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Mind-Bending Math: Riddles and Paradoxes

Where to Watch Mind-Bending Math: Riddles and Paradoxes

24.
The Paradox of Paradoxes
2015-07-24
Close the course by asking the big questions about puzzles and paradoxes: Why are we so obsessed with them? Why do we relish the mental dismay that comes from contemplating a paradox?

Watch Mind-Bending Math: Riddles and Paradoxes Season 1 Episode 24 Now

23.
Banach-Tarski's 1 = 1 + 1
2015-07-24
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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22.
When Measurement Is Impossible
2015-07-24
Prove that some sets can't be measured - a result that is crucial to understanding the Banach-Tarski paradox, the strangest theorem in all of mathematics, which is presented in Lecture 23. Start by asking why mathematicians want to measure sets.

Watch Mind-Bending Math: Riddles and Paradoxes Season 1 Episode 22 Now

21.
More with Less, Something for Nothing
2015-07-24
Many puzzles are optimization problems in disguise. Discover that nature often reveals shortcuts to the solutions.

Watch Mind-Bending Math: Riddles and Paradoxes Season 1 Episode 21 Now

20.
Twisted Topological Universes
2015-07-24
Consider the complexities of topological surfaces. For example, a Möbius strip is non-orientable, which means that left and right switch as you move around it.

Watch Mind-Bending Math: Riddles and Paradoxes Season 1 Episode 20 Now

19.
Crazy Kinds of Connectedness
2015-07-24
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.

Watch Mind-Bending Math: Riddles and Paradoxes Season 1 Episode 19 Now

18.
Filling the Gap between Dimensions
2015-07-24
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.

Watch Mind-Bending Math: Riddles and Paradoxes Season 1 Episode 18 Now

17.
Bending Space and Time
2015-07-24
Search for the solutions to classic geometric puzzles, including the vanishing leprechaun, in which 15 leprechauns become 14 before your eyes. Next, scratch your head over a missing square, try to connect an array of dots with the fewest lines, and test yourself with map challenges.

Watch Mind-Bending Math: Riddles and Paradoxes Season 1 Episode 17 Now

16.
Surprises of the Small and Speedy
2015-07-24
Investigate the paradoxes of near-light-speed travel according to Einstein's special theory of relativity. Separated twins age at different rates, dimensions contract, and other weirdness unfolds.

Watch Mind-Bending Math: Riddles and Paradoxes Season 1 Episode 16 Now

15.
Enigmas of Everyday Objects
2015-07-24
Classical mechanics is full of paradoxical phenomena, which Professor Kung demonstrates using springs, a slinky, a spool, and oobleck (a non-Newtonian fluid). Learn some of the physical principles that make everyday objects do strange things.

Watch Mind-Bending Math: Riddles and Paradoxes Season 1 Episode 15 Now

14.
Losing to Win, Strategizing to Survive
2015-07-24
Continue your exploration of game theory by spotting the hidden strange loop in the unexpected exam paradox. Next, contemplate Parrando's paradox that two losing strategies can combine to make a winning strategy.

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13.
Games with Strange Loops
2015-07-24
Leap into puzzles and mind-benders that teach you the rudiments of game theory. Divide loot with bloodthirsty pirates, ponder the two-envelope problem, learn about Newcomb's paradox, visit the island where everyone has blue eyes, and try your luck at prisoner's dilemma.

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12.
Why No Distribution Is Fully Fair
2015-07-24
See how the founders of the U.S. struggled with a mathematical problem rife with paradoxes: how to apportion representatives to Congress based on population. Consider the strange results possible with different methods and the origin of the approach used now. As with voting, discover that no perfect system exists.

Watch Mind-Bending Math: Riddles and Paradoxes Season 1 Episode 12 Now

11.
Voting Paradoxes
2015-07-24
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.

Watch Mind-Bending Math: Riddles and Paradoxes Season 1 Episode 11 Now

10.
Gödel Proves the Unprovable
2015-07-24
Study the discovery that destroyed the dream of an axiomatic system that could prove all mathematical truths - Kurt Gödel's demonstration that mathematical consistency is a mirage and that the price for avoiding paradoxes is incompleteness. Outline Gödel's proof, seeing how it relates to the liar's paradox from Lecture 1.

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9.
Impossible Sets
2015-07-24
Delve into Bertrand Russell's profoundly simple paradox that undermined Cantor's theory of sets. Then follow the scramble to fix set theory and all of mathematics with a new set of axioms, designed to avoid all paradoxes and keep mathematics consistent - a goal that was partly met by the Zermelo-Fraenkel set theory.

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8.
Cantor's Infinity of Infinities
2015-07-24
Randomly pick a real number between 0 and 1. What is the probability that the number is a fraction, such as ¼?

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7.
More Than One Infinity
2015-07-24
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.

Watch Mind-Bending Math: Riddles and Paradoxes Season 1 Episode 7 Now

6.
Infinity Is Not a Number
2015-07-24
The paradoxes associated with infinity are... infinite! Begin with strategies for fitting ever more visitors into a hotel that has an infinite number of rooms, but where every room is already occupied. Also sample a selection of supertasks, which are exercises with an infinite number of steps that are completed in finite time.

Watch Mind-Bending Math: Riddles and Paradoxes Season 1 Episode 6 Now

5.
Zeno's Paradoxes of Motion
2015-07-24
Tour a series of philosophical problems from 2,400 years ago: Zeno's paradoxes of motion, space, and time. Explore solutions using calculus and other techniques.

