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.
Lecture 13. Fermat's method of ascent -- lecture 14. Fermat's last theorem -- lecture 15. Factorization and algebraic number theory -- lecture 16. Pythagorean triples -- lecture 17. An introduction to algebraic geometry -- lecture 18. The complex structure of elliptic curves -- lecture 19. The abundance of irrational numbers -- lecture 20. Transcending the algebraic numbers -- lecture 21. Diophantine approximation -- lecture 22. Writing real numbers as continued fractions -- lecture 23. Applications involving continued fractions -- lecture 24. A Journey's end and the journey ahead.
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