Mathematics Courses and Certifications

GreeneMath.com

Unit Vectors I and J - Dot Product - Angle Between Vectors - Orthogonal Vectors

Learn essential vector concepts: unit vectors, dot product, angles between vectors, and orthogonality. Master calculations and applications through clear explanations and practical examples.

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

Wrath of Math

Math Teacher vs AP Calc AB Exam from 1988 - No Calculator, No Problem

Comprehensive walkthrough of 1988 AP Calculus AB exam, offering in-depth solutions and explanations for both multiple-choice and free-response questions without a calculator.

• YouTube
• 2 hours 58 minutes
• On-Demand
• Free Video

Wrath of Math

Proving All the Sequence Limit Laws - Real Analysis

Comprehensive proof of five fundamental sequence limit laws in real analysis, covering sum, difference, constant multiple, product, and quotient of convergent sequences with practical applications.

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

Wrath of Math

What Numbers Satisfy This Inequality? - IMO 1962 Problem 2

Detailed solution to IMO 1962 Problem 2, exploring a complex square root inequality through mathematical analysis, intermediate value theorem, and algebraic manipulation.

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

GreeneMath.com

Simple Interest Word Problems Practice Test Full Solutions

Step-by-step solutions for simple interest word problems using I = prt formula. Practice with five diverse scenarios to master calculating interest earned or owed in various financial situations.

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

Steve Brunton

Complex Analysis - The Complex Logarithm, Log(z)

Explore the complex logarithm, its infinite values, branch cuts, and principle n-th roots. Gain insights into this inverse of the complex exponential and its unique properties.

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

Mathologer

Real Mathematical Magic - The King’s Algorithm and Sallow’s Geomagic

Explore mathematical magic with Bachet's algorithm and Sallow's geomagic squares. Discover the king's method for creating magic squares and delve into geometric magic squares, blending history and mathematics.

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

Freya Holmér

The Continuity of Splines

Comprehensive exploration of spline mathematics, covering Bézier curves, continuity types, geometric continuity, and various spline forms. Includes practical applications and in-depth analysis of spline properties.

• YouTube
• 1 hour 14 minutes
• On-Demand
• Free Video

Freya Holmér

The Beauty of Bézier Curves

Explore the mathematics and applications of Bézier curves, from basic concepts to advanced topics like derivatives, curvature, and arc length parameterization, with visual demonstrations.

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

3Blue1Brown

Olympiad Level Counting - How Many Subsets of {1,…,2000} Have a Sum Divisible by 5?

Explore advanced counting techniques using generating functions and complex numbers to solve a challenging subset sum problem, with applications to Olympiad-level mathematics.

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

3Blue1Brown

Solving Wordle Using Information Theory

Explore information theory and entropy through the lens of solving Wordle, learning strategies to optimize guesses and improve game performance.

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

3Blue1Brown

Alice, Bob, and the Average Shadow of a Cube

Explore problem-solving approaches to calculate a cube's average shadow area, comparing two methods and their implications for understanding geometric principles.

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

3Blue1Brown

Newton's Method Produces This Fractal, Why Don't We Teach It in Calculus Classes?

Explore the fascinating fractal produced by Newton's method for finding roots of polynomials, revealing unexpected complexity in a seemingly simple mathematical technique.

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

3Blue1Brown

How -and Why- to Raise e to the Power of a Matrix

Explore matrix exponentiation through engaging examples, from love dynamics to quantum mechanics, with clear animations and intuitive explanations of complex mathematical concepts.

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

3Blue1Brown

Tips to Be a Better Problem Solver - Lockdown Live Math

Explore problem-solving techniques in mathematics through engaging examples from geometry, trigonometry, and probability. Enhance your analytical skills with practical tips and interactive exercises.

• YouTube
• 1 hour 8 minutes
• On-Demand
• Free Video