Math Fundamentals Courses and Certifications

Michael Penn

A Gnarly Inverse Trig Integral

Explore a challenging inverse trigonometric integral, delving into advanced calculus techniques for solving complex mathematical problems.

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

Michael Penn

Solving a Calculus Problem Using Linear Algebra

Explore how linear algebra techniques can be applied to solve complex calculus problems, demonstrating the interconnectedness of mathematical disciplines.

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

Michael Penn

The Return of Big Integrals

Explore advanced integration techniques for complex mathematical problems, enhancing problem-solving skills and deepening understanding of calculus concepts.

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

Michael Penn

Discrete Calculus - My Favorite Topic for a Student Seminar Talk

Explore discrete calculus through derivatives, antiderivatives, and fundamental theorems. Learn power rules, exponential functions, and Fibonacci numbers in this engaging mathematical seminar.

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

Michael Penn

Real Analysis - The Fundamental Theorem of Calculus

Comprehensive proof of both parts of the Fundamental Theorem of Calculus, demonstrating the relationship between differentiation and integration in real analysis.

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

Michael Penn

Problem Solving - Complex Number Basics

Explore essential complex number techniques for problem-solving contests, covering arithmetic operations, Euler's formula, and nth roots of unity with practical examples.

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

Michael Penn

Real Analysis - L'Hospital's Rule - Infinity-Infinity Case

Rigorous proof of L'Hospital's rule for infinity/infinity case, demonstrating its application in calculating limits of indeterminate forms in real analysis.

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

Michael Penn

A Nice Integral

Explore advanced integration techniques using Feynman's trick and Fubini's theorem to solve a challenging integral, enhancing problem-solving skills in mathematical analysis.

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

Michael Penn

A Sum Two Ways

Explore two distinct methods for calculating the closed form of an intriguing infinite series, demonstrating advanced mathematical techniques and problem-solving approaches.

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

Michael Penn

Pi Is Irrational

Explore a simple proof demonstrating pi's irrationality, delving into mathematical concepts and reasoning behind this fundamental property of the famous constant.

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

Michael Penn

An Infinite Tangent Product

Explore the evaluation of an infinite tangent product using identities and telescoping techniques, delving into advanced mathematical concepts and problem-solving strategies.

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

Michael Penn

Do We Even Need the Real Numbers?

Explore the possibility of calculus using only rational numbers and discover the crucial role of the axiom of completeness in fundamental calculus theorems.

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

Michael Penn

Lobachevsky's Integral Formula and a Nice Application

Explore Lobachevsky's integral formula and its application to calculate specific integrals using Fourier expansion, with a focus on sin(x)/x and abs(sin x)sin(x)/x.

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

Michael Penn

A Trigonometric Integral

Explore strategies for solving complex trigonometric integrals using recursively defined sequences, enhancing your mathematical problem-solving skills.

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

Michael Penn

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