[...] The story suggest that assertions, or simply Boolean expressions, are really needed in programming. But it is not enough to know how to write Boolean expressions; one needs to know how to reason with them, how to simplify them, to prove that one follows from another, and to prove that one is not true in some state, and so forth. And, later on, we will see that it is necessary a kind of assertion that it is not part of the usual Boolean expression language of Pascal, PL/1 or FORTRAN, the "quantified" assertion. [...] More importantly, the study of program correctness proofs has led to the discovery and elucidation of methods for developing programs. Basically one attempts to develop a program and its proofs hand-in-hand, with the proof ideas leading the way! If the methods are practiced with care, they can lead to programs that are free of errors, that take less time to develop and debug, and that are much more easily understood (by those who have studied the subject).

David Gries: The Science of Programming. Part O:
Why Use Logic? Why Prove Programs Correct?

• Reminder: Final Exam, Wednesday, March 14, 2001, 9:00-11:00am in Tech L150. It will cover the whole syllabus. You may use the posted "Notes on Discrete Mathematics" and your personal class notes during the exam.

• About homework:

  • As you know, homework is assigned weekly and will be collected and graded by the TA. After being graded I will return it to you in class. If you cannot pick it up in class, you can do it at a later date in the TA office.

  • Note that the volume of homework to be graded may exceed the teaching duties of the TA. In that case only part of the problems or questions assigned will be graded.

725-310-0 Mathematical Foundations of Computer Science

Basic concepts of finite and structural mathematics. Sets, axiomatic systems, the propositional and predicate calculi, and graph theory. Application to computer science: sequential machines, formal grammars, and software design. Prerequisites: 725-A10 or 725-A11 and 435-B14-3. Prerequisite for: 725-C22, 725-C32, 725-C39, 725-C43, 725-C51.