Topics for the midterm
(Also read the sections in the book on these topics.)

I) Propositional Logic

Truth Tables
Going from a Boolean Formula to a Truth Table.
Going from a Truth Table to a Boolean Formula
Going from a Boolean Formula to a Circuit
Circuits for arithmetic Operations
Half Adders and Full Adders

II) Predicate Logic

Quantifiers
Domains
Expressing Mathematics in terms of logic
Simple proves (e.g., to show that a EXISTS x is true, give me an x)

III) Number Theory
Mods (Elt. Crypto, equations that have more roots than they should)
Proving numbers irrational using both mods and Unique Factorization Theorem
Proving primes infinite

IV) Induction
Weak Induction (thats the P(0) and P(n)-->P(n+1))
Strong Induction
Constructive Induction

V) Combinatorics
Permutations
Combinations
Pigeon hole principle

VI) Probability
Bayes Theorem
Poker
Birthday paradox, Hat Check Problem, Loaded dice.

VII) Countability and Uncountability
N,Q,Z contable
A,B countable --> A x B countable
A_1,A_2,... countable --> A1 UNION A2 UNION ... countable
{0,1}^omega, R, RxR, all uncountable and the same size.

VIII) (Notation that we've covered in bits and pieces so this is not chronological)

Sets- cross produces, power set

Relations- Trans, Symm, Ref, all combinations

Functions- Injective, surjective, bijective