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The Joy of Mathematics

Season 1
Humans have been having fun and games with mathematics for thousands of years. Along the way, they've discovered the amazing utility of this field - in science, engineering, finance, games of chance, and many other aspects of life. This course of 24 half-hour lectures celebrates the sheer joy of math, taught by a mathematician who is literally a magician with numbers.
200724 episodesTV-PG
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Episodes

  1. S1 E1 - The Joy of Math - The Big Picture
    April 10, 2007
    31min
    TV-PG
    Professor Benjamin introduces the ABCs of math appreciation: The field can be loved for its applications, its beauty and structure, and its certainty. Most of all, mathematics is a source of endless delight through creative play with numbers.#Science & Mathematics
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  2. S1 E2 - The Joy of Numbers
    April 10, 2007
    29min
    TV-PG
    How do you add all the numbers from 1 to 100 - instantly? What makes a square number square and a triangular number triangular? Why do the rules of arithmetic really work, and how do you calculate in bases other than 10?
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  3. S1 E3 - The Joy of Primes
    April 10, 2007
    30min
    TV-PG
    A number is prime if it is evenly divisible by only itself and one: for example, 2, 3, 5, 7, 11. Professor Benjamin proves that there are an infinite number of primes and shows how they are the building blocks of our number system.
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  4. S1 E4 - The Joy of Counting
    April 10, 2007
    28min
    TV-PG
    Combinatorics is the study of counting questions such as: How many outfits are possible if you own 8 shirts, 5 pairs of pants, and 10 ties? A trickier question: How many ways are there to arrange 10 books on a shelf? Combinatorics can also be used to analyze numbering systems, such as ZIP Codes or license plates, as well as games of chance.
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  5. S1 E5 - The Joy of Fibonacci Numbers
    April 10, 2007
    30min
    TV-PG
    The Fibonacci numbers follow the simple pattern 1, 1, 2, 3, 5, 8, etc., in which each number is the sum of the two preceding numbers. Fibonacci numbers have many beautiful and unexpected properties, and show up in nature, art, and poetry.
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  6. S1 E6 - The Joy of Algebra
    April 10, 2007
    31min
    TV-PG
    Arguably the most important area of mathematics, algebra introduces the powerful idea of using an abstract variable to represent an unknown quantity. This lecture demonstrates algebra's golden rule: Do unto one side of an equation as you do unto the other.
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  7. S1 E7 - The Joy of Higher Algebra
    April 10, 2007
    31min
    TV-PG
    This lecture shows how to solve quadratic (second-degree) equations from the technique of completing the square and the quadratic formula. The quadratic formula reveals the connection between Fibonacci numbers and the golden ratio.
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  8. S1 E8 - The Joy of Algebra Made Visual
    April 10, 2007
    32min
    TV-PG
    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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  9. S1 E9 - The Joy of 9
    April 10, 2007
    32min
    TV-PG
    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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  10. S1 E10 - The Joy of Proofs
    April 10, 2007
    31min
    TV-PG
    Professor Benjamin begins his discussion of mathematical proofs with intuitive cases like "even plus even is even" and "odd times odd is odd." He builds to more complex proofs by existence and induction, and ends with a checkerboard challenge.
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  11. S1 E11 - The Joy of Geometry
    April 10, 2007
    31min
    TV-PG
    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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  12. S1 E12 - The Joy of Pi
    April 10, 2007
    31min
    TV-PG
    Pi is the ratio of the circumference of a circle to its diameter. It starts 3.14 and continues in an infinite nonrepeating sequence. Professor Benjamin shows how to learn the first hundred digits of this celebrated number, making it look as easy as pie.
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  13. S1 E13 - The Joy of Trigonometry
    April 10, 2007
    32min
    TV-PG
    Trigonometry deals with the sides and angles of triangles. This lecture defines sine, cosine, and tangent, along with their reciprocals, the cosecant, secant, and cotangent. Extending these definitions to the unit circle allows a handy measure of angle: the radian.
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  14. S1 E14 - The Joy of the Imaginary Number i
    April 10, 2007
    31min
    TV-PG
    Could the apparently nonsensical number the square root of - 1 be of any use? Very much so, as this lecture shows. Such imaginary and complex numbers play an indispensable role in physics and other fields, and are easier to understand than they appear.
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  15. S1 E15 - The Joy of the Number e
    April 10, 2007
    30min
    TV-PG
    Another indispensable number to learn is e = 2.71828 ... Defined as the base of the natural logarithm, e plays a central role in calculus, and it arises naturally in many spheres of mathematics, including calculations of compound interest.
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  16. S1 E16 - The Joy of Infinity
    April 10, 2007
    30min
    TV-PG
    What is the meaning of infinity? Are some infinite sets "more" infinite than others? Could there possibly be an infinite number of levels of infinity? This lecture explores some of the strange ideas associated with mathematical infinity.
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  17. S1 E17 - The Joy of Infinite Series
    April 10, 2007
    31min
    TV-PG
    Starting with the analysis of the proposition 0.999999999 ... = 1, this lecture ex­plores what it means to add up an infinite series of numbers. Some infinite series con­verge on a definite value, while others grow arbitrarily large.
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  18. S1 E18 - The Joy of Differential Calculus
    April 10, 2007
    32min
    TV-PG
    Calculus is the mathematics of change, and answers questions such as: How fast is a function growing? This lecture introduces the concepts of limits and derivatives, which allow the slope of a curve to be measured at any point.
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  19. S1 E19 - The Joy of Approximating with Calculus
    April 10, 2007
    31min
    TV-PG
    Exploiting the idea of the derivative, we can approximate just about any function using simple polynomials. This lecture also shows why a formula sometimes known as "God's equation" (involving e, i, p, 1, and 0) is true, and how to calculate square roots in your head.
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  20. S1 E20 - The Joy of Integral Calculus
    April 10, 2007
    32min
    TV-PG
    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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  21. S1 E21 - The Joy of Pascal's Triangle
    April 10, 2007
    32min
    TV-PG
    A geometric arrangement of binomial coefficients called Pascal's triangle is a treasure trove of beautiful number patterns. It even provides an answer to the song "The Twelve Days of Christmas": Exactly how many gifts did my true love give to me?
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  22. S1 E22 - The Joy of Probability
    April 10, 2007
    30min
    TV-PG
    Mathematics can draw detailed inferences about random events. This lecture covers major concepts in probability, such as the law of large numbers, the central limit theorem, and how to measure variance.
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  23. S1 E23 - The Joy of Mathematical Games
    April 10, 2007
    31min
    TV-PG
    This lecture applies the law of total probability and other concepts from the course to predict the long-term losses to be expected from playing games such as roulette and craps and understand what is known as the "Gambler's Ruin Problem."
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  24. S1 E24 - The Joy of Mathematical Magic
    April 10, 2007
    31min
    TV-PG
    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.
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Subtitles
None available
Producers
The Great Courses
Cast
Arthur T. Benjamin
Studio
The Great Courses
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