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Number Theory

Name: Number Theory
Rating: 4.6 (324 reviews)

Explore, Learn and Master Fundamental Topics in Number Theory

Highest Rated

Created byMiran Fattah

Last updated 1/2018

English

What you'll learn

Have a thorough understanding of Number Theory.
Know different Numbers, Number Sets, Patterns, and Properties.
Know different Number Bases like Binary and Hexadecimal Base and how to do Arithmetics (+, -, x, ÷) in those bases.
Master Factorials, Double Factorials, Factorions, and many other related topics.
Master Divisibility, Divisibility Rules, Euclidean Division Theorem, and many other topics.
Learn Primes, Prime Powers, Factorial Primes, and Euclid's First Theorem.
Know what Fundamental Theorem of Arithmetic is.
Master Modular Arithmetics.
Learn about Finite, Infinite, and Periodic Continued Fractions.
Explore Public Key Cryptography, Diffie-Hellman Protocol, and RSA Encryption.

Course content

10 sections • 64 lectures • 8h 33m total length

Introduction7:08

What is Number Theory?7:36
Number Sets8:50
In this lecture you will learn the different number sets like: Natural numbers, Integers, Rational numbers, etc...
Number Patterns10:00
Even & Odd Numbers11:05
In this lecture you will learn what Odd & Even numbers are.
Number Properties9:47
In this lecture you will learn number properties like Associativity and Commutativity.
Proofs11:23
In this lecture you will learn importance of proofs, and different types of proofs.
Quiz

Number Bases11:33
Binary Base11:36
In this lecture you will learn what Binary Base is and how you can turn numbers from Decimal Base to Base Tow and back.

Base 10 <--> base 2 converter:

http://www.unitconversion.org/numbers/base-10-to-base-2-conversion.html

Words to base 2 converter:

http://www.unit-conversion.info/texttools/convert-text-to-binary/
Binary Arithmetics15:18
In this lecture, you will learn how to do Addition, Subtraction, Multiplication, and Division in Base 2.
Binary Calculator:
http://www.calculator.net/binary-calculator.html
Quiz
Hexadecimal Base13:13
In this lecture, you will learn what Hexadecimal Numbers are and how to go from base 16 to base 10 and vise versa.
Base 10 <-->16 converter:
http://www.unitconversion.org/numbers/base-10-to-hexadecimals-conversion.html
Hexadecimal Arithmetics14:18
In this lecture you will learn how to do Addition, Subtraction, Multiplication and Division in Base 16.

Hexadecimal Calculator:

http://www.calculator.net/hex-calculator.html?number1=&c2op=%2F&number2=&calctype=op&x=64&y=29
Quiz

Divisibility7:01
In this lecture you will understand the definition of Divisibility in Mathematics.
Divisibility Rules4:21
Euclidean Division Theorem8:26
In this lecture you will learn what Euclidean Division Theorem is.
GCD & LCM10:33
In this lecture you will know what Greatest Common Divisor and Least Common Multiple is.
Bézout's Identity7:41
Quiz
Perfect Numbers3:41
Practical Numbers5:08
In this lecturer you will learn what are Practical numbers, and what it means for a set to be closed under multiplication.
Amicable Numbers3:43
In this lecture you will learn what Amicable Numbers are.
Fibonacci Sequence8:40
In this lecture you learn what Fibonacci Numbers are.

- Short video: https://www.youtube.com/watch?v=4ToUaU4vPks

- Short Documentary: https://www.youtube.com/watch?v=SjSHVDfXHQ4
Tribonacci Sequence5:23
Golden Ratio10:42
In this lecture you will learn what Golden Ratio, Golden Spiral and Golden Angle is.
Quiz

Prime Numbers8:56
In this lecture you will learn the formal definition of Prime numbers, and a lot more.
Link to the website to view Ulam Spiral: https://www.alpertron.com.ar/ULAM.HTM
Fundamental Theorem of Arithmetics (FTA)9:58
Almost Primes7:15
In this lecture you will learn what are Almost prime numbers, Semiprimes, and Brilliant numbers.
Prime Powers1:45
Factorial Prime2:59
Euclid's Theorems8:47
In this lecture you will learn Euclid's first and second theorem, on primes.
the Prime Number Theorem3:48
Quiz
Unsolved Problems6:18
In this lecture you will learn some unsolved prime number problems like the Twin Prime Conjecture, The Goldbach Conjecture and, Legendre's Conjecture.
Here is the link to the documentary on Zhang's life and proof.
https://www.youtube.com/watch?v=XIIyKWxGhEA
NumberEmpire7:26

