Number Theory Fundamentals

Learn the theory and problem solving techniques required for Number Theory

What you’ll learn
Learn the basic of Number Theory.
Understand the standard theorems and lemmas.
Learn problem solving techniques for Number theory in Olympiads
Practice lots of problems.

Requirements
No pre-requisites needed.

Description
Learn the basic concepts in Number theory through a set of guided problem-solving sessions. We cover all the theory required for National and International Math Contests. The course covers the standard curriculum of Divisibility problems, congruences, modulo arithmetic, prime numbers, arithmetic functions and even the Quadratic Reciprocity Law. You will also find lots of contest problems to help you develop a better understanding of these ideas. The course is divided into two sections – Theory and Problem-solving lectures. You can do them in a sequence or you can switch between the two sections and get your hands dirty with some problems. I will be adding more problem-solving videos to the course as students join in. Feel free to reach out to me on Udemy in case you need help with a particular topic and I will be happy to add more content around that topic. This course is a collaborative learning experience and your feedback makes the course better. There are very few pre-requisites for the course. Some familiarity with high school algebra is all that is required for understanding the topics. It is not possible to truly understand and enjoy Number Theory without solving problems, so I would encourage all students to work through the videos with pen and paper nearby, so that they can try out the problems themselves before looking at the solutions. Happy learning.

Overview
Section 1: Theory

Lecture 1 Linear Congruences

Lecture 2 Quadratic Residues

Lecture 3 Fermat’s Theorem and Period of a (modulo m)

Lecture 4 Euler’s Totient Function & Wilson’s Theorem

Lecture 5 Dirichlet’s Theorem

Lecture 6 Powers modulo m by Successive Squares method

Lecture 7 Quadratic Reciprocity & Euler’s Criterion

Lecture 8 When is a number the sum of two squares?

Lecture 9 Floor, Ceiling & Fractional Part Functions

Section 2: Problem Solving

Lecture 10 Divisibility problems

Lecture 11 More practice problems

Lecture 12 Problem Solving Session

Lecture 13 Applying Quadratic Reciprocity Law in problems

Lecture 14 Five Olympiad Problems

Lecture 15 More Practice Problems

This course is geared towards parents of students who are writing Math Olympiads and need help with Number theory.