This course aims to teach students the fundamentals of number theory through various mathematical proofs and problem-solving techniques. By the end of the course, students will be able to understand and apply concepts such as irrational numbers, prime numbers, modular arithmetic, and congruences. The teaching method involves a combination of theoretical explanations, problem-solving demonstrations, and real-life applications. This course is intended for individuals interested in exploring the beauty and complexity of number theory, regardless of their mathematical background.
Overview
Syllabus
The Legendary n^2+n+41 (why do we need math proofs?).
An Easy Putnam Exam Problem!.
Proving sqrt(2) is irrational by using the rational zero theorem.
Sqrt(2) is irrational! (Classic Proof).
Why do you rationalize the denominator? (here's my reason).
That Time Euler Was Wrong.
You, me, and my first IMO problem.
A Repeating Decimal Equation.
A Strong Induction Proof.
There are infinitely many primes (Euclid's proof).
Fibonacci Sequence (with a twist).
You, Me and The Legend of Question 6.
A "Can This Be Prime" Putnam Exam Problem.
Prime factor 1002004008016032.
The Harmonic Number Is Never An Integer When n Is BIGGER Than 1.
What does a ≡ b (mod n) mean? Basic Modular Arithmetic, Congruence.
Solving congruences, 3 introductory examples.
System of congruences, modular arithmetic.
When can we divide in a congruence?.
45^2+45+41 is NOT prime?.
Integral Calculus Marathon Livestream.
solving a quadratic congruence but the modulus is NOT prime.
Taught by
blackpenredpen
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Reviews
5.0 rating, based on 1 Class Central review
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Marwa ElhilaliThis course was interesting, wonderful and very useful. I hope to succeed and thank you for these useful free courses. I am a 13-year-old student. I love mathematics and I am very smart in it.
