Section 1 Introduction to Math 3200
Welcome to Math 3200, Geometry. Geometry is an ancient subject, which has been around about as long as agriculture. The literal translation of the name is “Earth measurement”. The material we will study ranges from the ancient (Euclid and Ancient Greece) to the relatively recent (linear algebra and modern geometry date from the late 19th century). I hope we’ll be able to have fun exploring it together.
There are many of us in this class, coming from many different backgrounds and situations. If the “default settings” for the class don’t work for you, please don’t hesitate to ask for accommodation.
We begin with some introductions: to the university, to the staff, and to the course.
Subsection 1.1 Welcome to the University of Lethbridge
Oki, and welcome to the University of Lethbridge. Our University’s Blackfoot name is Iniskim, meaning Sacred Buffalo Stone. The University of Lethbridge acknowledges and deeply appreciates the Siksikaitsitapii peoples’ connection to their traditional territory. We, as people living and benefiting from Blackfoot Confederacy traditional territory, honour the traditions of people who have cared for this land since time immemorial. We recognize the diverse population of Indigenous Peoples who attend the University of Lethbridge and the contributions these Indigenous Peoples have made in shaping and strengthening the University community in the past, present, and in the future.
As usual, everything you need to know for the course will flow through our Moodle learning management system. Make sure you check in regularly to keep on top of what’s happening in the course.
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moodle.uleth.caDon’t hesitate to reach out if you have questions. I’ll do my best to answer all of your course-related questions as quickly as possible. If you have questions that are not related to the course, you can ask those too, and I’ll try to answer, or to direct you to someone who can. Some resources can be found on the University’s Health and Safety website.
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uleth.ca/services-for-students/health-safetySubsection 1.2 Course staff and contact information
My name is Sean Fitzpatrick. I can be reached via email at sean.fitzpatrick@uleth.ca.
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www.cs.uleth.ca/~fitzpat4
mailto:sean.fitzpatrick@uleth.ca
Student hours: you are not going to get everything you need during class time. I will be available throughout the week for consultation, either one-on-one, or in small groups. Drop-in hours will be Monday and Wednesday from 1–3 p.m., and I will have appointments available throughout the day on Thursday.
Subsection 1.3 Course description
Classical (Euclidean) geometry is a great playground for learning rigorous proof. The books of Euclid’s Elements formed a canonical textbook, used for over two millennia as part of a standard mathematics education.
From Euclid, we see how to begin from a set of postulates (those truths that we hold to be self-evident), and proceed from there to see what else can be deduced. In Euclidean geometry, we will see how to use a (digital) compass and straightedge to construct things like equilateral triangles.
We will also explore geometry beyond Euclid. It turns out that at least one of Euclid’s axioms was not as self-evident as it seemed! Mathematicians spent centuries trying to prove that Euclid’s “parallel postulate” could be derived from his other axioms. It was only at the end of the 19th century that some thought to ask a simple question: what happens if the parallel postulate is false? By removing it, we are able to pass from the “Flatland” of Euclidean geometry to other worlds, where space can be curved, parallel lines can intersect, and all sorts of fun can happen.
We will cover the first six chapters of the course textbook. As time permits, we will also look at selected topics from chapters 7 and 8.
