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The Power of Mathematical Visualization

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24
Bringing Visual Mathematics Together
2016-10-21
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.

Watch The Power of Mathematical Visualization Season 1 Episode 24 Now

23
Visualizing Fixed Points
2016-10-21
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?

Watch The Power of Mathematical Visualization Season 1 Episode 23 Now

22
Visualizing Balance Points in Statistics
2016-10-21
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.

Watch The Power of Mathematical Visualization Season 1 Episode 22 Now

21
Symmetry: Revitalizing Quadratics Algebra
1970-01-01
Learn why quadratic equations have "quad" in their name, even though they don't involve anything to the 4th power. Then try increasingly challenging examples, finding the solutions by sketching a square.

Watch The Power of Mathematical Visualization Season 1 Episode 21 Now

20
Symmetry: Revitalizing Quadratics Graphing
2016-10-21
Throw away the quadratic formula you learned in algebra class. Instead, use the power of symmetry to graph quadratic functions with surprising ease.

Watch The Power of Mathematical Visualization Season 1 Episode 20 Now

19
The Visuals of Graphs
2016-10-21
Inspired by a question about the Fibonacci numbers, probe the power of graphs. First, experiment with scatter plots.

Watch The Power of Mathematical Visualization Season 1 Episode 19 Now

18
Visualizing the Fibonacci Numbers
2016-10-21
Learn how a rabbit-breeding 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.

Watch The Power of Mathematical Visualization Season 1 Episode 18 Now

17
Visualizing Orderly Movement, Random Effect
1970-01-01
Start with a simulation called Langton's ant, which follows simple rules that produce seemingly chaotic results. Then watch how repeated folds in a strip of paper lead to the famous dragon fractal.

Watch The Power of Mathematical Visualization Season 1 Episode 17 Now

16
Visualizing Random Movement, Orderly Effect
2016-10-21
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.

Watch The Power of Mathematical Visualization Season 1 Episode 16 Now

15
Visualizing Pascal's Triangle
2016-10-21
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.

Watch The Power of Mathematical Visualization Season 1 Episode 15 Now

14
Visualizing Combinatorics: Art of Counting
2016-10-21
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?

Watch The Power of Mathematical Visualization Season 1 Episode 14 Now

13
Visualizing Probability
2016-10-21
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.

Watch The Power of Mathematical Visualization Season 1 Episode 13 Now

12
Surprise! The Fractions Take Up No Space
2016-10-21
Drawing on the bizarre conclusions from the previous lecture, reach even more peculiar results by mapping all of the fractions (i.e.

Watch The Power of Mathematical Visualization Season 1 Episode 12 Now

11
Visualizing Mathematical Infinities
2016-10-21
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.

Watch The Power of Mathematical Visualization Season 1 Episode 11 Now

10
Pushing the Picture of Fractions
2016-10-21
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.

Watch The Power of Mathematical Visualization Season 1 Episode 10 Now

9
Visualizing Decimals
2016-10-21
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?

Watch The Power of Mathematical Visualization Season 1 Episode 9 Now

8
Pushing Long Division to Infinity
1970-01-01
"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.

Watch The Power of Mathematical Visualization Season 1 Episode 8 Now

7
Pushing Long Division to New Heights
2016-10-21
Put your dots-and-boxes machine to work solving long-division problems, making them easy while shedding light on the rationale behind the confusing long-division algorithm taught in school. Then watch how the machine quickly handles scary-looking division problems in polynomial algebra.

Watch The Power of Mathematical Visualization Season 1 Episode 7 Now

6
The Power of Place Value
2016-10-21
Probe the computational miracle of place value--where a digit's position in a number determines its value. Use this powerful idea to create a dots-and-boxes machine capable of performing any arithmetical operation in any base system--including decimal, binary, ternary, and even fractional bases.

Watch The Power of Mathematical Visualization Season 1 Episode 6 Now

5
Visualizing Area Formulas
2016-10-21
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.

Watch The Power of Mathematical Visualization Season 1 Episode 5 Now

4
Visualizing Extraordinary Ways to Multiply
2016-10-21
Consider the oddity of the long-multiplication algorithm most of us learned in school. Discover a completely new way to multiply that is graphical--and just as strange!

