Catalog Search Results
Series
Great Courses volume 9
Language
English
Description
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 to an elegant and fascinating branch of philosophy known as formal logic, which is philosophy’s equivalent to calculus. Formal logic is a breathtakingly versatile tool. Much like a Swiss army...
Language
English
Description
We commonly define the Pythagorean theorem using the formula a2 + b2 = c2. But Pythagoras himself would have been confused by that. Explore how this famous theorem can be explained using common geometric shapes (no fancy algebra required), and how it’s a critical foundation for the rest of geometry.
Language
English
Description
Visit the land of topology, where one shape morphs into another by stretching, pushing, pulling, and deforming - no cutting allowed. Start simply, with figures such as the Möbius strip and torus. Then get truly strange with the Alexander horned sphere and Klein bottle. Study the minimum number of colors needed to distinguish their different regions.
Language
English
Description
Delve into decision trees, which are graphs that use a branching method to determine all possible outcomes of a decision. Trees for continuous outcomes are called regression trees, while those for categorical outcomes are called classification trees. Learn how and when to use each, producing inferences that are easily understood by non-statisticians.
Language
English
Description
Learn how Georg Cantor tamed infinity and astonished the mathematical world by showing that some infinite sets are larger than others. Then use a matching game inspired by dodge ball to prove that the set of real numbers is infinitely larger than the set of natural numbers, which is also infinite.
Language
English
Description
Enter another dimension - a fractional dimension! First, hone your understanding of dimensionality by solving the riddle of Gabriel's horn, which has finite volume but infinite surface area. Then venture into the fractal world of Sierpinski's triangle, which has 1.58 dimensions, and the Menger sponge, which has 2.73 dimensions.
Language
English
Description
Classify all different types of four-sided polygons (called quadrilaterals) and learn the surprising characteristics about the diagonals and interior angles of rectangles, rhombuses, trapezoids, and more. Also see how real-life objects—like ironing boards—exhibit these geometric characteristics.
Language
English
Description
Negative numbers are often confusing, especially negative parenthetical expressions in algebra problems. Discover a simple visual model that makes it easy to keep track of what's negative and what's not, allowing you to tackle long strings of negatives and positives--with parentheses galore.
Language
English
Description
Learn that determining the will of the voters can require a mathematician. Delve into paradoxical outcomes of elections at national, state, and even club levels. Study Kenneth Arrow's Nobel prize-winning impossibility theorem, and assess the U.S. Electoral College system, which is especially prone to counterintuitive results.
Language
English
Description
"If there is something in life you want, then just make it happen!" Following this advice, learn to solve polynomial division problems that have negative terms. Use your new strategy to explore infinite series and Mersenne primes. Then compute infinite sums with the visual approach.
Language
English
Description
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 key to astounding feats of mental calculation.
Language
English
Description
When two lines intersect, they form a system of linear equations. Discover two methods for finding a solution to such a system: by graphing and by substitution. Then try out a real-world example, involving a farmer who wants to plant different crops in different proportions.
Language
English
Description
There's more than one way to be truly random! Delve deeper into probability by surveying several discrete probability distributions - those defined by discrete variables. Examples include Bernoulli, binomial, geometric, negative binomial, and Poisson distributions - each tailored to answer a specific question. Get your feet wet by analyzing several sets of data using these tools.
Language
English
Description
Delve into irrational numbers--those that can't be expressed as the ratio of two whole numbers (i.e., as fractions) and therefore don't repeat. But how can we be sure they don't repeat? Prove that a famous irrational number, the square root of two, can't possibly be a fraction.
Language
English
Description
The Banach-Tarski paradox shows that you can take a solid ball, split it into five pieces, reassemble three of them into a complete ball the same size as the original, and reassemble the other two into another complete ball, also the same size as the original. Professor Kung explains the mathematics behind this astonishing result.
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