Chapter+1+Review

Do you feel you have a clear understanding of the difference between inductive and deductive reasoning, after working through this chapter? Do you understand the role each plays in math?

I think this was a great way for Jacobs to start the text, because it helps us see that inductive reasoning – pattern finding – does have a role in mathematical discovery. And we also got to see the limitations of inductive reasoning. A pattern can be quite compelling, but not carry through into new examples. (In the circle, it seemed so obvious that the number of regions would be 32, after it had been 1,2,4,8, and 16. But ...)

Mathematicians studying number theory would love to find a pattern for the prime numbers. (A prime number has no factors other than 1 and itself.) They’ve found lots of patterns that sometimes work, but none that always work.

After we’ve completed a few more chapters, I’ll look forward to finding out if this chapter was the hardest one. Trying to solve puzzles like these may be quite a bit harder than what we’ll be doing in the next few chapters.

Jacobs has included some logic puzzles (Tom, Dick, and Harry) in this summary. You can get whole books of puzzles like these. I used to do them for fun, and would be so addicted, I’d stay up until my eyes got all dry and gritty, trying to figure out who did what. Years ago, Games magazine published a really hard one using the 8 reindeer that pull Santa’s sleigh. A friend gave it to me, and I avoided it for months because it looked so intimidating. Once I sat down to doing it, I loved it. It took a lot of searching online, and I finally found it. Enjoy!

- Notes by Sue VanHattum