311 Foundations of Geometry – Syllabus

Math 311: Foundations of geometry.

Andrés E. Caicedo.
Contact Information: See here.
Time: TTh 12 – 1:15 pm.
Place: Mathematics Building, Room 124.
Office Hours: T, 1:30 – 3:00 pm.

Textbook: Our main reference will be:

• Gerard A. Venema. Foundations of geometry. Second edition, 2012, Pearson.

There are many other excellent texts that cover similar material, and you may benefit from consulting some of them on occasion. I am partial to:

• Nikolaĭ Vladimirovich Efimov. Higher geometry.1980, Mir.

You may also find useful to consult Euclid‘s Elements or Hilbert‘s Foundations of Geometry. I will suggest additional references if needed.

Contents: The department’s course description reads:

Euclidean, non-Euclidean, and projective geometries from an axiomatic point of view.

We will discuss the axiomatic systems for geometry that the textbook discusses, but also discuss axiomatics in general, and their role in modern mathematics. This is a theoretical course, and you are expected to produce proofs on your own as required.

Grading: Based on homework. Some routine problems will be assigned frequently, to be turned in from one lecture to the next, and some more challenging problems will be posted periodically, and more time will be provided for those. No extensions will be granted, and no late work will be accepted. I expect there will be no exams, but if we see the need, you will be informed reasonably in advance. Even if you collaborate with others and work in groups, the work you turn in should be written on your own. Give credit as appropriate: Make sure to list all books, websites, and people you collaborated with or consulted while working on the homework. If relevant, indicate what software packages you used, and include any programs you may have written, or additional data. Failure to provide credit or to indicate these sources will affect your grade.

I may ask you to meet with me to discuss details of homework sets, and I suggest that before you turn in your work, you make a copy, so you can consult it if needed.

Occasionally, I post links to supplementary material on Google+ and Twitter.