Exam I will be in the usual classroom on Tuesday, February 14, 2006. It will cover the material up through methods of proof, but not the material on sets.

Calculators or other mechanical assistance are not needed and are not to be used. Blank paper will be provided, so all you will need is something to write with.

The exam will have problems similar to those on the homework, and questions related to the lectures. The exam scores in this course are usually very spread out--- some people will do almost all the problems, while many people will miss quite a few (and will still be able to do OK in the course). Just relax and do your best. It should not be difficult to complete the exam in 75 minutes, but as on any exam, it is wise to start with the problems that you feel confident that you know how to do, before moving on to others.

The main topics are basic logic and connectives, quantified statements and their negations, and basic methods of proof. The following will definitely be covered, although the exam not necessarily limited to these topics:

1.	Logic notation, connectives, and tautologies.
2.	Using a truth table to analyze a compound statement or verify a tautology.
3.	Existentially and universally quantified statements, and multiply quantified statements. Converting between quantified statements given in words and in mathematical notation.
4.	Negation of quantified statements.
5.	Proving implications by direct proof.
6.	Proving or disproving quantified statements.
7.	Proof by contradiction: what it is, why it works, using it to prove statements.

One should be familiar with the standard notations ( N, Z, Q, R, C ) that we used for the sets of natural numbers, integers, rational numbers, real numbers, and complex numbers.

You do not need to memorize tautologies, although you should be familiar with the common ones that we used in class such as DeMorgan's laws. It is not important to be able to verify tautologies by manipulating equivalent statements, but you do need to be able to simplify complicated statements involving negation. You do not need to master the ways to deal with proving compound implications such as P => ( Q or R ). Focus on the three basic proof situations ( in 5, 6, and 7 above ), and on how to approach them in examples such as those we did in class and those that appear on the homework. Learn the general model for each kind of argument, and master your own favorite examples so that you will always a clear idea of how the basic kinds of arguments work.

The following do not appear on this exam: interpretation of quantified statements using “truth sets,”, the book's “rules of inference,” “vacuously true” statements, advice on good writing (but please try to use it), fine points that were mentioned only in passing.

Exams from last fall's class can be found on its course page (links to my previous course pages appear on the course pages page). That course had 50-minute classes, so our exam will be somewhat longer. Different classes are different, and the exams will different, but in general it's a good technique to rehearse an exam using others from previous classes. This can reveal the weak points in your knowledge, and make you less stressed on “game day”.