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The Joy of Mathematics

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Why Study Logic?
Episode 1 of An Introduction to Formal Logic
Influential philosophers throughout history have argued that humans are purely rational beings. But cognitive studies show we are wired to accept false beliefs. Review some of our built-in biases, and discover that logic is the perfect corrective. Then survey what…
Math in Your Head!
Episode 1 of Secrets of Mental Math
Dive right into the joys of mental math. First, learn the fundamental strategies of mental arithmetic (including the value of adding from left to right, unlike what you do on paper). Then, discover how a variety of shortcuts hold the…
An Introduction to the Course
Part of the Series: Algebra I
Professor Sellers introduces the general topics and themes for the course, describing his approach and recommending a strategy for making the best use of the lessons and supplementary workbook. Warm up with some simple problems that demonstrate signed numbers and…
The Power of a Mathematical Picture
Part of the Series: The Power of Mathematical Visualization
Professor Tanton reminisces about his childhood home, where the pattern on the ceiling tiles inspired his career in mathematics. He unlocks the mystery of those tiles, demonstrating the power of visual thinking. Then he shows how similar patterns hold the…
Everything in This Lecture Is False
Part of the Series: Mind-Bending Math: Riddles and Paradoxes
Plunge into the world of paradoxes and puzzles with a "strange loop," a self-contradictory problem from which there is no escape. Two examples: the liar's paradox and the barber's paradox. Then "prove" that 1+1=1, and visit the Island of Knights…
Algebra
The 18 videos in this collection focus on all aspects of Algebra, from logarithms to quadratic equations and partial fractions. Clip #1: "Mathematical Language" - Clip #2: "Powers or Indices" - Clip #3: "Logarithms" - Clip #4: "Substitution and Formulae"…
18 videos
Introduction to Logical Concepts
Episode 2 of An Introduction to Formal Logic
Practice finding the logical arguments hidden in statements by looking for indicator words that either appear explicitly or are implied--such as "therefore" and "because." Then see how to identify the structure of an argument, focusing on whether it is deductive…
Informal Logic and Fallacies
Episode 3 of An Introduction to Formal Logic
Explore four common logical fallacies. Circular reasoning uses a conclusion as a premise. Begging the question invokes the connotative power of language as a substitute for evidence. Equivocation changes the meaning of terms in the middle of an argument. And…
An Introduction to Formal Logic
Logic is intellectual self-defense against such assaults on reason and also a method of quality control for checking the validity of your own views. But beyond these very practical benefits, informal logic--the kind we apply in daily life--is the gateway…
24 videos
N is a Number: A Portrait of Paul Erdös
A man with no home and no job, Paul Erdos was the most prolific mathematician who ever lived. Born in Hungary in 1913, Erdos wrote and co-authored over 1,500 papers and pioneered several fields in theoretical mathematics. At the age…
Inside Einstein's Mind
Part of the Series: NOVA
PBS
On November 25th, 1915, Einstein published his greatest work: general relativity. The theory transformed our understanding of nature's laws and the entire history of the cosmos, reaching back to the origin of time itself. Now, in celebration of the 100th…
The Joy of Math - The Big Picture
Episode 1 of The Joy of Mathematics
Professor Benjamin introduces the ABCs of math appreciation: The field can be loved for its applications, its beauty and structure, and its certainty. Most of all, mathematics is a source of endless delight through creative play with numbers.
Geometry—Ancient Ropes and Modern Phones
Episode 1 of Geometry
Explore the origins of one of the oldest branches of mathematics. See how geometry not only deals with practical concerns such as mapping, navigation, architecture, and engineering, but also offers an intellectual journey in its own right--inviting big, deep questions.
Mental Addition and Subtraction
Episode 2 of Secrets of Mental Math
Professor Benjamin demonstrates how easily you can mentally add and subtract one-, two-, and three-digit numbers. He also shows you shortcuts using the complement of a number (its distance from 100 or 1000) and demonstrates the uses of mental addition…
Order of Operations
Part of the Series: Algebra I
The order in which you do simple operations of arithmetic can make a big difference. Learn how to solve problems that combine adding, subtracting, multiplying, and dividing, as well as raising numbers to various powers. These same concepts also apply…
Mastering Rubik’s Cube
Episode 9 of The Mathematics of Games and Puzzles
It's one of the most famous puzzles ever invented. But Professor Benjamin has an easy-to-learn, eight-step method for solving this mind-bending puzzle quickly and accurately--every time. After examining the mathematics behind the cube, you'll follow him step-by-step through an algorithm…
Fallacies of Cause and Effect
Episode 5 of An Introduction to Formal Logic
Consider five fallacies that often arise when trying to reason your way from cause to effect. Begin with the post hoc fallacy, which asserts cause and effect based on nothing more than time order. Continue with neglect of a common…
Percents, Decimals, and Fractions
Part of the Series: Algebra I
Continue your study of math fundamentals by exploring various procedures for converting between percents, decimals, and fractions. Professor Sellers notes that it helps to see these procedures as ways of presenting the same information in different forms.
Fallacies of Faulty Authority
Episode 4 of An Introduction to Formal Logic
Deepen your understanding of the fallacies of informal logic by examining five additional reasoning errors: appeal to authority, appeal to common opinion, appeal to tradition, fallacy of novelty, and arguing by analogy. Then test yourself with a series of examples,…
Solving Sudoku
Episode 10 of The Mathematics of Games and Puzzles
What's the key to solving Sudoku problems when you're at your wits' end? Training your mind to look for patterns and to use careful logic, just like mathematicians. This episode is packed with helpful techniques and strategies for overcoming even…