FA19:Prelim 1 guide
Prelim 1 will cover material all material covered in lecture and the homework up to and including material covered on Wednesday 9/25. Material that you've had homework and discussion problems on will be stressed more heavily. The exam will be closed book, closed notes, and will be 90 minutes long.
Update: here are the board notes from review session 1. Video for most of the review session can be found here; unfortunately I had a malfunction part way through, so the video is incomplete. A student (Ryan Tremblay, thanks!) has provided a complete audio recording, which you can find here.
Here is a brief summary of what we've covered; for an exhaustive list see the Main Page.
- Proof techniques
- be able to write good proofs. Know how to use and prove various kinds of propositions
- Be able to do the proofs we've done in lecture or on the homework (here is a list of all claims on the wiki; of course this includes things we haven't proved yet, you you can still see how the proof techniques are being used)
- Be able to find the logical negation of a proposition
- Be able to write a proof by contradiction.
- Understand diagonalization proofs.
- Know and be able to apply definitions (both formal and informal):
- Set definitions: union, intersection, power set, cartesian product, empty set, .
- Functions: function, partial function, left inverse, right inverse, two-sided inverse, injectivity, surjectivity, and bijectivity , , , countable
- Relations: relation, reflexive, symmetric, transitive. These three properties together make a binary relation into an equivalence relation. We will give more examples of relations with these properties (and study the properties) on Friday's lecture. However, all you need to know for the exam are the definitions.