The Teaching Company - Introduction to Number Theory

The Teaching Company - Introduction to Number Theory DVD | 7 GB

Taught by Edward B. Burger, Williams College /Ph.D., The University of Texas at Austin | Publisher: The Teaching Company | ISBN: 1598034200
Course No. 1495 (24 lectures, 30 minutes/lecture)

2 DVD set with 24 lectures 30 minutes each for a total of 720 minutes Taught by: Professor Edward B. Burger, Williams College. Annotation Lectures 1-12 of 24. "Course No. 1495" Lecture 1. Number theory and mathematical research -- lecture 2. Natural numbers and their personalities -- lecture 3. Triangular numbers and their progressions -- lecture 4. Geometric progressions, exponential growth -- lecture 5. Recurrence sequences -- lecture 6. The Binet formula and towers of Hanoi -- lecture 7. The classical theory of prime numbers -- lecture 8. Euler's product formula and divisibility -- lecture 9. The prime number theorem and Riemann -- lecture 10. Division algorithm and modular arithmetic -- lecture 11. Cryptography and Fermat's little theorem -- lecture 12. The RSA encryption scheme. Summary Professor Burger begins with an overview of the high-level concepts. Next, he provides a step-by-step explanation of the formulas and calculations that lay at the heart of each conundrum. Through clear explanations, entertaining anecdotes, and enlightening demonstrations, Professor Burger makes this intriguing field of study accessible for anyone who appreciates the fascinating nature of numbers.

In an ancient kingdom, a king asked his servant what he most desired.

"Sire," said the mathematician, "Just place one grain of rice on a single square of a chessboard. Then fill each square by doubling the number of grains of rice for every other square. I would be content with the total sum of rice."

Little did the king know, he now owed his mathematician a grand total of 18,446,744,073,709,551,615 grains of rice—or more than 671 billion tons!

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