Week 8
Mathematical Induction
Read the material below. Then study the introductory material section 5.1 of the text
up to the examples. Study the procedures outlined in the examples 1 through 3 and then
try to follow the examples 8 and 10. Next do the ass

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Week 11
An Introduction to the Concept of Relations
Think of your family tree. It consists of your brothers, sisters, cousins, second cousins,
aunts, uncles, parents, grandparents, great grandparents etc. On this set of relatives there
is defined

Week 7 Solving Systems of Equations Using Matrices and
Network Analysis
This week is quite lengthy and has several parts. For now, I ask you to concentrate on parts 1
and 2. If we have time we will cover part 3.
A large number of applications can be model

Part 2: Systems of Equations Which Do Not Have A Unique Solution
On the previous pages we learned how to solve systems of equations using Gaussian
elimination. In each of the examples and exercises of part 1(except for exercise 1 parts d and e)
the system

Closures of Relations
Composition of Relations Revisited
Recall in the text the matrix of the relation S D R is written as MS D R and
MS D R = MR : MS. The purpose of the following example is to remind you of the process
and to reaffirm why it is necessar

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Week 10
Permutations, Combinations and the Binomial Coefficient
The first part of section 6.3 in the text is on permutations. You may recall that back in
week 2 I asked you to do exercise 25 of this section using the Rule of Products. I
wanted to

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Week 6
Sequences and Summations
Read section 2.4 through example 15. Exercise 19 is particularly interesting. Can you do it?
Definition: A sequence is a function from the set of positive integers cfw_1, 2, 3, . . . or from the set of
nonnegative

For the first part of week 4 please continue your study of proofs.
Sets:
You can think of Section 2.1 as a combination of notation and concepts.
Examples of notation are such items as the notation for the set of integers, the notation
for is an element of

Week 3: Quantifiers and Methods of Proof
Section 1.4 Predicates and Quantifiers
Assume that the universe of discourse is all the people who are participating in
this course. Also, let us assume that we know each person in the course. Consider the
followin

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Basic Counting TechniquesThe Rule of Products
WHAT IS COMBINATORICS?
One of the first concepts our parents taught us was the "art of counting." We were taught
to raise three fingers to indicate that we were three years old. The question of "how
m

The Row Reduction Method for Determining the Inverse of a Matrix
(This is extra material we will cover it only if time permits)
In week 5 in the notes we defined the inverse of an n x n matrix. We noted that not all
matrices have inverses, but when the in

Week 5: Functions
Before you read the text on function and try the assigned exercises read the material
below. I have developed most of the key ideas of functions and developed several
examples which I hope you find useful.
Introductory Remarks
When you f

Copyright 1996 (Previously in 1986 and 1994). These notes are for the exclusive use of
Prof. Alan Doerrs classes and may not be used and/or reproduced in any form or by any
means, without permission in writing from Prof. Alan Doerr.
Week 1: Introduction a

Week 2 Propositional Equivalences and an Introduction to the Product Rule
In table 1 below I summarize our discussions of lecture 1 and repeat table 2 for readability.
Table 1: Similarities Between Algebras
Objects
Binary
Operations
Unary Operations
Other