Michael Penn Courses

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
• On-Demand
• 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
• On-Demand
• 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
• On-Demand
• 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
• On-Demand
• 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
• On-Demand
• 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
• On-Demand
• 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
• On-Demand
• 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
• On-Demand
• Free Video

Some Important Facts About Congruence Modulo N

Explore key properties of congruence modulo n, a fundamental equivalence relation in number theory. Learn arithmetic properties and computational techniques for this important concept.

• YouTube
• 25 minutes
• On-Demand
• Free Video

Permutation Orbifolds of Vertex Operator Algebras

Explore permutation orbifolds in vertex operator algebras, delving into advanced algebraic structures and their applications in mathematical physics and string theory.

• YouTube
• 53 minutes
• On-Demand
• Free Video

Some Example Calculations in the Heisenberg Vertex Algebra

Explore in-depth calculations within the Heisenberg vertex algebra, demonstrating advanced mathematical concepts and techniques in this specialized field of study.

• YouTube
• 21 minutes
• On-Demand
• Free Video

The Number Theory You Need to Learn Abstract Algebra

Explore essential number theory concepts like division algorithm, Euclidean algorithm, and congruence modulo n, laying the foundation for abstract algebra studies.

• YouTube
• 44 minutes
• On-Demand
• Free Video

Brush Up on Number Theory Tricks

Explore a viewer-suggested number theory problem, enhancing your problem-solving skills and deepening your understanding of mathematical concepts.

• YouTube
• 20 minutes
• On-Demand
• Free Video

Proofs by Mathematical Induction

Explore the principle of mathematical induction through clear explanations and diverse examples, enhancing your ability to construct rigorous proofs in mathematics.

• YouTube
• 24 minutes
• On-Demand
• Free Video

Basic Proofs Involving Sets

Learn techniques for proving fundamental set theory results, enhancing your mathematical reasoning skills and deepening your understanding of set operations and relationships.

• YouTube
• 22 minutes
• On-Demand
• Free Video