Advice on the Writing Projects for Chapter 5

1. Obviously you will need to find a translated version if you want to read what Fibonacci actually said. The search technique of gradually working your way backwards usually works: If you can't find what you want in the place you start (here, for example, maybe with a standard mathematics history textbook), then search the references provided by that work, then check the references in the references, and so on backwards. There are several references listed on the MacTutor page on Fibonacci.

2. Articles, books, and Web sites at all levels have dealt with this subject. You might find something in, say, Scientific American (which is indexed in hard-copy and electronic versions of Readers' Guide); you might find some articles in materials for high-school students (see, for example, Mathematics Teacher, a magazine for high school teachers); and just browsing through the mathematics section of a public library or popular bookstore might yield something on this topic. Talk to someone who teaches a "math for poets" course at your school (i.e., a course with almost no mathematical prerequisite that deals with appreciating the beauty or applications of mathematics); some of the textbooks for that kind of course have material on this topic, as well as references to other sources of information. Here is one relevant Web site.

3. Paul Stockmeyer, a professor at the College of William and Mary, describes the Tower of Hanoi problem and its variations as his "main professional hobby." Consult his Web site for the original game instructions (in English and French) and some of his papers on the subject, as well as some great links on other topics.

4. There are many articles about the Catalan numbers, as well as treatments in textbooks. One article to start with might be [HiPe2]. If you search the Web for this topic, you might find this list of 17 different interpretations.

5. See [Ro3] for a brief introduction. An extensive discussion, as well as a long list of references, can be found in [Gu]. A recent Web article by the wonderful mathematics writer Ivars Peterson deals with this subject, in which he cites another wonderful mathematics writer, Martin Gardner.

6. One book on sieve methods is [HaRi]. A conference on sieve methods was held a few years ago; its Proceedings have been published.

7. See the article [Da2]. There is also relevant material in the chapter on arrangements with forbidden positions in [MiRo]. The references in the MacTutor page on Pierre Remond might have something.

8. A wonderful book on generating functions is [Wi2], and [GrKn] also has a lot of relevant material. There are sections on generating functions in the advanced combinatorics books mentioned our general advice page.

9. See advanced combinatorics texts, such as [Ro1] or [Tu1]. For another Writing Project, find out about George Polya, a fascinating figure in 20th century mathematics and mathematics education.

10. See [BoDo], which should also have pointers to historical sources. See also the MacTutor page on Lucas.

11. Advanced combinatorics texts, such as [Br2] or [Ro1], discuss this topic.