Mathematics
Video Lectures - Introduction to Number Theory
Publisher: Teaching Company, 2009, 24pp, 1st ed.
Called "the queen of mathematics" by the legendary mathematician Carl Friedrich Gauss, number theory is one of the oldest and largest branches of pure mathematics. Practitioners of number theory delve deep into the structure and nature of numbers, and explore the remarkable, often beautiful relationships among them. An Introduction to Number Theory is a great introduction to the field for anyone who loves numbers.
Table of contents
| 1. | Number Theory and Mathematical Research |
| 2. | Natural Numbers and Their Personalities |
| 3. | Triangular Numbers and Their Progressions |
| 4. | Geometric Progressions, Exponential Growth |
| 5. | Recurrence Sequences |
| 6. | The Binet Formula and the Towers of Hanoi |
| 7. | The Classical Theory of Prime Numbers |
| 8. | Euler's Product Formula and Divisibility |
| 9. | 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 |