Arthur Benjamin
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"The Magic of Math is the math book you wish you had in school. Using a delightful assortment of examples--from ice cream scoops and poker hands to measuring mountains and making magic squares--this book empowers you to see the beauty, simplicity, and truly magical properties behind those formulas and equations that once left your head spinning. You'll learn the key ideas of classic areas of mathematics like arithmetic, algebra, geometry, trigonometry,...
2) Secrets of mental math: the mathemagician's guide to lightning calculation and amazing math tricks
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An accessible guide to mathematical calculation reveals the secrets of rapid mental calculation, memorization, and other feats of the mind, with tips on how to add, subtract, multiply, divide, and work with fractions, squares, and cube roots.
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This course takes a mathematical approach to playing games and solving puzzles. In this course, you will be introduced to all kinds of games, from games of pure strategy (like chess) to games of pure luck (like many casino games) to games that mix strategy and luck (like blackjack, backgammon, and poker). You will analyze puzzles that have stumped people for centuries to modern favorites like sudoku and Rubik's Cube. You will improve your ability...
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Algebra can be used to solve geometrical problems, such as finding where two lines cross. The technique is useful in real-life problems, for example, in choosing a telephone plan. Graphs help us better understand everything from lines to equations with negative or fractional exponents.
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Adding the digits of a multiple of 9 always gives a multiple of 9. For example: 9 x 4 = 36, and 3 + 6 = 9. In modular arithmetic, this property allows checking answers by "casting out nines." A related trick: mentally computing the day of the week for any date in history.
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Geometry and trigonometry are used to determine the areas of simple figures such as triangles and circles. But how are more complex shapes measured? Calculus comes to the rescue with a technique called integration, which adds the simple areas of many tiny quantities.
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Geometry is based on a handful of definitions and axioms involving points, lines, and angles. These lead to important conclusions about the properties of polygons. This lecture uses geometric reasoning to derive the Pythagorean theorem and other interesting results.
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Closing the course with a magician's flair, Professor Benjamin shows a trick for producing anyone's phone number, how to create a magic square based on your birthday, how to play "mathematical survivor," a technique for computing cube roots in your head, and a card trick to ponder.