Watch The Power of Mathematical Visualization Season 1 Episode 4 Now

3
Visualizing Ratio Word Problems
2016-10-21
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.

Watch The Power of Mathematical Visualization Season 1 Episode 3 Now

2
Visualizing Negative Numbers
2016-10-21
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.

Watch The Power of Mathematical Visualization Season 1 Episode 2 Now

1
The Power of a Mathematical Picture
2016-10-21
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.

Watch The Power of Mathematical Visualization Season 1 Episode 1 Now

The Power of Mathematical Visualization from The Great Courses Signature Collection is a fascinating educational series that unveils the incredible, often overlooked beauty and utility of mathematics. This in-depth exploration goes far beyond the basic equations and theories we may remember from our early education, shedding light on the often underappreciated world of mathematics and emphasizing how it shapes and influences our everyday lives in more ways than one could imagine. Instructed by award-winning mathematics professor James S. Tanton of The Mathematical Association of America, the Power of Mathematical Visualization is a comprehensive crash course in math appreciation. Tanton's engaging teaching style makes often-intimidating complex mathematical concepts exciting and accessible to all, whether you are a lover of numbers or a curious novice. This 24-lecture series delves into the principles of geometry, algebra, calculus, and statistics, among other areas. However, it's not your typical math course; it’s revolutionary in the way it presents these traditional areas. Rather than focusing on dry equations, the series emphasizes the visual artistry inherent in mathematical principles and their exciting real-world application. The course helps viewers not only understand mathematical concepts but also see them and visualize how they fit together. This approach, guided by Professor Tanton's expertise, promises to challenge the viewer's perception of what math is and can be. Each lesson stretches the mind and the imagination, bringing mathematics to life in a unique and enlightening way. The course starts by looking at easy mathematical operations and builds up to concepts like infinity, fractals, the Pythagorean theorem, and prime numbers, among others. It introduces viewers to the hidden wonders of numbers and formulas as Tanton uses vivid examples and visuals. He takes viewers from mathematical novelties such as magic squares and sudoku, through more complex topics like the Fibonacci numbers and Pascal's triangle, and onto higher-level concepts like the visualization of calculus and geometry. Teachers, students, and anyone interested in the wonderful world of mathematics will find their understanding deepened and their imagination stretched. Additionally, The Power of Mathematical Visualization highlights the creative aspect of mathematics. More than just number-crunching, math is presented as an aesthetic discipline with its patterns, rhythm, and progression. It emphasizes how mathematical concepts can help in visualizing and understanding patterns and phenomena in nature and the physical world. This series gallantly refutes the notion that mathematics is a dull, purely academic discipline, replacing the stereotype with an enthralling vision of numeric beauty and inherent creativity. Furthermore, this series underscores the idea that mathematics transcends boundaries—it's the universal language that cuts across cultures and civilizations. It shows that mathematics has been part of human history and civilization from ancient times, encompassing the Egyptian pyramids, the Greek philosophers, and the Renaissance artists, to the modern era of computers and quantum physics. But the real apex is not only the academic understanding. The Power of Mathematical Visualization concludes by stressing the practical aspect of mathematical concepts and how our knowledge of mathematics can influence and change the way we perceive and interact with the world around us. At its heart, this series is aimed to inspire a passion and genuine interest in mathematics. It guides the viewer through a captivating, vivid journey of mathematical discovery, demonstrating how they can approach and appreciate mathematics with a fresh, creative perspective. The course is recommended for those curious about the world of numbers and patterns, for those wishing to enhance their problem-solving and critical thinking abilities, or even for those simply searching for a seemingly hidden universe of elegance, symmetry, and logic. In conclusion, The Power of Mathematical Visualization is an incredible resource that unveils the intriguing, fascinating world of mathematics, breaking the stereotype of mathematics as a dry, complex discipline and replacing it with a vibrant, creative, and fundamentally human realm of discovery and innovation. By viewing this series, you will gain a newfound appreciation for the aesthetic beauty and infinite possibility inherent in the world of mathematics.

The Power of Mathematical Visualization is a series categorized as a . Spanning 1 seasons with a total of 24 episodes, the show debuted on 2016. The series has earned a no reviews from both critics and viewers. The IMDb score stands at undefined.

Genres
Channel
The Great Courses Signature Collection
Cast
James S. Tanton
The Power of Mathematical Visualization is available on .