Michael Penn Courses

Abstract Algebra - Every PID is a UFD

Explore the connection between principal ideal domains and unique factorization domains, introducing key concepts like ascending chain condition and Noetherian rings.

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

A Classic Trig Identity - Featuring Chebyshev Polynomials

Explore a classic trigonometric identity derivation using Chebyshev polynomials, enhancing your understanding of advanced mathematical concepts and their applications.

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

Norwegian Mathematical Olympiad 2016 Q2

Explore a detailed solution to Question 2 from the 2016 Norwegian Mathematical Olympiad, also known as the Abel Competition, with expert guidance and explanations.

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

Catalan's Identity for Fibonacci Numbers

Explore Catalan's identity for Fibonacci numbers through matrix properties, building on previous proofs of Cassini's and d'Ocagne's identities in this mathematical deep dive.

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

Abstract Algebra - The Field of Fractions of an Integral Domain

Explore the concept of field fractions in integral domains, with examples and proofs demonstrating the construction of the smallest containing field.

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

Multivariable Calculus - When the Divergence Theorem Doesn't Apply

Explore surface integrals over special vector fields, including cases where the divergence theorem fails, in this advanced multivariable calculus analysis.

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

Multivariable Calculus - Verifying the Divergence Theorem

Explore a practical example of the divergence theorem in multivariable calculus, enhancing understanding through step-by-step verification and clear explanations.

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

An Interesting Infinite Sum, Featuring Fourier Series

Explore the derivation of a closed form for the infinite sum cos(n)/n^4 using Fourier series, featuring integration by parts and coefficient analysis.

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

Multivariable Calculus - Stoke's Theorem

Explore Stoke's Theorem in multivariable calculus, including its description and a proof outline, enhancing understanding of vector calculus and its applications in physics and engineering.

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

Re-Nesting Cube Roots with Ramanujan

Explore Ramanujan's fascinating theorem on re-nesting cube roots, proving the result and demonstrating its application to cubic polynomials in this engaging mathematical journey.

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

Some Simple Cryptographic Ciphers

Explore basic cryptographic techniques like Caesar cipher and tabular transposition, learning how to encode and decode secret messages using simple mathematical methods.

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

Abstract Algebra - Eisenstein's Criterion

Proof and examples of Eisenstein's criterion in abstract algebra, demonstrating its application in determining polynomial irreducibility over rational numbers.

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

Multivariable Calculus - Two Surface Integrals Over Vector Fields

Explore surface integrals over vector fields in this concise tutorial, enhancing your understanding of multivariable calculus concepts and applications.

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

An Interesting Trigonometry Problem - Featuring Roots of Unity

Explore a classic trigonometric identity involving multiples of pi/11, derived using roots of unity. Gain insights into advanced mathematical concepts and problem-solving techniques.

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

Multivariable Calculus - The Area of a Parameterized Surface

Derive a formula for calculating the area of parameterized surfaces in multivariable calculus, enhancing understanding of complex geometric concepts.

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