Modular Arithmetics8:49
Congruence13:07
In this lecture you will lean what Congruence and Congruence Class is. You will also learn Congruence as a Equivalence Relation.
Congruence Class11:33
Residue Systems4:10
In this lecture you will learn about Residue Classes, Complete Residue Systems, and reduced Residue Systems.
Quadratic Residues4:12
Moduler Operations6:10
In this lecture you will learn how to do Module Operations.
Inverses6:58
In this lecture you will how to do Division in modular arithmetics.
Quiz
Modular Exponentiation10:02
Wilson's Theorem5:08
Chines Remainder Theorem9:29
In this lecture you will learn what Chines Remainder Theorem is.
Fermat's Little Theorem4:39
In this lecture you will learn Fermat's Little Theorem.
Euler's Totient Function6:46
In this lecture you will learn Totives, Cototient, and Euler's Totient Function.
Euler-Fermat Theorem3:47
Chapter Quiz

Continued Fractions8:19
In this lecture you will the definition of Continued Fractions.
Negative Continued Fractions10:51
In this lecture you will learn how to find Negative Continued Fractions.
A Continued Fraction Calculator:
http://personal.maths.surrey.ac.uk/ext/R.Knott/Fibonacci/cfCALC.html
Finite Continued Fractions14:05
In this lecture you will learn what Finite Continued Fractions are.
Infinite Continued Fractions16:48
In this lecture you will learn what Infinite Continued Fractions are.
Periodic Continued Fractions9:32
In this lecture you will learn what Periodic Continued Fractions and Noble Numbers are.
Convergent11:57
In this lecture you will learn what Continued Fractions Convergent is and how to find it.

How to find determinant of 2x2 and 3x3 matrices:

https://www.youtube.com/watch?v=OI07C1HsOuc

Matrix Determinant Calculator:
https://matrix.reshish.com/determinant.php
Quiz

Requirements

Know basic arithmetic operations like +, -, x and ÷ (including long division)
Know what is a matrix

Description

WHAT IS THIS COURSE ABOUT?

Welcome to a course on Number Theory, better called “Higher Arithmetics” or “Queen of Mathematics”. This course will guide you and enable you to master fundamental topics in Number Theory.

Number theory is the study of patterns, relationships, and properties of numbers. Studying numbers is a part theoretical and a part experimental, as mathematicians seek to discover fascinating and unexpected mathematical relationships and properties. In this course, you will explore some of those fascinating mathematical relationships and properties and you will learn essential topics that are in the heart of Mathematics, Computer Science, and many other disciplines.

YOU WILL ALSO GET:

Lifetime Access
Q&A section with support
Certificate of completion
30-day money-back guarantee

HOW IS IT DELIVERED?

I know visually seeing a problem getting solved is the easiest and the most direct way for a student to learn so I designed the course keeping this in mind. The materials are delivered mostly through videos to make complex subjects easy to comprehend. More details on certain lessons are delivered through text files to provide more explanations or examples. The course is taught in plain English, away from cloudy, complicated mathematical jargons and that is to help the student learn the material rather than getting stuck with fancy words.

HOW DO I LEARN BETTER?

There are quizzes after each section so you can test your knowledge and see how much of the material has sunk in. I suggest you go through each lesson several times to better understand the content.

Who this course is for:

Mathematics Computer Science, and IT Students
Anyone interested in understanding the fundamentals of Number Theory, aka, Queen of Mathematics.

Number Theory

What you'll learn

Explore related topics

Course content

Introduction1 lecture • 7min

Basics6 lectures • 59min

Number Bases5 lectures • 1hr 6min

Factorials7 lectures • 30min

Divisibility11 lectures • 1hr 15min

Primes9 lectures • 57min

Modular Arithmetics13 lectures • 1hr 35min

Continued Fractions6 lectures • 1hr 12min

Cryptography5 lectures • 48min

Extra1 lecture • 4min

Requirements

Description

Who this course is for: