CS 381 - Introduction to Theory of Computing, Summer 2005

Interesting and informative sites

Books on reserve

In addition to the course text, you may find the following books useful. They are available on reserve in the Engineering Library, Carpenter Hall. (The course textbook itself is also available there).

On writing good proofs

Here are my own guidelines for writing clear and easy-to-understand formal proofs in 381, and beyond.

And here are some further words of advice, adapted from Dexter Kozen.

The ability to deal with abstraction is the most important intellectual skill any computer scientist can have. It requires the ability to think clearly, to formulate precise definitions, and to reason logically in terms of those definitions. Do not worry if you have had only limited experience with this; you will gain plenty of experience in this course. One of our chief purposes is to cultivate this skill.

Accordingly, we will hold you to a high standard of rigor in the presentation of your homework solutions. When justifying an answer, you do not need to be overly verbose; just make sure your argument is logically sound from start to finish and that you include enough information so that we can follow all the steps in your reasoning. For instance, including step-by-step justifications such as "by the definition of ..." is a very good idea. Such explanations are brief, but still demonstrate that your solution is based on a solid understanding.

You should take as much care composing your solutions as you would composing an essay for an English course. A common mistake is to write down a sequence of statements without making clear the chain of thought connecting them. An isolated statement can be an assumption, a conclusion, a definition, or a proof goal; it is often difficult to determine which was meant. Even if familiarity with the solution enables us to infer your intended meaning, you will still lose points if your presentation is not sufficiently clear.

Here are some tips to avoid these problems:

Students often ask whether "show" means the same thing as "prove". The answer is yes. So do "demonstrate", "argue", and half a dozen other synonyms. Unless otherwise noted, all these expressions mean "prove formally".