Advice on the Writing Projects for Chapter 6

1. See the same references as suggested for fuzzy logic in Writing Project 1 of Chapter 1, as well as [Zi]. Fuzzy relations are included in the topic of set theory, as organized by Mathematical Reviews

2. There are numerous textbooks on databases. Try to consult one that is fairly recent, because, as in many areas of computer science, progress is so fast that books soon become out-dated. You will find them in the QA 76.9 area of the library's shelves. Two recommended ones are are [Da1] and [Ma1]. You'll find many listed by amazon.com.

3. Try author or key-word search in an appropriate database (e.g., one provided by Mathematical Reviews). Consult the oldest reference you can find that talks about these topics, and it will probably lead you to the original sources. (If you have access to MathSciNet, then it won't be hard to find these sources immediately.) Simultaneous discovery occurs in many branches of intellectual pursuit, not just mathematics and computer science. See Writing Project 11 in Chapter 8 for something along the same lines.

4. The abstraction and difficulty here is part of what makes fractions hard for many children (and some adults) to handle. Be careful to avoid 0 in the denominator! You should be able to figure this out without consulting other sources (especially if you follow the hint), and it is a good Project to work on with other people. One can also define the real numbers in a similar manner, but it is much more subtle. Real analysis textbooks (such as [Ru2],) show you how.

5. See the hints for Writing Project 3. See also the MacTutor page on Hasse.

6. Entire books have been written on security issues in computer systems ([Pf], for one), and it should not be hard to find a chapter or two on the subject in many more general books (try [De1]).

7. Textbooks on project scheduling should be a good source of information (see [Mo], for example). Scheduling is a topic in a branch of mathematics known as Operations Research. It has its own journals, conferences, subspecialties, software, etc.

8. See the suggestions for Writing Project 7.

9. There are hints on the concept of duality in many of the exercise solutions in the Student Solutions Guide. A book on lattice theory (such as [Gr1]) will make the concept more precise.

10. As mentioned in the previous suggestion, you can find entire books on lattice theory. In fact, Mathematical Reviews devotes a whole category (numbered 06) to lattices and other kinds of ordered sets and ordered algebraic structures. Projective geometry is category 51N15, and modular lattices are category 06C.