SP20:Prelim 1 guide
Prelim 1 will cover material all material covered in lecture and the homework up to and including material covered on Friday 2/28. 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.
- 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 proof by contradiction.
- Understand diagonalization proofs.
- Be comfortable with proofs by weak induction and strong induction
- 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, equivalence relation, equivalence class, A/R, well-defined functions from A/R. (Note: these will be covered Monday and Wednesday in lecture).
- Know and be able to apply basic results