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.

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.
*

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. *

Several optional textbooks which you can download for free cover this material:

- Elementary Number Theory - Clark/Hefferon Available Here
- Introductions to Gauss's Number Theory - Andrew Granville Available Here
- Elementary Number Theory: Primes, Congruences, and Secrets - William Stein Available Here

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
*

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

Example Proofs About Sets

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.

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

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)