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Course: Number Theory

Number Theory

  • Life Time Access
  • Certificate on Completion
  • Access on Android and iOS App
  • Self-Paced
About this Course

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. 

How is the course 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 subject easy to comprehend. More details on certain lessons are delivered through text files to provide more explanation 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 can I learn better? 

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

Basic knowledge
  • Know basic arithmetic operations like +, -, x and ÷ (including long division)
  • Know what is a matrix
What you will 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
Curriculum
Number of Lectures: 62
Total Duration: 08:27:12
Introduction
  • Introduction  
Basics
  • What is Number Theory?  
  • Number Sets  

    In this lecture you will learn the different number sets like: Natural numbers, Integers, Rational numbers, etc...

  • Number Patterns  
  • Even & Odd Numbers  

    In this lecture you will learn what Odd & Even numbers are. 

  • Number Properties  

    In this lecture you will learn number properties like Associativity and Commutativity

  • Proofs  

    In this lecture you will learn importance of proofs, and different types of proofs

Number Bases
  • Number Bases  
  • Binary Base  

    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 Arithmetics  

    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

  • Hexadecimal Base  

    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 Arithmetics  

    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

Factorials
  • Factorial  

    In this lecture you will what Factorial is. 

  • Double Factorial  

    In this lecture you will learn how to find Double Factorials

  • Superfactorial  
  • Exponential Factorial  

    In this lecture you will learn what is Exponential Factorial

  • Factorion  
  • Stirling's Formula  
  • Number of Digits  
Divisibility
  • Divisibility  

    In this lecture you will understand the definition of Divisibility in Mathematics. 

  • Divisibility Rules  
  • Euclidean Division Theorem  

    In this lecture you will learn what Euclidean Division Theorem is. 

  • GCD & LCM  

    In this lecture you will know what Greatest Common Divisor and Least Common Multiple is. 

  • Bézout's Identity  
  • Perfect Numbers  
  • Amicable Numbers  

    In this lecture you will learn what Amicable Numbers are. 

  • Fibonacci Sequence  

    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 Sequence  
  • Golden Ratio  

    In this lecture you will learn what Golden Ratio, Golden Spiral and Golden Angle is. 

Primes
  • Prime Numbers  

    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)  
  • Almost Primes  

    In this lecture you will learn what are Almost prime numbers, Semiprimes, and Brilliant numbers. 

  • Prime Powers  
  • Factorial Prime  
  • Euclid's Theorems  

    In this lecture you will learn Euclid's first and second theorem, on primes. 

  • the Prime Number Theorem  
  • Unsolved Problems  

    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

  • NumberEmpire  
Modular Arithmetics
  • Modular Arithmetics  
  • Congruence  

    In this lecture you will lean what Congruence and Congruence Class is. You will also learn Congruence as an Equivalence Relation

  • Congruence Class  
  • Residue Systems  

    In this lecture you will learn about Residue Classes, Complete Residue Systems, and reduced Residue Systems

  • Quadratic Residues  
  • Module Operations  

    In this lecture you will learn how to do Module Operations. 

  • Inverses  

    In this lecture you will how to do Division in modular arithmetics

  • Modular Exponentiation  
  • Wilson's Theorem  
  • Chines Remainder Theorem  

    In this lecture you will learn what Chines Remainder Theorem is. 

  • Fermat's Little Theorem  

    In this lecture you will learn Fermat's Little Theorem

  • Euler's Totient Function  

    In this lecture you will learn Totives, Cototient, and Euler's Totient Function.

  • Euler-Fermat Theorem  
Continued Fractions
  • Continued Fractions  

    In this lecture you will the definition of Continued Fractions

  • Negative Continued Fractions  

    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 Fractions  

    In this lecture you will learn what Finite Continued Fractions are. 

  • Infinite Continued Fractions  

    In this lecture you will learn what Infinite Continued Fractions are. 

  • Periodic Continued Fractions  

    In this lecture you will learn what Periodic Continued Fractions and Noble Numbers are. 

  • Convergent  

    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

Cryptography
  • Cryptography  

    In this lecture you will learn what Cryptography is. 

  • Early Ciphers  

    In this lecture you will some types of Early Cyphers like Caesar Cipher, and Substitution Cipher


    Caesar Cipher calculator:  https://planetcalc.com/1434/

  • Public Key Cryptography  

    In this lecture you will learn what Public Key Cryptography is. 

  • RSA Encryption  
  • Diffie-Hellman Protocol  
Extras
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