Master Number Theory 2020: The Secrets Of Numbers

Name: Master Number Theory 2020: The Secrets Of Numbers
Rating: 4.2 (283 reviews)

Learn The Secrets Of The Integers And Prime Numbers And Gain A New Perspective On Mathematics

Created byKody Amour

Last updated 6/2020

English

What you'll learn

Learn about Prime Numbers
Understand Factorization at an Advanced Level
Introduce the Algebra of Congruences
Look into Diophantine Equations
Understand Primitive Roots
Understand Quadratic Reciprocity Theorem

Course content

3 sections • 51 lectures • 7h 24m total length

Introduction Video1:05

Introduction6:47
In this introduction, I introduce myself and give a little information about the course. Again, my email is kdamours@asu.edu and you can email me for any math questions at any time.
Basic Notation13:17
This lecture covers all of the needed material that will be used in Number Theory. By watching this video, you will have all of the tools to understand what is happening in this course.
Introductory Notations, Definitions and Axioms
Induction13:38
Induction is a tool that will be used in a couple of lectures throughout number theory, and so it is important to understand this method of proving in order to understand Lecture 4 and maybe other math courses as well.
Induction Quiz
Open Problems In Number Theory1:43:00
Don't doubt yourself! Most elementary number theory problems are solved by students who have never done research before. Find a problem on this pdf or any website that has open number theory problems, and start trying them!

Fibonacci Sequence17:56
Fibonacci
Divisibility9:59
This lecture introduces a new perspective on the integers and how numbers relate to each other by division.
Chapter 1 Homework1:00
Division Algorithm15:34
In this lecture, we prove the division algorithm which is essentially long division, but with a more precise approach.
Divisibility and Division Algorithm
Prime Numbers6:19
We will discuss in full detail everything about prime numbers and their properties.
Greatest Common Divisors16:16
The greatest common divisor has many important properties that will be used later on. In this lecture, we introduce these properties.
Chapter 3 Homework1:00
The Euclidean Algorithm9:42
The Euclidean Algorithm is one of the fastest methods of calculating the gcd of any two numbers. This algorithm will be explained in it's entirety.
The Fundamental Theorem of Arithmetic8:41
The Fundamental Theorem of Arithmetic says that any number can be factored into prime numbers. Though the message is simple, the proof is involved and we will go through it completely.
Factorization Methods17:20
Factorization has been a very tricky process for hundreds of years, and mathematicians still don't have a grasp on it. We will describe some basic methods of factoring quickly and we will describe some of the fastest methods known to date.
Can You Factor Numbers?
Congruences Part 119:33
In this lecture, we introduce a new type of algebra.
Congruences Part 27:26
This is a continuation of the last lecture.
Linear Congruences Part 18:14
Now, we will attempt to solve some algebraic systems in this new algebra.
Linear Congruences Part 214:13
This is a continuation of the last lecture.
Linear Congruences Part 38:40
This is a continuation of the last lecture.
Extended Euclidean Algorithm13:30
In this lecture, we go back to the extended euclidean algorithm, and make an additional step that will allow us to know more information about the gcd. We will use this to find multiplicative inverses.
Solving Congruences5:01
We will go through some examples of algebraic systems and solve them using the tools that we had learned.
Chinese Remainder Theorem Part 114:10
In this lecture, we introduce the importance of the Chinese Remainder Theorem.
Chinese Remainder Theorem Part 218:01
In this lecture, we introduce the Chinese Remainder Theorem.
Chinese Remainder Theorem Part 38:51
This is a continuation of the last lecture.
Solving Polynomial Congruences8:23
In this lecture, we use the knowledge of solving linear congruences and the Chinese Remainder Theorem to solve polynomial congruences.
Chapter 4 Homework1:00
Test Your Congruence Skills
Test 11:00
You have 75 minutes to complete this test.
Wilson's Theorem17:51
In this lecture, we introduce Wilson's Theorem, and prove it in two different ways.
Fermat's Little Theorem12:56
In this lecture, we state and prove Fermat's Little Theorem and use it to prove Wilson's Theorem one more time.
Psuedoprimes6:43
Psuedoprimes are numbers that act like prime numbers, but they are not. We try to characterize these numbers.
Euler's Generalization of Fermat's Little Theorem13:57
In this lecture, we give a generalization of Fermat's Little Theorem.
Successive Squaring16:56
In this lecture, we learn how to compute exponentiation very quickly.
Euler's Theorem and Successive Squaring Review
Chapter 6 Homework1:00
Order7:39
We will introduce Order a little soon because it relates so much to Euler's Theorem.
The Euler-Phi Function Part 116:13
In this lecture, we investigate everything about the totient function.
Euler-Phi Function Part 25:58
This is a continuation of the last lecture.
Other Multiplicative Functions12:54
In this lecture, we take a look at a few more multiplicative functions like sigma and tow.
Perfect Numbers and Mersenne Primes6:31
Here, we look at types of numbers that hold many unique properties and reveal many modern open problems in number theory.
Chapter 7 Homework1:00
Cryptography7:34
In this lecture, I introduce security and what it has to do with number theory (hint: the answer is everything).
Primitive Roots13:20
Here, we find numbers that have an order equal to the totient function, and why they are so important.
Chapter 9 Homework1:00
Quadratic (Non)residues13:26
In this lecture, we characterize perfect squares and how some numbers like 2 can sometimes be perfect squares.
The Law of Quadratic Reciprocity9:21
In this lecture, we introduce all of the properties of quadratic (non)residues.
Continued Fractions9:10
In this lecture, we bring back a very old concept called continued fractions which haven't been touched since the 19th century.
Chapter 11 Homework1:00
Pythagorean Triples9:14
In this lecture, we discuss very modern number theory pertaining to right triangles and we discuss Fermat's Last Theorem.
Chapter 13 Homework1:00
Final Quiz
Test 21:00
You have 75 minutes to complete this test.
Conclusion2:06
You have finally completed number theory in its entirety! Congrats.

Requirements

Algebra 1
NO CALCULUS NEEDED!

Description

For thousands of years, mathematicians have been curious about numbers. Where did they come from? What properties do they have? The truth is that you will never learn the secrets of numbers until you take Number Theory, and all you need is a curious mind to understand (no prerequisites to this course!). One of the biggest problems in history has been: how do you factor a number into prime factors? Well, 26=13*2, but try factoring 1432479... Not so easy now? What if I asked what the next prime number was after 1432479 is? These are tough questions and their answers involve a different type of math - one that you don't need calculus for - but you need a lot of curiosity.

In this course, you will look into the secrets of the integers and the many properties that they hold. You do not need Calculus or any advanced mathematics to understand this course, however this is an advanced mathematics course. The material will not involve "solve for..." problems. This course is designed to prove things, and so most of the lectures will cover proofs, and not problem solving. This is a great introduction to what pure mathematics actually deals with, and what many modern professors research.

Learn and Master Arithmetic, Prime Numbers and Factorization

Solving Diophantine Equations
Quadratic Reciprocity Theorems and Legendre Symbol
Continued Fractions
Primitive Roots
Extended Euclidean Algorithm
Advanced Modern Factorization
Algebra of Prime Numbers
Pythagorean Triples

See the Algebra of Modern Mathematics

This is not just a basic math course. This course offers over 7 hours of content that will blow your mind. You will learn more material than most Universities offer in their own Number Theory courses. We go into depth on everything with clear examples that helps you understand.

How in depth do we go? Take for example the proof of Wilson's Theorem. We will prove it Once, Twice, Three times each in a different way. And that's just one theorem in this course.

So what are you waiting for?

Who this course is for:

College Students interested in Mathematics
Any student interested in modern Mathematics
Students in a Number Theory College Course
Students who have taken a Number Theory College Course

Master Number Theory 2020: The Secrets Of Numbers

What you'll learn

Explore related topics

Course content

Introduction Video1 lecture • 1min

Introduction to Number Theory4 lectures • 2hr 17min

Number Theory46 lectures • 7hr

Requirements

Description

Who this course is for: