Overview

Dig into one of the oldest and largest branches of pure mathematics with this captivating course on the structure and nature of numbers. “An Introduction to Number Theory” offers a thrilling exploration of significant mathematical concepts and the relationships among numbers through 24 engaging lectures.

Course Instructor

Taught by veteran Teaching Company instructor Edward B. Burger, this course provides an accessible journey into number theory, intended for anyone interested in deepening their understanding of mathematics.

Video Lessons

• Number Theory and Mathematical Research
  • Duration: 31 min
  • Description: An introduction to the field of number theory and its significance in mathematics.

• Natural Numbers and Their Personalities
  • Duration: 32 min
  • Description: Explore natural numbers and their foundational characteristics in mathematics.

3. Triangular Numbers and Their Progressions
   • Duration: 28 min
   • Description: Investigate triangular numbers through examples involving arithmetic patterns.

4. Geometric Progressions, Exponential Growth
   • Duration: 32 min
   • Description: Learn how geometric progressions operate and their applications in real-world scenarios.

• Recurrence Sequences
  • Duration: 30 min
  • Description: Delve into Fibonacci numbers and the structure of recurrence relations.

6. The Binet Formula and the Towers of Hanoi
   • Duration: 30 min
   • Description: Discover the Binet formula for Fibonacci numbers and its connections to the Towers of Hanoi problem.

7. The Classical Theory of Prime Numbers
   • Duration: 31 min
   • Description: Explore the foundational history of prime numbers and their significance.

8. Euler’s Product Formula and Divisibility
   • Duration: 31 min
   • Description: Understand Euler’s contributions to prime number theory and divisibility.

9. The Prime Number Theorem and Riemann
   • Duration: 33 min
   • Description: Investigate the Prime Number Theorem and its implications, including the Riemann Hypothesis.

10. Division Algorithm and Modular Arithmetic
    • Duration: 32 min
    • Description: Learn the principles of modular arithmetic and its practical uses in calculations.

11. Cryptography and Fermat’s Little Theorem
    • Duration: 31 min
    • Description: Examine the intersection of number theory and cryptography through Fermat’s theorem.

12. The RSA Encryption Scheme
    • Duration: 31 min
    • Description: Explore the practical applications of Fermat’s theorem in modern encryption.

13. Fermat’s Method of Ascent
    • Duration: 30 min
    • Description: Discover Diophantine equations and Fermat’s ingenious methods to solve them.

14. Fermat’s Last Theorem
    • Duration: 29 min
    • Description: Discuss the history and significance of Fermat’s last theorem and its puzzle.

• Factorization and Algebraic Number Theory
  • Duration: 31 min
  • Description: Delve into factorization properties and their implications in algebraic number theory.

16. Pythagorean Triples
    • Duration: 30 min
    • Description: Explore the properties of Pythagorean triples and their historical context.

17. An Introduction to Algebraic Geometry
    • Duration: 29 min
    • Description: Connect algebra and geometry through the study of algebraic equations.

18. The Complex Structure of Elliptic Curves
    • Duration: 30 min
    • Description: Learn about elliptic curves and their relationship to various mathematical concepts.

19. The Abundance of Irrational Numbers
    • Duration: 32 min
    • Description: Investigate irrational numbers and their prevalence in mathematics.

20. Transcending the Algebraic Numbers
    • Duration: 31 min
    • Description: Explore the world of transcendental numbers and their significance in mathematics.

21. Diophantine Approximation
    • Duration: 30 min
    • Description: Understand Diophantine approximation and its applications in problem-solving.

22. Writing Real Numbers as Continued Fractions
    • Duration: 32 min
    • Description: Learn about representing real numbers through continued fractions.

• Applications Involving Continued Fractions
  • Duration: 32 min
  • Description: Investigate practical applications of continued fractions.

• A Journey’s End and the Journey Ahead
  • Duration: 31 min
  • Description: Reflect on the insights gained through the course and the broader implications of number theory.