Explore number theory concepts through a series of engaging lectures and problem-solving sessions. Dive into topics like irrational numbers, prime numbers, modular arithmetic, and congruences. Learn classic proofs, tackle Putnam Exam problems, and discover intriguing mathematical phenomena. Investigate the Fibonacci sequence, harmonic numbers, and quadratic congruences. Gain insights into the importance of mathematical proofs and develop problem-solving skills applicable to various mathematical challenges, including International Mathematical Olympiad (IMO) problems.
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.