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4.
Strangeness in Statistics
2015-07-24
While some statistics are deliberately misleading, others are the product of confused thinking due to Simpson's paradox and similar errors of statistical reasoning. See how this problem arises in sports, social science, and especially medicine, where it can lead to inappropriate treatments.

Watch Mind-Bending Math: Riddles and Paradoxes Season 1 Episode 4 Now

3.
Probability Paradoxes
2015-07-24
Investigate a puzzle that defied some of the most brilliant minds in mathematics: the Monty Hall problem, named after the host of Let's Make a Deal! Hall would let contestants change their guess about the location of a hidden prize after revealing new information about where it was not.

Watch Mind-Bending Math: Riddles and Paradoxes Season 1 Episode 3 Now

2.
Elementary Math Isn't Elementary
2015-07-24
Discover why all numbers are interesting and why 0.99999... is nothing less than the number 1. Learn that your intuition about breaking spaghetti noodles is probably wrong. Finally, see how averages - from mileage to the Dow Jones Industrial Average - can be deceptive.

Watch Mind-Bending Math: Riddles and Paradoxes Season 1 Episode 2 Now

1.
Everything in This Lecture Is False
2015-07-24
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.

Watch Mind-Bending Math: Riddles and Paradoxes Season 1 Episode 1 Now

Mind-Bending Math: Riddles and Paradoxes is an engaging and intellectually stimulating series that invites viewers to explore the captivating world of mathematics through the lens of riddles and paradoxes. Offered through The Great Courses Signature Collection, this course is designed for anyone with a curious mind, whether a math enthusiast or someone simply looking to challenge their reasoning and problem-solving skills.

Throughout the series, viewers are encouraged to think critically and creatively, as the instructor, an expert in the field, presents intricate puzzles and mind-bending concepts that highlight the beauty and complexity of mathematics. The course deftly balances theory and practice, making abstract mathematical ideas accessible and relatable through real-world examples and engaging scenarios.

The series starts by introducing viewers to fundamental concepts in mathematics, such as numbers, patterns, and sequences. With a focus on logical reasoning and creative problem-solving, viewers will encounter a diverse array of mathematical riddles that require them to stretch their thinking beyond conventional boundaries. Each episode provides a unique riddle or paradox that challenges participants to solve it using a blend of intuition and logic, encouraging deeper reflection on the underlying mathematical principles at play.

One of the highlights of Mind-Bending Math is its ability to illuminate the often surprising connections between various branches of mathematics. The instructor introduces topics such as combinatorics, probability, geometry, and number theory, seamlessly weaving them into the fabric of the riddles. This interconnected approach not only showcases the richness of mathematics but also encourages viewers to appreciate the discipline as a cohesive whole rather than a collection of isolated topics.

As the series progresses, viewers will encounter classic paradoxes that have intrigued mathematicians and philosophers for centuries. The exploration of these paradoxes serves to provoke thought and discussion, urging participants to question their own assumptions about logic and reasoning. The instructor skillfully guides the audience through each paradox, providing insights and context that enhance comprehension and foster a greater appreciation for the nuances of mathematical thinking.

Audience engagement is a central theme of Mind-Bending Math. The series employs interactive elements that prompt viewers to pause and tackle challenges directly alongside the instructor. These opportunities for active participation enhance the learning experience, as they allow viewers to apply the concepts in real-time, fostering a deeper understanding of how to approach complex problems.

Moreover, the course is rich in visual aids and illustrative examples that bring the concepts to life. Viewers will see diagrams, animations, and graphs that not only clarify the mathematical principles being discussed but also highlight the aesthetic beauty of mathematics. This visual component is particularly effective in grounding abstract ideas and helping viewers develop a more intuitive grasp of the topics covered.

In addition to the riddles and paradoxes presented, Mind-Bending Math delves into the historical context of many mathematical concepts. The series touches upon the contributions of notable mathematicians and the evolution of ideas over time, providing a narrative that connects the current understanding of mathematics with its rich history. This historical perspective adds depth to the learning experience, illustrating how mathematics has shaped human thought and culture throughout the ages.

The pacing of the course is well-considered, allowing viewers to absorb each concept thoroughly before moving on to more complex riddles and ideas. This structure ensures that the content remains accessible, even for those who may feel intimidated by mathematics. By emphasizing the enjoyment of problem-solving and the thrill of discovery, Mind-Bending Math encourages a positive attitude towards learning and engagement with mathematics.

Ultimately, Mind-Bending Math: Riddles and Paradoxes is more than just a course on mathematical concepts; it is an invitation to explore the wonders of reasoning, logic, and creativity. Viewers will leave with a renewed appreciation for the power of mathematics to provoke thought, inspire curiosity, and encourage innovative thinking. Whether you're looking to develop your mathematical skills, enjoy a unique intellectual challenge, or simply appreciate the beauty of math, this series promises to expand your understanding and leave you with a sense of accomplishment. The experience is not just about finding the answers; it's about embracing the journey of exploration and discovery that mathematics offers.

Mind-Bending Math: Riddles and Paradoxes is a series categorized as a new series. Spanning 1 seasons with a total of 24 episodes, the show debuted on 2015. The series has earned a no reviews from both critics and viewers. The IMDb score stands at undefined.

How to Watch Mind-Bending Math: Riddles and Paradoxes

How can I watch Mind-Bending Math: Riddles and Paradoxes online? Mind-Bending Math: Riddles and Paradoxes is available on The Great Courses Signature Collection with seasons and full episodes. You can also watch Mind-Bending Math: Riddles and Paradoxes on demand at Amazon Prime, Kanopy, Amazon online.

Genres
Channel
The Great Courses Signature Collection
Cast
David Kung