Bernd Schröder

Introduction to Number Theory

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The videos below are part of a remotely delivered course on introductory number theory, following Rosen's book. For the "license", click here.

For mathematics presentations in general, the pause button is your best friend. But I must emphasize this statement for classes that involve proofs, such as this one. Because material can be presented rapidly with slides, there is no slowing down as I write stuff by hand on the board. That means you really need to pause the videos frequently to make sure that you can digest the points that are being made. The best approach is to first read the book and then follow the presentations. (That actually goes for any mathematics class, including those presented face to face.) 

For best performance, the videos should be downloaded and then run locally.

  1. Introduction
    Video. (15MB, 14:08min)                  Slides.
  2. Numbers and Sequences
    Video. (36MB, 34:01min)                  Slides.
  3. Induction
    Video. (13MB, 14:09min)                  Slides.
  4. Sums and Products
    Video. (25MB, 28:26min)                  Slides.
  5. Fibonacci Numbers
    Video. (18MB, 18:55min)                  Slides.
  6. Divisibility
    Video. (20MB, 21:19min)                  Slides.
  7. Base r Representation of Integers
    Video. (61MB, 59:21min)                  Slides.
  8. Prime Numbers
    Video. (24MB, 21:07min)                  Slides.
  9. Fundamental Theorem of Arithmetic
    Video. (40MB, 38:57min)                  Slides.
  10. Greatest Common Divisor
    Video. (23MB, 22:57min)                 Slides.
  11. Factorization Methods
    Video. (31MB, 29:34min)                 Slides.
  12. Congruence Modulo m
    Video. (38MB, 37:44min)                 Slides.
  13. Linear Congruences and the Chinese Remainder Theorem
    Video. (37MB, 37:11min)                 Slides.
  14. Polynomial Congruences
    Video. (37MB, 38:16min)                 Slides.
  15. Applications of Congruences
    Video. (57MB, 53:01min)                 Slides.
  16. Fermat's Little Theorem and Euler's Theorem
    Video. (48MB, 47:05min)                 Slides.
  17. Public Key Encryption
    Video. (41MB, 37:02min)                 Slides.
  18. Multiplicative Functions
    Video. (47MB, 47:56min)                 Slides.
  19. More on Encryption (not covered in summer 2012, postponed indefinitely)
    Video.                  Slides.
  20. Primitive Roots Modulo m
    Video. (58MB, 59:22min)                 Slides.
  21. Discrete Logarithms (modulo m)
    Video. (77MB, 68:53min)                 Slides.
  22. Quadratic Residues
    Video. (60MB, 62:31min)                 Slides.

 

 

 

 

 

 

"License".

Obviously, if I post something, I want people to use it. If you are a teacher, feel free to use the videos and the slides in classes. The goal is to get people to do better in mathematics.

One caveat: If you want to create an on-line course with the videos, note that I have already done so. Please consider sending your students to my course  :)

Slides for a presentation on on-line delivery (focused on Differential Equations)