Michael Penn Courses

Primitive Roots - Number Theory

Explore primitive roots in number theory, delving into advanced mathematical concepts and their applications in this comprehensive video lecture.

• YouTube
• 34 minutes
• Self-Paced
• Free Video

The Order of an Integer Modulo N - Number Theory

Explore the concept of order for integers modulo n in number theory, covering key propositions, primitive roots, and proofs to deepen understanding of modular arithmetic.

• YouTube
• 37 minutes
• Self-Paced
• Free Video

Hensel's Lemma - Number Theory

Explore Hensel's Lemma in number theory, learning its application to congruences and solving equations in p-adic number systems.

• YouTube
• 35 minutes
• Self-Paced
• Free Video

Wilson's Theorem - Number Theory

Explore Wilson's Theorem in number theory, including its proof, examples, and applications. Gain insights into this fundamental concept and its significance in mathematical reasoning.

• YouTube
• 29 minutes
• Self-Paced
• Free Video

Euler's Totient Function - Number Theory

Explore Euler's Totient Function in number theory, learning its properties, applications, and significance in mathematical calculations and cryptography.

• YouTube
• 35 minutes
• Self-Paced
• Free Video

Euler's Theorem - Number Theory

Explore Euler's Theorem in number theory, understanding its significance and applications in mathematical concepts like modular arithmetic and cryptography.

• YouTube
• 24 minutes
• Self-Paced
• Free Video

Chinese Remainder Theorem - Number Theory

Explore the Chinese Remainder Theorem, a fundamental concept in number theory, and its applications in solving systems of linear congruences.

• YouTube
• 27 minutes
• Self-Paced
• Free Video

Divisibility Rules - Number Theory

Explore divisibility rules in number theory, learning efficient methods to determine if numbers are divisible by specific integers without performing full division calculations.

• YouTube
• 27 minutes
• Self-Paced
• Free Video

Modular Arithmetic - Number Theory

Explore fundamental concepts of modular arithmetic in number theory, including congruence relations, modular operations, and their applications in mathematics.

• YouTube
• 26 minutes
• Self-Paced
• Free Video

Proofs and Conjectures Involving Primes - Number Theory

Explore advanced number theory concepts, focusing on proofs and conjectures involving prime numbers. Delve into constructive proofs, prime formats, and composite primes through engaging problem-solving exercises.

• YouTube
• 26 minutes
• Self-Paced
• Free Video

The Euclidean Algorithm - Number Theory

Explore the Euclidean Algorithm, a fundamental concept in number theory, and its applications in finding greatest common divisors efficiently.

• YouTube
• 22 minutes
• Self-Paced
• Free Video

The Division Algorithm - Number Theory

Explore the division algorithm in number theory, covering natural numbers, division with remainder, and related concepts through clear explanations and exercises.

• YouTube
• 27 minutes
• Self-Paced
• Free Video

Mathematical Induction - Number Theory

Explore mathematical induction in number theory through examples, proofs, and practice problems. Learn to apply this powerful technique to prove statements about integers and sequences.

• YouTube
• 32 minutes
• Self-Paced
• Free Video

Problem Solving - Techniques from Number Theory

Explore key Number Theory concepts and techniques for solving math competition problems, with practical examples including a 1985 AIME question.

• YouTube
• 28 minutes
• Self-Paced
• Free Video

No Simple Groups of Order 66 or 144

Explore advanced group theory using Sylow's Theorems to prove the non-existence of simple groups with specific orders, demonstrating powerful algebraic techniques.

• YouTube
• 29 minutes
• Self-Paced
• Free Video