| Quote: |
 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!
How is this possible?
It's all due to a simple but powerful calculation, the sum of geometric progression�just one of the fascinating concepts you'll encounter in An Introduction to Number Theory. Taught by veteran Teaching Company instructor Edward B. Burger, this 24-lecture course offers an exciting adventure into the world of numbers.
An Introduction to Number Theory is a great introduction to the field for anyone who loves numbers, is fascinated by math, and wants to go further into the relationships among these mysterious objects. |
Lectures are 30 min each.
Avi (~275mb)
Course Lecture Titles:
01.Number Theory and Mathematical Research
02.Natural Numbers and Their Personalities
03.Triangular Numbers and Their Progressions
04.Geometric Progressions, Exponential Growth
05.Recurrence Sequences
06.The Binet Formula and the Towers of Hanoi
07.The Classical Theory of Prime Numbers
08.Euler's Product Formula and Divisibility
09.The Prime Number Theorem and Riemann
10.Division Algorithm and Modular Arithmetic
11.Cryptography and Fermat's Little Theorem
12.The RSA Encryption Scheme
13.Fermat's Method of Ascent
14.Fermat's Last Theorem
15.Factorization and Algebraic Number Theory
16.Pythagorean Triples
17.An Introduction to Algebraic Geometry
18.The Complex Structure of Elliptic Curves
19.The Abundance of Irrational Numbers
20.Transcending the Algebraic Numbers
21.Diophantine Approximation
22.Writing Real Numbers as Continued Fractions
23.Applications Involving Continued Fractions
24.A Journey's End and the Journey Ahead
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