Chapter 4
Truth Tables
4.1
Objectives
The technique objectives are:
1. Definenot,and,or,implies andifandonlyif using truth tables.
2. Evaluate logical expressions using truth tables.
3. Use truth tables to establish the equivalence of logical expressions
Chapter 2
Our First Proof
2.1
Objectives
The technique objectives are:
1. Definestatement,hypothesis,conclusion andimplication.
2. Learn how to structure the analysis of a proof.
3. Carry out the analysis of a proof.
The content objectives are:
1. Defined
Chapter 5
Introduction to Sets
5.1
Objectives
The technique objectives are:
1. Define and gain experience withset,element,setbuildernotation,definingproperty,
subset,superset,equalityofsets,emptyset,universalset,complement,cardinality, union,
intersection
Chapter 1
In the beginning
1.1
What Makes a Mathematician a Mathematician?
Welcome to MATH 135!
Let me begin with a question. What makes a mathematician a mathematician?
Many people would answer that someone who works with numbers is a mathematician.
But
Chapter 10
Simple Induction
10.1
Objectives
The technique objectives are:
1. Learn how to use sum and product notation, and recognize recurrence relations.
2. Learn how to useSimpleInduction.
10.2
Notation
A number of examples we will discuss use sum, pro
Chapter 6
More on Sets
6.1
Objectives
The technique objectives are:
1. To gain more experience working with sets.
6.2
Showing Two Sets Are Equal
Let's take a look at two proofs of the same statement about sets. The first uses a chain of if and only
if sta
Chapter 8
Nested Quantifiers
8.1
Objectives
The technique objectives are:
1. Recognizenestedquantifiers.
2. Learn how to parse nested quantifiers.
3. Learn which techniques to apply to a sentence containing nested quantifiers.
The content objectives are:
Chapter 9
Practice, Practice, Practice:
Quantifiers and Sets
9.1
Objectives
This class provides an opportunity to practice working with quantifiers and sets.
9.2
Example 1
Worked Examples
For each of the following definitions, identify each quantifier, it
Chapter 7
Quantifiers
7.1
Objectives
The technique objectives are:
1. Learn the basic structure of quantifiers.
2. Learn how to use the Object, Construct and Select Methods.
7.2
Quantifiers
Not all mathematical statements are obviously in the form "IfA, t
Chapter 3
Discovering Proofs
3.1
Objectives
The technique objectives are:
1. Discover a proof using the Direct Proof technique.
2. Write a proof.
3. Read a proof.
The content objectives are:
1. Prove theDivisibilityofIntegerCombinations.
2. Prove theBound