# Teaching

This is my website for teaching. You can find information about courses I am involved with here.
Andrew Fiori's website.

My office is: Hidden on the 5th floor of UHall. C546.
My office hours are: Generally Posted on Moodle, but also posted on my door.
My email address is: ....@uleth.ca ....=andrew.fiori.

### Math 4405/5405 - General Abstract Algebra

I taught this course in the Fall of 2020.

This course is cross-listed as a senior undergraduate and introductory graduate course. This course is designed to provide important background in Abstract Algebra.

The main topics for this couse are:
Groups, Group Actions, Sylow's Theorems, Solvable Groups, Nilpotent Groups, Composition Series, Free Groups, Short Exact Sequences of Groups.
Rings, UFDs, PIDs, Noetherian, Euclidean
Modules, Direct Sums, Direct Products, Structure of Modules over PIDs.

### Math 3461 - Elementary Number Theory

I taught this course in the Winter-Spring of 2020

This course provides an introduction to several topics in Number Theory that can be approached with elementary ideas.
Number Theory involves, unsurprisingly, the study of numbers and their most basic properties. The origins can be seen in trying to solve problems concerning integer solutions to polynomial equations involving integer coefficients. The study of such problems quickly leads to an interest in prime numbers which are often now seen as the central object of study in the field.
The term Elementary refers primarily to the fact that individual steps, deductions or pieces of reasoning are straight forward. It does not imply that the manner in which one assembles these steps and ideas are easy, indeed many of these involve unexpected clever and beautiful ideas.
The main topics in this course are: Division algorithm. Fundamental Theorem of Arithmetic. Euclidean Algorithm. Linear Diophantine equations. Congruences. Chinese Remainder Theorem. Quadratic reciprocity.

The first does not cover all of the content of the course, the second two cover much more than the content of this course.

### Math 4460 - Advanced Number Theory - Mathematics of Public Key Cryptography

This is a topics course that I taught in the Fall of 2019.

We will be discussing various mathematical aspects, particularly number theoretic, of various public key cryptosystems.
Topics include
quadratic reciprocity, continued fractions, linear recurences and their applications to
Efficient Primality Testing (discussions of pseudoprimes, Carmicheal numbers, and deterministic methods).
Efficient Factoring Algorithms (random squares, use of continued fractions, quadratic sieve)
Subexponential methods for discrete logarithms.
Connection between group theory and cryptography.
Connection between labelled graphs and generalizations of Diffie-Hellman key exchange schemes.
Introduction to Lattice Based cryptography

### Math 2000 - Mathematical Concepts

I have taught this course several times.

The course is an introduction to logic, proofs and several core mathematical concepts.
This version of the course is based on the book Proofs and Concepts by Dave and Joy Morris.

The lecture slides I use are below (note almost all proofs done in class are on the board and not included in the slides!):
Introduction to Propositional Logic
Introduction to Proofs
Introduction to Sets
Introduction to Quantifiers
Proofs with Quantifiers
Introduction to Divisibility
Introduction to Limits
Introduction to Functions
Introduction to Equivalence Relations
Introduction to Induction
Introduction to Cardinality
These were based very loosely around lecture notes by Dave Morris.

### Math 3410 - Linear Algebra 2

I have taught this course several times.

This course is an introduction to the abstract theory of Linear Algebra, that is vector spaces and linear transformations, the maps between them. This course also covers topics such as: inner products spaces and Jordan canonical form.
A core component of this course involves writing proofs based around the abstract concepts introduced.

Out of date versions of the lecture slides I have used are below.
(Current students should get up to date versions from Moodle!)
Review of Vectors
Review of Matricies
Review of Complex Numbers
Review of Proofs
Introduction to Abstract Vector Spaces
Subspaces
Generators
Linear Independence
Basis and Dimension
Direct Sums
Introduction to Abstract Linear Transformations
Matricies and Linear Transformations
Changes of Basis
Images of Linear Transformations
Kernels of Linear Transformations
Invertibility of Linear Transformations
Systems of Equations
Maps of Direct Sums
Canonical Forms: Polynomials and Transformations
Canonical Forms: Invariant Subspaces
Canonical Forms: Rational Canonical Form
Canonical Forms: Jordan Canonical Form

#### Previous Teaching

At the University of Calgary I have previously taught:
Linear Methods (Math 211)
Calculus 1 (Math 265)
Calculus 2 (Math 267)

At Queen's University I have previously taught:
Differential and Integral Calculus (for the Arts and Humanities) (Math 126)
Calculus 1 (for Engineers) (APSC 171j)
Introduction to Linear Algebra (for Engineers) (APSC 174j)
Linear Algebra (Math 111)