Page 660 - Discrete Mathematics and Its Applications

Writing Projects 639

Writing Projects

Respond to these with essays using outside sources.

1. Discuss the concept of a fuzzy relation. How are fuzzy 5. Explain how Helmut Hasse used what we now call Hasse
relations used? diagrams.
2. Describe the basic principles of relational databases, go- 6. Describe some of the mechanisms used to enforce infor-
ing beyond what was covered in Section 9.2. How widely mation flow policies in computer operating systems.
used are relational databases as compared with other types 7. Discuss the use of the Program Evaluation and Review
of databases? Technique (PERT) to schedule the tasks of a large com-
3. Look up the original papers by Warshall and by Roy (in plicated project. How widely is PERT used?
French) in which they develop algorithms for finding tran- 8. Discuss the use of the Critical Path Method (CPM) to find
sitive closures. Discuss their approaches. Why do you the shortest time for the completion of a project. How
suppose that what we call Warshall’s algorithm was dis- widely is CPM used?
covered independently by more than one person? 9. Discuss the concept of duality in a lattice. Explain how
4. Describe how equivalence classes can be used to define duality can be used to establish new results.
the rational numbers as classes of pairs of integers and 10. Explain what is meant by a modular lattice. Describe
how the basic arithmetic operations on rational numbers some of the properties of modular lattices and describe
can be defined following this approach. (See Exercise 40 how modular lattices arise in the study of projective ge-
in Section 9.5.) ometry.