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Book Categories |
1 | Counting | 1 |
1.1 | One, two, three | 1 |
1.2 | Some counting problems and estimates | 5 |
1.3 | A fundamental counting principle | 8 |
1.4 | Permutations | 13 |
1.5 | Two complications | 19 |
1.6 | Combinations | 25 |
1.7 | Notes | 31 |
2 | Probability | 33 |
2.1 | What are the odds? | 33 |
2.2 | Measuring likelihood | 37 |
2.3 | Independent trials | 44 |
2.4 | Expectation | 48 |
2.5 | Conditional probability | 54 |
2.6 | Notes | 59 |
3 | Statistics | 61 |
3.1 | Analysis of data | 61 |
3.2 | Population and sample | 67 |
3.3 | What if it were? | 70 |
3.4 | Liars | 75 |
3.5 | Notes | 77 |
4 | Geometry | 79 |
4.1 | Area | 79 |
4.2 | The Pythagorean theorem | 84 |
4.3 | Squaring the circle | 90 |
4.4 | Numbers and points | 93 |
4.5 | Plotting more points | 96 |
4.6 | Plotting still more points | 100 |
4.7 | Geometric sensitivity | 105 |
4.8 | Paths | 113 |
4.9 | Geometric means | 121 |
4.10 | Counting again | 123 |
4.11 | Notes | 130 |
5 | Logic | 133 |
5.1 | Think of the possibilities | 133 |
5.2 | What's my number? | 134 |
5.3 | The liar paradox | 137 |
5.4 | Subject and predicate | 139 |
5.5 | Syllogisms | 142 |
5.6 | Notes | 146 |
6 | Exponential growth | 149 |
6.1 | The power of powers | 149 |
6.2 | Doubling time | 152 |
6.3 | Half-life | 154 |
6.4 | Explosions | 156 |
6.5 | Rates of interest | 161 |
6.6 | Logarithms | 172 |
6.7 | Notes | 173 |
7 | An average chapter | 175 |
7.1 | The arithmetic mean | 175 |
7.2 | Weighted arithmetic means | 179 |
7.3 | The geometric mean | 184 |
7.4 | The harmonic mean | 189 |
7.5 | Comparing the means | 195 |
7.6 | The Farey mean | 198 |
7.7 | Notes | 204 |
8 | What are natural numbers made of? | 205 |
8.1 | The building block of addition | 205 |
8.2 | How can I build thee? Let me count the ways | 207 |
8.3 | Building blocks for subtraction | 211 |
8.4 | The Euclidean algorithm | 214 |
8.5 | The building blocks of multiplication | 217 |
8.6 | Notes | 223 |
9 | Changing bases | 225 |
9.1 | Earlier number systems | 225 |
9.2 | Base five | 230 |
9.3 | Base twelve | 236 |
9.4 | Base two | 239 |
9.5 | Notes | 244 |
10 | Clock arithmetic | 247 |
10.1 | The twelve-hour clock | 247 |
10.2 | Arithmetic of even and odd; casting out nines | 253 |
10.3 | Zero divisors | 256 |
10.4 | Pigeonholes and inverses | 258 |
10.5 | The perfect shuffle | 261 |
10.6 | Fermat's little theorem | 265 |
10.7 | Notes | 268 |
11 | Secret writing | 269 |
11.1 | Simple substitution | 269 |
11.2 | The Gold-Bug | 272 |
11.3 | Letters are numbers | 275 |
11.4 | Block encoding | 278 |
11.5 | Trap-door functions | 282 |
11.6 | Notes | 284 |
12 | Infinite sets | 287 |
12.1 | Finite and infinite | 287 |
12.2 | Decimal representations of real numbers | 289 |
12.3 | Comparing sizes of sets | 291 |
12.4 | More comparisons | 295 |
12.5 | More infinities | 299 |
12.6 | Notes | 302 |
13 | Number theory selections | 305 |
13.1 | Primes and divisibility | 305 |
13.2 | Some rules for divisibility | 308 |
13.3 | A general divisibility rule | 312 |
13.4 | Sums of divisors | 315 |
13.5 | Deficiency and abundancy | 318 |
13.6 | Perfection | 321 |
13.7 | Amicability | 324 |
13.8 | How are primes distributed? | 326 |
13.9 | Sums of squares | 333 |
13.10 | Pythagorean triples | 336 |
13.11 | Notes | 339 |
A | Mathematics encounters | 341 |
A.1 | Temperature conversion | 342 |
A.2 | The Greek ladder method | 343 |
A.3 | The collapsing compass | 344 |
A.4 | Catalan's conjecture | 345 |
A.5 | Egyptian fractions | 346 |
A.6 | The Pythagoreans | 347 |
A.7 | Triangle numbers | 348 |
A.8 | The four-color problem | 349 |
A.9 | Morley's Theorem | 350 |
B | Notation and arithmetic | 351 |
B.1 | The alphabet and punctuation of mathematics | 351 |
B.2 | Arithmetic of the integers | 358 |
B.3 | Arithmetic of fractions | 363 |
B.4 | Arithmetic of exponents | 370 |
B.5 | Arithmetic of equations | 375 |
B.6 | A standard deck of cards | 379 |
Index | 381 |
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Add Mathematics for the Liberal Arts Student, This book communicates the spirit of mathematics by means of simple ideas and problems, emphasizing exploration rather than drill. Its accessible approach encourages appreciation of mathematics and is ideal for readers with weak backgrounds, yet is intere, Mathematics for the Liberal Arts Student to the inventory that you are selling on WonderClubX
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Add Mathematics for the Liberal Arts Student, This book communicates the spirit of mathematics by means of simple ideas and problems, emphasizing exploration rather than drill. Its accessible approach encourages appreciation of mathematics and is ideal for readers with weak backgrounds, yet is intere, Mathematics for the Liberal Arts Student to your collection on WonderClub |