TELEVISION

The Joy of Mathematics

The Big Picture

Series: Great Courses
4.4
(47)
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Episodes
24
Rating
TVPG
Year
2007
Language
English
Publisher
The Great Courses

About

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.

Related Subjects

Episodes

1. The Joy of Math

30m

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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.

2. The Joy of Numbers

30m

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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?

3. The Joy of Primes

30m

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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.

4. The Joy of Counting

30m

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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.

5. The Joy of Fibonacci Numbers

30m

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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.

6. The Joy of Algebra

30m

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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.

7. The Joy of Higher Algebra

30m

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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.

8. The Joy of Algebra Made Visual

30m

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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.

9. The Joy of 9

30m

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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.

10. The Joy of Proofs

30m

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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.

Extended Details

  • Closed CaptionsEnglish