Lecturer: Joshua Maglione (joshua.maglione at universityofgalway.ie).
Lectures:
Tutorials: Start on the 14th of September – more information on Canvas.
Assessment: Details of this are on Canvas.
Additional Materials:
These exercise sheets are not marked. You do not need to turn them in. They will be covered in the tutorials.
Sheet 3 Solutions coming soon!
First algebra test Solutions coming soon!
Lecture 01 : A brief (and unfinished) introduction to modular arithmetic
Lecture 02 : Divisibility and the Euclidean algorithm
Lecture 03 : We solve linear Diophantine equations in two variables using Bézout’s theorem
Lecture 04 : More on linear Diophantine equations in two variables and starting modular arithmetic
Extra: Back-substition : Two examples and two exercises around back-substitution
Lecture 05 : We show that (integer) congruence is an equivalence relation
Lecture 06 : We do some algebra on $\mathbb{Z}_m$
Lecture 07 : We play with PPSNs and discuss multiplicative inverses
Lecture 08 : We discuss when multiplicative inverses exist and how to find them
Lecture 09 : We solve general congruences and consider systems of congruences
Lecture 10 : We look at the Chinese Remainder Theorem and Fermat’s Little Theorem
Extra: Additional problems Solutions : Practice problems from weeks 1–4
Lecture 11 : We generalize Fermat’s little Theorem using Euler’s totient function