Notes for Recitation 4
1 Strong Induction
Recall the principle of strong induction:
Principle of Strong Induction. Let P (n) be a predicate. If
P (0) is true, and
for all n N, P (0) P (1) . . . P (n) implies P (n + 1),
then P (n) is true for all n N.
As

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2016-04-24, 9:16 PM
Your Project Title
This heading is written in a Title cell and the title is centred using the Alignment menu.
My Name
This heading is written in a Subtitle cell and the subtitle is centred using the Alignment menu.
I suggest t

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2016-04-24, 9:16 PM
Concordia University
Mast 232 - Mathematics with Computer Algebra
2016 Fred E Szabo
Course Outline
This course is based on the following components: ten lectures, one assignment per lecture,
one reflection per lecture, two onl

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2016-04-24, 9:20 PM
Concordia University
Mast 232 - Mathematics with Computer Algebra
2016 Fred E Szabo
Source: Learning with Mathematica, by Fred E Szabo
Lecture 6 - Matrix equations
Linear systems
A linear system is a list (ordered set) of line

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2016-04-24, 9:19 PM
Concordia University
Mast 232 - Mathematics with Computer Algebra
2016 Fred E Szabo
Source: Learning with Mathematica, by Fred E Szabo
Lecture 5 - Polynomials and power series
Polynomials in one or more matrices are among the

Untitled
2016-04-24, 9:19 PM
Concordia University
Mast 232 - Mathematics with Computer Algebra
2016 Fred E Szabo
Source: Learning with Mathematica, by Fred E Szabo
Lecture 4 - Curves and surfaces
https:/moodle.concordia.ca/moodle/pluginfile.php/2177568/mo

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2016-04-24, 9:18 PM
Concordia University
Mast 232 - Mathematics with Computer Algebra
2016 Fred E Szabo
Source: Learning with Mathematica, by Fred E Szabo
Week 1 - INTRODUCTION TO MATHEMATICA
Topics
Arithmetic
Arithmetic of lists
Building lists
T

W2016-Lecture Notes-Week 2 Freeform
2016-04-24, 9:18 PM
Concordia University
Mast 232 - Mathematics with Computer Algebra
2016 Fred E Szabo
Source: Learning with Mathematica, by Fred E Szabo
Week 2 - Free-form Input and Wolfram Alpha Queries
Note: Assignm

Lecture 7 Matrix Decompositions
2016-04-24, 9:21 PM
Concordia University
Mast 232 - Mathematics with Computer Algebra
2016 Fred E Szabo
Source: Learning with Mathematica, by Fred E Szabo
Lecture 7 - Matrix decomposition
Matrix decomposition (also called m

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2016-04-24, 9:21 PM
Concordia University
Mast 232 - Mathematics with Computer Algebra
Quiz 2 - Topics to review
Quiz 1 will be a one-hour in-class quiz worth 15% of your final mark.
The quiz will consist of 6 questions of equal value and cover th

Notes for Recitation 9
1 Bipartite Graphs
Graphs that are 2-colorable are important enough to merit a special name; they are called
bipartite graphs. Suppose that G is bipartite. Then we can color every vertex in G ei
ther black or white so that adjacent

Notes for Recitation 7
1 RSA
In 1977, Ronald Rivest, Adi Shamir, and Leonard Adleman proposed a highly secure cryp
tosystem (called RSA) based on number theory. Despite decades of attack, no signicant
weakness has been found. (Well, none that you and me w

Notes for Recitation 8
1 Graphs and Trees
The following two denitions of a tree are equivalent.
Denition 1: A tree is an acyclic graph of n vertices that has n 1 edges.
Denition 2: A tree is a connected graph such that u, v V , there is a unique path
conn

Notes for Recitation 11
1 The Quest
An explorer is trying to reach the Holy Grail, which she believes is located in a desert
shrine d days walk from the nearest oasis. In the desert heat, the explorer must drink
continuously. She can carry at most 1 gallo

Notes for Recitation 5
1 Wellordering principle
Every nonempty set of natural numbers has a minimum element.
Do you believe this statement? Seems obvious, right? Well, it is. But dont fail to realize
how tight it is. Crucially, it talks about a nonempty s

Notes for Recitation 6
1 The Pulverizer
We saw in lecture that the greatest common divisor (GCD) of two numbers can be written
as a linear combination of them.1 That is, no matter which pair of integers a and b we are
given, there is always a pair of inte

Notes for Recitation 1
1 Logic
A proposition is a statement that is either true or false. Propositions can be joined by
and, or, not, implies, or if and only if. For each of these connective, the deni
tion and notational shorthand are given in the table b

Notes for Recitation 3
1 Induction
Recall the principle of induction:
Principle of Induction. Let P (n) be a predicate. If
P (0) is true, and
for all n N, P (n) implies P (n + 1),
then P (n) is true for all n N.
As an example, lets try to nd a simple ex

Notes for Recitation 2
1 Case Analysis
The proof of a statement can sometimes be broken down into several cases, which then
can be tackled individually.
1.1
The Method
In order to prove a proposition P using case analysis:
Write, We use case analysis.

Notes for Recitation 12
1 Solving linear recurrences
Guessing a particular solution. Recall that a general linear recurrence has the form:
f (n) = a1 f (n 1) + a2 f (n 2) + + ad f (n d) + g(n)
As explained in lecture, one step in solving this recurrence i

Project Structure
2016-04-24, 9:22 PM
Project Cell Types
Fred E Szabo
Some comments on the intended use of the sample projects
The structure of your project should be based on the available cell types in the default style of
Mathematica notebooks. The ava