion; Sample Variance and Standard Deviation......Page 174
 Measures of Position; Quartiles and Percentiles......Page 178
 Bivariate Data, Scatterplots, and Linear Regression......Page 179
 Sampling Distributions......Page 206
 The Central Limit Theorem......Page 209
 Confidence Intervals for Population Means......Page 210
 Chi-Square Test for Goodness of Fit......Page 215
 Introduction......Page 230
 Euler Circuits......Page 231
 The Letter Carrier Problem......Page 233
 Hamiltonian Circuits......Page 234
 Complete Graphs......Page 235
 Traveling Salesperson Problem......Page 236
 Directed Graphs......Page 238
 Trees......Page 239
 Spanning Trees......Page 240
 Elections with Two Candidates......Page 262
 Voting Systems with Preference List Ballots and More Than Two Candidates......Page 263
 Basic Objects of Plane Geometry......Page 281
 Angle Measurement......Page 284
 Planar Figures......Page 286
 Euclid's Postulates: The Development of Plane Geometry......Page 289
 Pythagorean Theorem......Page 290
 Non-Euclidean Geometry......Page 291
 Units of Measurement and Formulas for Reference......Page 293
 Linear Inequalities in the Plane......Page 313
 Systems of Linear Inequalities and Corner Points......Page 314
 Applications of Systems of Linear Inequalities......Page 315
 A Minimum Linear Programming Problem......Page 317
Appendix A: Tables......Page 325
Appendix B: Standard Normal Curve Areas......Page 339
 The Hamilton Method and the Quota Criterion......Page 341
 The Hamilton Method and the Population, Alabama, and New States Paradoxes......Page 343
 Apportionment Methods That Avoid Paradoxes......Page 345
 The Jefferson, Webster, Hill-Huntington Methods and the Quota Criterion......Page 348
 The Balinski-Young Impossibility Theorem......Page 350
Index......Page 355