I was pleasantly surprised, when I sat down to try these problems out, by how fun and interesting they were.

A few of the problems had us look at patterns and make predictions. I'm surprised Jacobs didn't ask, "And, what type of reasoning is this?" (Inductive) or "Do we know these patterns will hold true for all numbers?" (No) I was so excited by seeing these patterns, and I wanted to know why the patterns hold. Why do square numbers only end in certain digits? Why is there a pattern to the last digits? Maybe I'll keep playing with these problems, and try to prove that some of these patterns will always hold.

If you haven't done these yet, do yourself a favor when you get to #9 in Set II (3rd edition), and use a calculator.

In Set III, Jacobs uses the periodic table. How fascinating, that the elements have these patterns. He doesn't say why. I think it has something to do with the sizes of the electron shells, but I don't really know. I took intro to chemistry my first year of college. Big lecture hall, hundreds of students. First week, I was sitting right up front. The prof mentioned something about the shells, and I asked "How do you know?" He brushed me off, said something about electron microscopes, I believe. 20 years later, my officemate, a chem teacher, told me that was nonsense. They've figured out the shell sizes using mathematics. Blew me away! If I'd seen the connection to math, maybe I could've enjoyed chemistry a bit. As it was, I fell asleep every time I tried to read the text. Got C's for 2 terms and never took more.

A few of the problems had us look at patterns and make predictions. I'm surprised Jacobs didn't ask, "And, what type of reasoning is this?" (Inductive) or "Do we know these patterns will hold true for all numbers?" (No) I was so excited by seeing these patterns, and I wanted to know why the patterns hold. Why do square numbers only end in certain digits? Why is there a pattern to the last digits? Maybe I'll keep playing with these problems, and try to prove that some of these patterns will always hold.

If you haven't done these yet, do yourself a favor when you get to #9 in Set II (3rd edition), and use a calculator.

In Set III, Jacobs uses the periodic table. How fascinating, that the elements have these patterns. He doesn't say why. I think it has something to do with the sizes of the electron shells, but I don't really know. I took intro to chemistry my first year of college. Big lecture hall, hundreds of students. First week, I was sitting right up front. The prof mentioned something about the shells, and I asked "How do you know?" He brushed me off, said something about electron microscopes, I believe. 20 years later, my officemate, a chem teacher, told me that was nonsense. They've figured out the shell sizes using mathematics. Blew me away! If I'd seen the connection to math, maybe I could've enjoyed chemistry a bit. As it was, I fell asleep every time I tried to read the text. Got C's for 2 terms and never took more.

- Notes by Sue VanHattum