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24. Bringing Visual Mathematics Together
October 21, 2016
By repeatedly folding a sheet of paper using a simple pattern, you bring together many of the ideas from previous lectures. Finish the course with a challenge question that reinterprets the folding exercise as a problem in sharing jelly beans. But don't panic! This is a test that practically takes itself!
23. Visualizing Fixed Points
October 21, 2016
One sheet of paper lying directly atop another has all its points aligned with the bottom sheet. But what if the top sheet is crumpled? Do any of its points still lie directly over the corresponding point on the bottom sheet? See a marvelous visual proof of this fixedpoint theorem.
22. Visualizing Balance Points in Statistics
October 21, 2016
Venture into statistics to see how Archimedes' law of the lever lets you calculate data averages on a scatter plot. Also discover how to use the method of least squares to find the line of best fit on a graph.
20. Symmetry: Revitalizing Quadratics Graphing
October 21, 2016
Throw away the quadratic formula you learned in algebra class. Instead, use the power of symmetry to graph quadratic functions with surprising ease. Try a succession of increasingly scarylooking quadratic problems. Then see something totally magical not to be found in textbooks.
19. The Visuals of Graphs
October 21, 2016
Inspired by a question about the Fibonacci numbers, probe the power of graphs. First, experiment with scatter plots. Then see how plotting data is like graphing functions in algebra. Use graphs to prove the fixedpoint theorem and answer the Fibonacci question that opened the lecture.
18. Visualizing the Fibonacci Numbers
October 21, 2016
Learn how a rabbitbreeding question in the 13th century led to the celebrated Fibonacci numbers. Investigate the properties of this sequence by focusing on the single picture that explains it all. Then hear the world premiere of Professor Tanton's amazing Fibonacci theorem!
16. Visualizing Random Movement, Orderly Effect
October 21, 2016
Discover that Pascal's triangle encodes the behavior of random walks, which are randomly taken steps characteristic of the particles in diffusing gases and other random phenomena. Focus on the inevitability of returning to the starting point. Also consider how random walks are linked to the "gambler's ruin" theorem.
15. Visualizing Pascal's Triangle
October 21, 2016
Keep playing with the approach from the previous lecture, applying it to algebra problems, counting paths in a grid, and Pascal€™s triangle. Then explore some of the beautiful patterns in Pascal€™s triangle, including its connection to the powers of eleven and the binomial theorem.
14. Visualizing Combinatorics: Art of Counting
October 21, 2016
Combinatorics deals with counting combinations of things. Discover that many such problems are really one problem: how many ways are there to arrange the letters in a word? Use this strategy and the factorial operation to make combinatorics questions a piece of cake.
13. Visualizing Probability
October 21, 2016
Probability problems can be confusing as you try to decide what to multiply and what to divide. But visual models come to the rescue, letting you solve a series of riddles involving coins, dice, medical tests, and the granddaddy of probability problems that was posed to French mathematician Blaise Pascal in the 17th century.
12. Surprise! The Fractions Take Up No Space
October 21, 2016
Drawing on the bizarre conclusions from the previous lecture, reach even more peculiar results by mapping all of the fractions (i.e., rational numbers) onto the number line, discovering that they take up no space at all! And this is just the start of the weirdness.
11. Visualizing Mathematical Infinities
October 21, 2016
Ponder a question posed by mathematician Georg Cantor: what makes two sets the same size? Start by matching the infinite counting numbers with other infinite sets, proving they're the same size. Then discover an infinite set that's infinitely larger than the counting numbers. In fact, find an infinite number of them!
10. Pushing the Picture of Fractions
October 21, 2016
Delve into irrational numbersthose 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.
9. Visualizing Decimals
October 21, 2016
Expand into the realm of decimals by probing the connection between decimals and fractions, focusing on decimals that repeat. Can they all be expressed as fractions? If so, is there a straightforward way to convert repeating decimals to fractions using the dotsandboxes method? Of course there is!
7. Pushing Long Division to New Heights
October 21, 2016
Put your dotsandboxes machine to work solving longdivision problems, making them easy while shedding light on the rationale behind the confusing longdivision algorithm taught in school. Then watch how the machine quickly handles scarylooking division problems in polynomial algebra.
6. The Power of Place Value
October 21, 2016
Probe the computational miracle of place valuewhere a digit's position in a number determines its value. Use this powerful idea to create a dotsandboxes machine capable of performing any arithmetical operation in any base systemincluding decimal, binary, ternary, and even fractional bases.
5. Visualizing Area Formulas
October 21, 2016
Never memorize an area formula again after you see these simple visual proofs for computing areas of rectangles, parallelograms, triangles, polygons in general, and circles. Then prove that for two polygons of the same area, you can dissect one into pieces that can be rearranged to form the other.
4. Visualizing Extraordinary Ways to Multiply
October 21, 2016
Consider the oddity of the longmultiplication algorithm most of us learned in school. Discover a completely new way to multiply that is graphicaland just as strange! Then analyze how these two systems work. Finally, solve the mystery of why negative times negative is always positive.
3. Visualizing Ratio Word Problems
October 21, 2016
Word problems. Does that phrase strike fear into your heart? Relax with Professor Tanton's tips on cutting through the confusing details about groups and objects, particularly when ratios and proportions are involved. Your handy visual devices include blocks, paper strips, and poker chips.
2. Visualizing Negative Numbers
October 21, 2016
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 positiveswith parentheses galore.
1. The Power of a Mathematical Picture
October 21, 2016
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.
Description
The Power of Mathematical Visualization is a series that is currently running and has 1 seasons (21 episodes). The series first aired on October 21, 2016.
Where to Watch The Power of Mathematical Visualization
The Power of Mathematical Visualization is available for streaming on the The Great Courses Signature Collection website, both individual episodes and full seasons. You can also watch The Power of Mathematical Visualization on demand at Amazon Prime and Amazon.
CastJames S. Tanton

Channel

Premiere DateOctober 21, 2016