This was a “flipped” version of the LUC elementary number theory course that I ran in collaboration with Steve Doty. Lectures took the form of videos that the students could watch at their leisure. Class time was spent with students presenting proofs at the board or working problems in groups.

The material below is indebted to Kenneth Rosen’s *Elementary number theory and its applications*, which was the official text of the course. In particular, many of the exercises are versions of exercises appearing in this text. There are many points, however, where we give our own take on things, especially starting with congruences.

**Topics**

Steve and I took turns generating the material for course topics. You can figure out who did what topic by clicking on the video links.

- The combined lectures.
- Propositions and logical connectives. (Lecture, Video, Exercises)
- Logical equivalence and proof method. (Lecture, Video(a), Video(b), Exercises)
- Basic set theory. (Lecture, Video, Exercises)
- Functions and cardinality. (Lecture, Video, Exercises)
- Well-ordering property and mathematical induction. (Lecture, Video, Exercises)
- Division algorithm and base-b representation. (Lecture, Video, Exercises)
- The Euclidean algorithm. (Lecture, Video, Exercises)
- Linear diophantine equations. (Lecture, Video, Exercises)
- Primes and FTA I. (Lecture, Video, Exercises)
- Primes and FTA II. (Lecture, Video, Exercises)
- Fun with FTA. (Lecture, Video, Exercises)
- Congruences. (Lecture, Video, Exercises)
- Arithmetic modulo
*m*. (Lecture, Video, Exercises) - Linear congruences. (Lecture, Video, Exercises)
- CRT. (Lecture, Video, Exercises)
- Divisibility tests. (Lecture, Video, Exercises)
- Modular exponentiation. (Lecture, Video, Exercises)
- Theorems of Wilson, Fermat and Euler. (Lecture, Video, Exercises)
- The Euler phi-function. (Lecture, Video, Exercises)
- The structure of unit groups. (Lecture, Video, Exercises)
- Units modulo a prime. (Lecture, Video, Exercises)
- Discrete logarithms. (Lecture, Video, Exercises)
- The ElGamal cryptosystem. (Lecture, Video, Exercises)