Schaum's Outline of Mathematics for Liberal Arts Majors (Schaum's Outline Series)

Contents......Page 7
1.2 Tally Marks......Page 11
1.3 Egyptian Numbers......Page 12
1.4 Roman Numerals......Page 14
1.5 The Babylonian Number System......Page 15
1.6 Binary Numbers......Page 17
1.7 Hexadecimal Numbers......Page 19
1.8 A Fast Algorithm for Changing Bases......Page 20
2.1 Sets......Page 26
2.2 Subsets......Page 27
2.3 Unions and Intersections......Page 28
2.4 Venn Diagrams......Page 30
2.6 Cantor\'s Diagonal Proof......Page 33
3.1 Definitions......Page 39
3.2 Statements......Page 40
3.3 Conjunctions......Page 41
3.4 Truth Tables......Page 42
3.6 Conditional Statements......Page 44
3.7 Contrapositives and Converses......Page 45
3.8 Comparing the World of Mathematics to Cartoons......Page 46
4.1 Sharing among Two People......Page 52
4.2 Sharing among Three People......Page 53
4.3 The Last-Diminisher Method......Page 54
4.4 Sharing the Indivisible by Making Bids......Page 55
5.1 Computing with Functions......Page 63
5.2 Graphing Functions......Page 64
5.3 Inverses to Functions......Page 67
5.4 Exponential Functions......Page 70
5.5 Logarithms......Page 73
5.6 Logarithmic Scales......Page 74
6.1 Lengths......Page 81
6.2 Areas......Page 83
6.3 Volumes......Page 87
6.4 Angles......Page 90
6.5 How Eratosthenes Measured the Earth around 250 B.C.......Page 93
6.6 Non-Euclidean Geometry......Page 96
6.7 Higher Dimensions......Page 99
7.1 The Bridges of Königsberg......Page 107
7.2 Graphs......Page 108
7.3 Euler Paths and Circuits......Page 110
7.4 Hamiltonian Paths and Circuits......Page 113
7.5 The Traveling Salesman Problem......Page 116
8.2 Compound Interest......Page 123
8.4 Compound Interest with Payments......Page 125
8.6 Paying Off a Loan......Page 127
8.7 The Time Required to Pay Off a Debt......Page 128
9.1 Expectations......Page 131
9.2 Equally Likely Events......Page 132
9.3 Independent Events......Page 133
9.4 Complementary Events......Page 134
9.5 Combinations and Permutations......Page 136
9.6 Probabilities with Combinations......Page 137
10.1 The Depiction of Data......Page 142
10.2 Averages: Mean, Median, Midrange, and Mode......Page 146
10.3 Standard Deviation......Page 148
10.4 The Normal Curve and the Empirical Rule......Page 149
10.5 Z Scores......Page 150
10.6 Collecting Statistics......Page 152
11.1 Describing Weighted Voting Systems......Page 157
11.2 Dictators, Dummies, and Veto Power......Page 158
11.4 The Banzhaf Power Index......Page 159
12.1 Majorities and Pluralities......Page 164
12.2 Preference Schedules and Instant Runoff Voting......Page 165
12.3 Pairwise Comparisons and the Condorcet Criterion......Page 168
12.4 The Borda Count Voting Method......Page 171
12.5 Two More Fairness Criteria......Page 173
12.6 Arrow\'s Impossibility Theorem......Page 177
13.1 Translations......Page 182
13.2 Translation Symmetry......Page 185
13.3 Reflections......Page 187
13.4 Reflection Symmetry......Page 190
13.5 Rotations......Page 193
13.6 Rotation Symmetry......Page 194
13.7 Combinations of Transformations......Page 196
13.8 Groups of Symmetries......Page 197
14.1 Fractals......Page 207
14.2 The Golden Ratio......Page 208
14.3 Sequences......Page 210
14.4 Series......Page 211
15.1 Similar Triangles......Page 214
15.2 The Pythagorean Theorem......Page 217
15.3 Pythagorean Triples......Page 218
15.4 Trigonometric Functions......Page 219
15.5 Trigonometry on a Calculator......Page 221
15.6 Using Trigonometric Functions......Page 222
15.7 Inverse Trigonometric Functions......Page 224
15.8 Using Inverse Trigonometric Functions......Page 225
15.9 The Law of Sines......Page 226
15.10 The Law of Cosines......Page 228
D......Page 233
H......Page 234
P......Page 235
T......Page 236
Z......Page 237