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Notes Topic Download
1

 

Mathematical Induction

 Well-Ordering Principle

 Introduction to Primes

PDF (new)

2

 

Complete Mathematical Induction

Problem with the Proof that everyone is the same age

Series with Positive Terms: Convergence and Divergence

Composite and Prime Numbers

PDF
3

 

Modular Arithmetic and Introduction to Congruences

Basic Theorems (Congruences)

Fundamental Theorem of Arithmetic

PDF
4

 

More Fundamental Theorem of Arithmetic

Fermat's Little Theorem and Corollary

Wilson's Theorem

Euler's Function

PDF
5

 

Relatively Prime Numbers

Euler's Theorem

Introduction to Rational Numbers

The Proof that Root 2 is Irrational

PDF
6

 

RSA Coding

RSA Coding Example

 

PDF
7

 

The Euclidean Algorithm

 

PDF
8  

Rational and Irrational Numbers

PDF

9

 

Irrational Numbers

Algebraic Numbers

Intermediate Value Theorem

Upper and Lower Bounds

PDF (new)

10

 

Introduction to Real Numbers

Real Number Thorems

Dedekind Cuts

PDF
11  

Complex Numbers

PDF
12

 

Fundamental Theorem of Algebra Proof

Winding Numbers

PDF
13

 

Factor Theorem

Size of Sets (Infinite and Finite)

Introduction to Cardinality

PDF (new)
14

 

Cardinality Part I

PDF (new)
15

 

Cardinality Part II

PDF (new)
16

 

Cardinality Part III

PDF (new)
17

 

Cardinality Part IV

Introduction to Compass and Straight Edge Problems

PDF (new)
18

 

Constructible Numbers

Fields and Surds

PDF
19

 

Proof that one can not trisect an angle of 60

degrees with Compass and Straight Edge

PDF
20

 

Regular Polygons and Constructible Angles

PDF
21

 

More on Constructible Numbers, and Angles

PDF
22  

Cardinality Aside (Very Short Notes )

PDF (new)
23  

Topology Part I

PDF (new)

Set Topology Handout

HTML Format
24  

Toplogy Part II

PDF