Number Theory
4.3 (8 ratings)
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Number Theory

Explore, Learn and Master Fundamental Topics in Number Theory
4.3 (8 ratings)
Instead of using a simple lifetime average, Udemy calculates a course's star rating by considering a number of different factors such as the number of ratings, the age of ratings, and the likelihood of fraudulent ratings.
106 students enrolled
Created by Miran Fattah
Last updated 4/2017
English
Curiosity Sale
Current price: $10 Original price: $80 Discount: 88% off
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Includes:
  • 8.5 hours on-demand video
  • 2 Supplemental Resources
  • Full lifetime access
  • Access on mobile and TV
  • Certificate of Completion
What Will I 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.
View Curriculum
Requirements
  • Know basic arithmetic operations like +, -, x and ÷ (including long division)
  • Know what is a matrix
Description

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.

Who is the target audience?
  • Mathematics Computer Science, and IT Students
  • Anyone interested in understanding the fundamentals of Number Theory, aka, Queen of Mathematics.
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Curriculum For This Course
64 Lectures
08:33:34
+
Introduction
1 Lecture 07:08
+
Basics
6 Lectures 58:41

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

Number Sets
08:50

Number Patterns
10:00

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

Even & Odd Numbers
11:05

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

Number Properties
09:47

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

Proofs
11:23

Quiz
7 questions
+
Number Bases
5 Lectures 01:05:58
Number Bases
11:33

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 Base
11:36

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

Binary Arithmetics
15:18

Quiz
13 questions

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 Base
13:13

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

Hexadecimal Arithmetics
14:18

Quiz
13 questions
+
Factorials
7 Lectures 30:21

In this lecture you will what Factorial is. 

Factorial
05:01

In this lecture you will learn how to find Double Factorials

Double Factorial
08:47

Superfactorial
02:32

In this lecture you will learn what is Exponential Factorial

Exponential Factorial
02:42

Factorion
05:22

Stirling's Formula
03:20

Number of Digits
02:37

Quiz
13 questions
+
Divisibility
11 Lectures 01:15:19

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

Divisibility
07:01

Divisibility Rules
04:21

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

Euclidean Division Theorem
08:26

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

GCD & LCM
10:33

Bézout's Identity
07:41

Quiz
16 questions

Perfect Numbers
03:41

In this lecturer you will learn what are Practical numbers, and what it means for a set to be closed under multiplication

Practical Numbers
05:08

In this lecture you will learn what Amicable Numbers are. 

Amicable Numbers
03:43

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

Fibonacci Sequence
08:40

Tribonacci Sequence
05:23

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

Golden Ratio
10:42

Quiz
5 questions
+
Primes
9 Lectures 57:12

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

Prime Numbers
08:56

Fundamental Theorem of Arithmetics (FTA)
09:58

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

Almost Primes
07:15

Prime Powers
01:45

Factorial Prime
02:59

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

Euclid's Theorems
08:47

the Prime Number Theorem
03:48

Quiz
15 questions

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

Unsolved Problems
06:18

NumberEmpire
07:26
+
Modular Arithmetics
13 Lectures 01:34:50
Modular Arithmetics
08:49

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

Congruence
13:07

Congruence Class
11:33

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

Residue Systems
04:10

Quadratic Residues
04:12

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

Module Operations
06:10

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

Inverses
06:58

Quiz
16 questions

Modular Exponentiation
10:02

Wilson's Theorem
05:08

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

Chines Remainder Theorem
09:29

In this lecture you will learn Fermat's Little Theorem

Fermat's Little Theorem
04:39

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

Euler's Totient Function
06:46

Euler-Fermat Theorem
03:47

Chapter Quiz
7 questions
+
Continued Fractions
6 Lectures 01:11:32

In this lecture you will the definition of Continued Fractions

Continued Fractions
08:19

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


Negative Continued Fractions
10:51

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

Finite Continued Fractions
14:05

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

Infinite Continued Fractions
16:48

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

Periodic Continued Fractions
09:32

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

Convergent
11:57

Quiz
8 questions
+
Cryptography
5 Lectures 47:55

In this lecture you will learn what Cryptography is. 

Cryptography
08:45

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

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

Early Ciphers
11:18

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

Public Key Cryptography
12:32

RSA Encryption
10:52

Diffie-Hellman Protocol
04:28

Quiz
6 questions
+
Extra
1 Lecture 04:38
Bonus Lecture
04:38
About the Instructor
Miran Fattah
4.4 Average rating
528 Reviews
6,241 Students
7 Courses
B.S. in Mathematics & Geophysics

Fattah has B.S. in Mathematics and Geophysics from theUniversity of Oklahoma in Oklahoma, USA. He has taught and tutored many college students both in the United States and Iraq. His love for teaching made him one of four students in Iraq to receive a full scholarship to pursue a B.S. degree in the States so to return back to his home country and teach. 

He is passionate about Math & Science and loves to share his passion with others. To him, Mathematics and Sciences are crucial for everyone to learn no matter how little. He is a BIG believer in visual learning, and his aim is to deliver the concepts in an easy and direct way so as to make the learning process fast for everyone.