Mathematics of choice: How to count without counting by Ivan Morton Niven

Mathematics of choice: How to count without counting



Download Mathematics of choice: How to count without counting




Mathematics of choice: How to count without counting Ivan Morton Niven ebook
Page: 213
Format: djvu
ISBN: 0883856158, 9780883856154
Publisher: Mathematical Assn of America


Counts the number of permutations of n objects, that is, the number of different ways to take n distinct objects and arrange them in an ordered list. Two roads diverged in a yellow wood, And sorry I could not travel both, And be one traveler, long I stood, And looked down one as far as I could, To where it bent in the undergrowth; . In this post, I will share a couple of examples (one from each side of the political spectrum) of mathematical manipulation that struck me as good reasons why having critical quantitative thinking is so important. Math by Starting with Counting? At any rate, this is not how votes are counted, so it is not very useful information (at least as evidence of wrongdoing). As you see, this “counting” is a little more challenging than the kind of “counting” you learned in your salad days. Well, there are n objects we could choose to put first; once we've made that choice, there are n-1 remaining objects we could choose to go second; then n-2 choices for the third object, and so on, for a total of n (n-1) (n-2) \dots 1 = n choices. After all, even the person most allergic to math, most traumatized by math, still remembers how to count! The first So for example, Amazonas, which had 73 thousand voters, counts the same as Miranda, which had around 1.5 million voters. Yet math tests in the early grades focus instead on how well and how quickly students can solve basic arithmetic problems, often using counting—a skill less connected to students' later math achievement, the study found. For example: Shakespeare wrote fifteen comedies and ten histories. In the Unites States and many other countries, the choice was made - perhaps unreflectively - long ago to take our facility for counting as the starting point, and thus to start the mathematical journey with the natural numbers. If option #1 has P alternatives and option #2 has Q alternatives (assuming that the two sets of alternatives have no overlap), then total number of different pairs we can form is P*Q.

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