Michael Penn Courses

e^π versus π^e - The Classic Math YouTube Problem Revisited

Explore the classic mathematical comparison between e^π and π^e through rigorous analysis and elegant proofs in this engaging problem-solving session.

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

2025 AMC 12B - All Problems and Solutions

Master the complete 2025 AMC 12B competition with detailed solutions to all problems, enhancing your mathematical problem-solving skills and contest preparation strategies.

• YouTube
• 1 hour 50 minutes
• Self-Paced
• Free Video

Interesting Integrals

Explore advanced integration techniques through challenging problems featuring logarithmic, trigonometric, and special function integrals with creative solution methods.

• YouTube
• 17 hours 43 minutes
• Self-Paced
• Free Video

Infinitely Many Primes of the Form an+b - Number Theory

Explore advanced number theory concepts proving infinitely many primes exist in specific arithmetic progressions like 3n+1, 4n+1, and 4n+3 forms.

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

Identities Involving Fibonacci Numbers

Discover fascinating mathematical relationships and prove elegant identities involving Fibonacci sequences through advanced techniques like generating functions and induction.

• YouTube
• 3 hours 53 minutes
• Self-Paced
• Free Video

Proof Writing - Introduction to Mathematical Proofs and Set Theory

Master the fundamentals of mathematical proof writing through sets, logic, induction, and functions with comprehensive examples and techniques.

• YouTube
• 7 hours 8 minutes
• Self-Paced
• Free Video

PreCalculus - Comprehensive Course on Functions, Equations, and Algebraic Concepts

Master essential PreCalculus concepts including radical equations, function domains, transformations, and polynomial operations through comprehensive problem-solving examples.

• YouTube
• 11 hours 3 minutes
• Self-Paced
• Free Video

Rogers-Ramanujan Identities

Explore the fascinating world of integer partitions and generating functions through the famous Rogers-Ramanujan identities, covering proofs and the Jacobi Triple Product.

• YouTube
• 2 hours 4 minutes
• Self-Paced
• Free Video

Multivariable Calculus

Master vector calculus fundamentals through comprehensive coverage of derivatives, integrals, and theorems in multiple dimensions with practical applications.

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

Multivariable Calculus - Multiple Integrals

Master multiple integrals, coordinate transformations, and fundamental theorems like Green's and Divergence through comprehensive examples and applications.

• YouTube
• 9 hours 13 minutes
• Self-Paced
• Free Video

Multivariable Calculus - Line Integrals

Master line integrals in multivariable calculus, from basic definitions to advanced theorems like Green's and Stokes', with comprehensive examples and applications.

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

Abstract Algebra - The Basics of Rings

Explore fundamental ring theory concepts including types, properties, homomorphisms, ideals, and polynomial rings through comprehensive examples and proofs.

• YouTube
• 4 hours 36 minutes
• Self-Paced
• Free Video

Multivariable Calculus - Multivariable Functions

Master multivariable functions, partial derivatives, gradients, tangent planes, limits, double integrals, and Lagrange multipliers through comprehensive mathematical analysis.

• YouTube
• 3 hours 41 minutes
• Self-Paced
• Free Video

Abstract Algebra - The Basics of Groups

Discover fundamental group theory concepts including subgroups, cosets, Lagrange's theorem, isomorphisms, homomorphisms, normal subgroups, and quotient groups through examples.

• YouTube
• 6 hours 31 minutes
• Self-Paced
• Free Video

Techniques of Integration

Master essential integration methods including substitution, parts, trigonometric substitution, and partial fractions through comprehensive worked examples.

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