Math 301 - Elementary Number Theory

This introductory number theory course covers many standard topics including primes, divisibility, unique factorization, multiplicative functions, modular arithmetic, Fermat's Theorem, Euler's Theorem, and quadratic residues.

I taught this course during the following quarters: Summer 2023.

Lectures

Recorded lectures from Summer 2023 are available on the following youtube playlist:

Problem Solving

I implemented a flipped classroom model for this course. Students watched lectures at home and then participated in stimuating problem solving activities in class. Students worked together in small groups to tackle a collection of problems, then presented their discoveries at the end of class. This approach turned out to be highly successful in terms of student engagement and learning outcomes, and I plan to continue implementing and refining this model for future versions of this course.

The problem sets are available below.

• Problem Set 1 (Mathematical Induction)
• Problem Set 2 (Divisibility, Euclidean algorithm)
• Problem Set 3 (Prime numbers, Unique factorization)
• Problem Set 4 (Multiplicative functions)
• Problem Set 5 (Modular arithmetic)
• Problem Set 6 (Linear congruences, Sun Tzu's remainder theorem)
• Problem Set 7 (Fermat's theorem, Euler's theorem)
• Problem Set 8 (Euler phi function, Squares modulo p)

Exams

This course included a midterm, which covered problem sets 1-4. Here is a link to the midterm as well as solutions. A practice midterm is also available.