# Mathematics

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## 273 Videos in *Mathematics*

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Math in Your Head!

Episode 1 of Secrets of Mental Math

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…

The Joy of Math - The Big Picture

Episode 1 of The Joy of Mathematics

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.

Why Study Logic?

Episode 1 of An Introduction to Formal 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…

An Introduction to the Course

Episode 1 of Algebra I

Episode 1 of 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…

Everything in This Lecture Is False

Episode 1 of Mind-Bending Math: Riddles and Paradoxes

Episode 1 of 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…

The Joy of Numbers

Episode 2 of The Joy of Mathematics

Episode 2 of The Joy of Mathematics

How do you add all the numbers from 1 to 100--instantly? What makes a square number square and a triangular number triangular? Why do the rules of arithmetic really work, and how do you calculate in bases other than 10?

Data Analytics - What's the "Big" Idea?

Episode 1 of Big Data

Episode 1 of Big Data

Sample the tremendous scope and power of data analytics, which is transforming science, business, medicine, public policy, and many other spheres of modern life. Investigate why this revolution is happening now, and look at some common misconceptions about data analysis.

Introduction to Logical Concepts

Episode 2 of An Introduction to Formal Logic

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…

The Power of a Mathematical Picture

Episode 1 of The Power of Mathematical Visualization

Episode 1 of 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…

Informal Logic and Fallacies

Episode 3 of An Introduction to Formal Logic

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…

Mental Addition and Subtraction

Episode 2 of Secrets of Mental Math

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…

Mastering Rubik’s Cube

Episode 9 of The Mathematics of Games and Puzzles

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…

How to Summarize Data with Statistics

Episode 1 of Learning Statistics

Episode 1 of Learning Statistics

Confront how ALL data has uncertainty, and why statistics is a powerful tool for reaching insights and solving problems. Begin by describing and summarizing data with the help of concepts such as the mean, median, variance, and standard deviation. Learn…

Let the Games Begin!

Episode 1 of The Mathematics of Games and Puzzles

Episode 1 of The Mathematics of Games and Puzzles

Explore some general strategies for successfully solving simple games and puzzles. As you hone your skills at games and puzzles, including 20 Questions, Mastermind, Ghost, The Tower of Hanoi, variations of Tic Tac Toe, and Cram (a cross between checkers…

Big Dream - Young Women Entering STEM Fields

This film follows the intimate stories of seven young women who are breaking barriers and overcoming personal challenges to follow their passion in science, math, computing & engineering (STEM) fields.
Through video diaries and verite moments, each of these girls…

Geometry—Ancient Ropes and Modern Phones

Episode 1 of Geometry

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.

The Joy of Primes

Episode 3 of The Joy of Mathematics

Episode 3 of The Joy of Mathematics

A number is prime if it is evenly divisible by only itself and one: for example, 2, 3, 5, 7, 11. Professor Benjamin proves that there are an infinite number of primes and shows how they are the building blocks…

Order of Operations

Episode 2 of Algebra I

Episode 2 of 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…

Fallacies of Cause and Effect

Episode 5 of An Introduction to Formal Logic

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…

Inductive Reasoning

Episode 7 of An Introduction to Formal Logic

Episode 7 of An Introduction to Formal Logic

Turn from informal fallacies, which are flaws in the premises of an argument, to questions of validity, or the logical integrity of an argument. In this lecture, focus on four fallacies to avoid in inductive reasoning: selective evidence, insufficient sample…