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.
In this lecture you will learn the different number sets like: Natural numbers, Integers, Rational numbers, etc...
In this lecture you will learn what Odd & Even numbers are.
In this lecture you will learn number properties like Associativity and Commutativity.
In this lecture you will learn importance of proofs, and different types of proofs.
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/
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
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
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
In this lecture you will what Factorial is.
In this lecture you will learn how to find Double Factorials.
In this lecture you will learn what is Exponential Factorial.
In this lecture you will understand the definition of Divisibility in Mathematics.
In this lecture you will learn what Euclidean Division Theorem is.
In this lecture you will know what Greatest Common Divisor and Least Common Multiple is.
In this lecturer you will learn what are Practical numbers, and what it means for a set to be closed under multiplication.
In this lecture you will learn what Amicable Numbers are.
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
In this lecture you will learn what Golden Ratio, Golden Spiral and Golden Angle is.
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
In this lecture you will learn what are Almost prime numbers, Semiprimes, and Brilliant numbers.
In this lecture you will learn Euclid's first and second theorem, on primes.
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
In this lecture you will lean what Congruence and Congruence Class is. You will also learn Congruence as a Equivalence Relation.
In this lecture you will learn about Residue Classes, Complete Residue Systems, and reduced Residue Systems.
In this lecture you will learn how to do Module Operations.
In this lecture you will how to do Division in modular arithmetics.
In this lecture you will learn what Chines Remainder Theorem is.
In this lecture you will learn Fermat's Little Theorem.
In this lecture you will learn Totives, Cototient, and Euler's Totient Function.
In this lecture you will the definition of 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
In this lecture you will learn what Finite Continued Fractions are.
In this lecture you will learn what Infinite Continued Fractions are.
In this lecture you will learn what Periodic Continued Fractions and Noble Numbers are.
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
In this lecture you will learn what Cryptography is.
In this lecture you will some types of Early Cyphers like Caesar Cipher, and Substitution Cipher.
Caesar Cipher calculator: https://planetcalc.com/1434/
In this lecture you will learn what Public Key Cryptography is.
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.