Last time we talked about sets, and introduced notation and formalisms for defining and manipulating sets. Now we
talk about ways mapping from one set to other. This is done through talk of "functions".
Writing the statement:
f: A -> B
Functions reprise and counting very very big sets!
First, one more set construction tool. the cartesian product.
way of constructing more complicated elements.
Last time we talked about functions as mappings from one set (usually
A) to another set (often
Sequences, Series and Such + intro to counting
So lets talk about sequences of numbers. Today's numbers are going to
be about exercising camels. Suppose you have a pyramid. It has
stairs. You are leading a camel up the stairs. It is a big camel, it
Propositions, Equivalence and Rules of Inference
We remind ourself about propositional equivalence:
First, one rule:
a -> b
~b -> ~a
~b -> ~a
~b v ~a
b v ~a
~a v b
First, why do we care about proofs?! Two reasons, (1) As a well educated person, you should know what a proof is,
and understand why mathematicians think their field is more concrete than those that deal with the falsifiable theories
Program Correctness, 2nd half of second lecture.
Consider the following program for selection sort:
pre: A is an array of n elements with no duplicates
post: forall i from 1.n-1, A[i]<=" font=">
while i *less than* n
i = i+1
Negations of quantified statements.
Last time we started with a few proofs, and we, in passing, discussed a few proof strategies. Let's explore proof
strategies more explicitly.
1. In a direct proof of a conditional state
Lecture Notes, Intro, Logic, Propositions, Connectives, Truth Tables.
This class is about Logic and Discrete Mathematics.
Discrete Mathematics deals with math on finite sets, no sin curves, or integrals, but rather with properties of integers
Goals: Use our logic basis to define Sets, Power Sets, and Recursively Defined Sets
First, we've talked about sets. We used them to define the meaning of quantifiers. But let's, for a moment, be a little bit
A set is a collection of elem