Michael Penn Courses

A Delightful Problem from the Harvard-MIT Math Tournament

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Discover an elegant mathematical challenge from the prestigious Harvard-MIT tournament with step-by-step problem-solving techniques and insights into competition mathematics.

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

A Much More Friendly Approach to the Cubic Formula

Explore a user-friendly approach to understanding and applying the cubic formula, making complex mathematical concepts more accessible and manageable.

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

Clever Tricks with the Alternating Harmonic Series - Rearrangement Strategies

Explore clever rearrangement strategies for the alternating harmonic series, uncovering mathematical insights and surprising results in this engaging video lecture.

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

A Periodically Perturbed Harmonic Series - Convergence Analysis

Explore the convergence of a periodically perturbed harmonic series through rigorous mathematical analysis and proof techniques.

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

Integral Calculation with an Unexpected Twist

Explore an intriguing integral problem with an unexpected twist, enhancing problem-solving skills and mathematical intuition.

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

Physics Students Learn This Better Than Math Students - Comparing Learning Approaches

Explore a surprising mathematical concept that physics students grasp more easily than math students, challenging conventional learning expectations.

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

An Arithmetic-Geometric Limit

Explore an intriguing arithmetic-geometric limit problem, delving into mathematical concepts and problem-solving techniques to unravel its solution.

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

How to Find the Median of a Function

Learn to calculate the median of a function, exploring mathematical concepts and problem-solving techniques for this unique statistical measure.

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

Solving a Higher Degree Diophantine Equation

Explore techniques for solving complex Diophantine equations of higher degrees, enhancing problem-solving skills in number theory and algebraic manipulation.

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

Finding a Taylor Series Using Differential Equations

Explore an innovative approach to deriving Taylor series using differential equations, offering a fresh perspective on this fundamental mathematical concept.

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

Euler's Other Constant

Explore Euler's lesser-known constant, its properties, and significance in mathematics. Gain insights into this fundamental mathematical concept beyond the famous Euler's number.

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

The Craziest Definition of the Derivative You Have Ever Seen

Explore an unconventional approach to defining derivatives, offering a fresh perspective on calculus concepts and challenging traditional mathematical thinking.

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

Can You Define Trig Functions via a Differential Equation

Explore an unconventional approach to defining trigonometric functions using differential equations, offering a fresh perspective on these fundamental mathematical concepts.

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

A Unique Approach to the Half-Derivative

Explore a novel perspective on the half-derivative concept, delving into its mathematical intricacies and applications in advanced calculus and analysis.

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

Why 1 Is Never Prime, and Sometimes Neither Are Some of Your Favorites

Explore the concept of prime numbers, focusing on why 1 is not considered prime and examining other surprising non-prime numbers in mathematics.

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