MATH 451 Axiomatic Geometry

MATH 451 Axiomatic Geometry

Section 001, Fall 2019

Instructor: Kevin McLeod

Office: EMS E481

Office hours:
MW 12:30-1:30 PM
T 10:00-10:45 AM
(or by appointment)
Phone: 229-5269


Home page:
Class schedule: TR 3:30-4:45 PM, NWQ 1975

Primary Text: Gerard A. Venema, Foundations of Geometry (2nd edition).

Course description

The goal of this course is for you to explore, and thereby deepen your understanding of, the foundations of geometry. In the process, you may find that some of what you thought you knew about geometry is not necessarily true or correct—if so, that will be a Good Thing. I hope to cover large parts of the first 6 chapters of the textbook, with excursions into some parts of later chapters, but this is an ambitious plan, and it is more important to cover topics in depth, with full understanding, than to cover a pre-selected set of topics. As the semester proceeds, please let me know whether you think we are going through the material too fast or too slow, and I can try to adjust to the needs of the class.

We will run the class on a “flipped classroom” model, in which you are expected to read the relevant sections of the textbook ahead of class, and we discuss them and work problems during class time.You will be expected to take an active role in the in-class activities and discussions. For this reason, attendance is particularly important: you will not be able to make up a missed class just by reading the textbook.

There is a class website at Any relevant information about the class, such as exam dates or other announcements, will be posted at the site, so you should get into the habit of checking it on a regular basis. Homework will also be posted there, so if you do have to miss a class you can still be prepared for the next one. If I find useful and relevant links during the semester, they will also be posted; if you find some yourself, please let me know. You are responsible for any information posted on the website, so please check it frequently.


Your grade for the course will be based on
the following factors:

  • Reading and Homework You will be assigned one or more sections of the textbook to read before each class period, and homework problems after each class. (The homework may be given out in class, but will always be posted on the class website.) I will often ask you to send me an e-mail question on the reading, and I often use those questions to help plan the class discussion. The homework problems will usually consist of exercises from the primary text, some of which will be collected and graded. 20%.
  • Paper You will be asked to write a paper on a topic connected to the material covered in class or, more generally, to the class goals. You will have a wide choice of topic, but you will be asked to submit a proposal for my approval before starting on the paper itself. 20%.
  • Midterm This will be a 1-hour exam, given close to the 7th week of the semester. (The exact date will depend on the pace of the class, and will be announced at least one week in advance.) 25%.
  • Final Exam The final exam will be comprehensive, and will take place from 3:00-5:00 pm on Thursday, December 19. 25%.
  • Class participation 10%.

There will be no make-up for the final exam. You may have a make-up for the midterm if I am convinced that you had a valid excuse for missing the original exam. The make-up must be taken within one week of the original midterm, and will be an oral exam.

Average Time Investment

The amount of time that an average student should expect to spend on this
class is as follows:

  • Classroom time (face to face instruction): 45 hours
  • Time taking exams (midterm, final exam): 3 hours
  • Time for preparation and study for exams: 16 hours
  • Time completing reading and other homework assignments: 86 hours

Total number of hours: 150.

Graduate Credit

If you are a graduate student who has registered for MATH 451G, please see me to discuss the additional work you wil be expected to complete, and the resulting changes in weighting of the components contributing to your grade.

Students with disabilities

If you feel you are a student with a disability, please feel free to contact me early in the semester for any help or accommodation you may need.

University policies

You should keep yourself informed of important dates in the University calendar.

The Secretary of the University has a page dedicated to university policies for religious observances, grade appeal procedures, military service and other matters. You should also familiarize yourself with the information on the Dean of Students Office webpage concerning proper student conduct at the university, both academic and non-academic misconduct. You will be held responsible for
the information and policies contained at these links.

Finally, please note that I reserve the right to make changes to this syllabus in the event of a
disruption to normal classroom activities, or other needs that may arise during the semester.

Kevin Mcleod