Mathematics Courses and Certifications

Khan Academy

Graphing Using Derivatives - Derivative Applications - Differential Calculus - Khan Academy

Learn how derivatives reveal a function’s shape and support graphing in differential calculus.

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

Khan Academy

Determinant and Area of a Parallelogram - Matrix Transformations - Linear Algebra - Khan Academy

Explains how the determinant of a 2×2 matrix gives the area of the parallelogram formed by its column vectors.

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

3Blue1Brown

Intuition for i to the Power i - Lockdown Live Math

Visualize and explain i^i through complex exponentials, Euler's formula, position vectors, and the ambiguity of complex powers.

• YouTube
• 1 hour 14 minutes
• Self-Paced
• Free Video

3Blue1Brown

The Power Tower Puzzle

Explore tetration through power-tower puzzles, numerical iteration, and graphical tests of whether infinite exponentiation converges.

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

3Blue1Brown

Imaginary Interest Rates - Lockdown Live Math

Explore how imaginary interest rates connect compound interest, Euler’s number, rotations, and spring motion.

• YouTube
• 1 hour 3 minutes
• Self-Paced
• Free Video

3Blue1Brown

What Is Euler's Formula Actually Saying? - Lockdown Live Math

A visual, interactive exploration of what Euler’s formula means: complex exponentials encode rotations, connect to the unit circle, and yield the celebrity equation.

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

Krista King

How to Solve Partial Derivatives

Learn to calculate first- and second-order partial derivatives, including mixed partials and evaluations at specific points.

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

Academic Lesson

Calculus for Beginners - Calculus for Machine Learning

An in-depth beginner course covering limits, derivatives, optimization, Newton’s method, and antiderivatives, with an emphasis on calculus concepts useful to machine learning.

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

Mathemaniac

Matrix Transpose Isn't Just Swapping Rows and Columns

Visualize matrix transpose as a change of perspective that preserves measurements through covectors.

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

Ben Eater

How Cyclic Redundancy Checks (CRCs) Work - Error Detection in Data Transmission

Explore cyclic redundancy check (CRC), a common error detection method, and learn about its mathematical principles and effectiveness in catching specific types of errors.

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

Michael Penn

The Most Interesting Differential Equation You Have Seen

A playful exploration of an intriguing differential equation presented through a chalkboard-themed mathematical story.

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

Michael Penn

What Is a Tensor Anyway? - From a Mathematician

A mathematician explains what tensors are.

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

Insights into Mathematics

Differential Geometry - Math History - NJ Wildberger

A historical introduction to differential geometry explores evolutes, catenaries, space curves, and Gaussian curvature from planar curves to surfaces.

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

Insights into Mathematics

Projective Geometry - Math History - NJ Wildberger

An introduction to projective geometry through Pascal’s theorem, Renaissance perspective, points at infinity, and the projective line.

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

Insights into Mathematics

Greek Geometry - Math History - NJ Wildberger

Explore how ancient Greek mathematicians developed geometry through Euclid’s Elements, straightedge-and-compass constructions, and the Platonic solids.

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