TTC Video The Joy of Mathematics

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TTC Video - The Joy of Mathematics
Course No. 1411 | .AVI, XviD, 640x464 | English, [email protected] kbps, 2 Ch | 24x30 mins | 4.3 GB
Lecturer: Professor Arthur T. Benjamin Ph.D. | Genre: eLearning/Mathematics

Ready to exercise those brain cells? Humans have been having fun 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 mathematics, taught by a mathematician who is literally a magician with numbers. Professor Arthur T. Benjamin of Harvey Mudd College is renowned for his feats of mental calculation performed before audiences at schools, theaters, museums, conferences, and other venues.

Although racing a calculator to solve a difficult problem may seem like a superhuman achievement, Professor Benjamin shows that there are simple tricks that allow anyone to look like a math magician. Professor Benjamin has another goal in this course: throughout these lectures, he shows how everything in mathematics is connected-how the beautiful and often imposing edifice that has given us algebra, geometry, trigonometry, calculus, probability, and so much else is based on nothing more than fooling around with numbers.

Fun with Numbers

Here is an example:

Think of a number between 1 and 10. Triple it. Add 6. Then triple again. Now take your answer, probably a two-digit number, and add the digits of your answer. If you still have a two-digit number, add those digits again. You should now be thinking of the magical number 9. The reason this works is based on algebra and the fact that the digits of any multiple of 9 must sum to a multiple of 9.

This is one of the many wonders of modular arithmetic, sometimes called clock arithmetic, where numbers wrap around in a circle. A useful application of this field is casting out nines, a simple and ancient technique for checking the answers to arithmetical problems.

Modular arithmetic also provides a very handy method for mentally computing the day of the week for any date in history.

This connection between entertaining number tricks and the deeper properties of mathematics reflects Dr. Benjamin's specialty, which is combinatorics, the branch of mathematics that deals with the subtleties of counting. Some examples: How many different six-symbol license plates are possible? And for the book collector, how many ways are there of arranging 10 books on a shelf? (Would you believe more than 3 million?) These simple questions introduce concepts such as the factorial function.

Course Lecture Titles:
01. The Joy of Math-The Big Picture
02. The Joy of Numbers
03. The Joy of Primes
04. The Joy of Counting
05. The Joy of Fibonacci Numbers
06. The Joy of Algebra
07. The Joy of Higher Algebra
08. The Joy of Algebra Made Visual
09. The Joy of 9
10. The Joy of Proofs
11. The Joy of Geometry
12. The Joy of Pi
13. The Joy of Trigonometry
14. The Joy of the Imaginary Number i
15. The Joy of the Number e
16. The Joy of Infinity
17. The Joy of Infinite Series
18. The Joy of Differential Calculus
19. The Joy of Approximating with Calculus
20. The Joy of Integral Calculus
21. The Joy of Pascal's Triangle
22. The Joy of Probability
23. The Joy of Mathematical Games
24. The Joy of Mathematical Magic

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