Best Number Theory Online Courses

## #1 Number Theory and The Secrets of Numbers

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.

## #2 Number Theory

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

## #3 Number Theory for Programmers

The main goal of this course is to teach the basics of Number Theory and how values are represented in the memory of computer. This is very basic knowledge that any programmer/ Computer Science student must posses. This course is to help all those aspiring programmers to build their sound fundamentals with Number Theory.

You will learn:

**Basic concept of Number Theory.****Standard number systems – Octal, Hexadecimal, Binary.****How to convert number from any of these system to decimal and vice versa.****1s and 2s complement technique. Negative number representation using 2s complement technique.****How subtraction is done using 2s complement in the memory.****Real number representation using IEEE 754 standard (Single and Double precision).**

*Please do not enrol if you are:*

**Not interested of doing basic math calculations using pen and paper.****Expecting representations using graphics and animation, I did all the writings on the whiteboard. They are really easy to understand.**

Feel free to ask questions in the Q/A section, you will find me always with you during the learning process.

Happy learning!

## Best Number Theory Books:

#1 Number Theory (Dover Books on Mathematics) by George E. Andrews

#2 Elementary Number Theory 7th Edition by David Burton

#3 An Introduction to the Theory of Numbers 6th Edition by G. H. Hardy & Edward M. Wright & Andrew Wiles

#4 An Introduction to the Theory of Numbers 6th Edition by G. H. Hardy & Edward M. Wright & Andrew Wiles

#5 Friendly Introduction to Number Theory, A (Classic Version) (4th Edition) (Pearson Modern Classics for Advanced Mathematics Series) 4th Edition by Joseph Silverman

#6 Number Theory: A Lively Introduction with Proofs, Applications, and Stories 1st Edition

by James Pommersheim & Tim Marks & Erica Flapan