Math 444: Geometry for Teachers
Summer 2015, Term A

Instructor: Alexandru Chirvasitu

Class times and location: Office: C-417 Padelford
Office hours: MWF 09:30 - 10:30, Tu 10:30 - 11:30, Th 5 - 6
Email: chirva AT

TA: Christopher McMurdie
Email: mcmurdie AT

This course has now concluded; the continuation is Math 445.

Announcement about Week 3

As I said before, I'll be away during Week 3 of classes (July 6 - 10). I will have a substitute for all three lectures, so please come to class in the usual room at the usual time, MWF.

There is no homework due Monday on that week, and no quiz. There is homework due Wednesday July 8 and Friday July 10, as indicated in the tables below.

I can't hold office hours that week, but our TA Chris McMurdie will hold some instead in his office, C-404 Padelford. They are 2:30 - 4 on Tuesday July 7 and Thursday July 9. I'll also be available by email.
Office hour schedule before final exam: Tuesday, July 21 2015, 09:30 - 11:30 and 3 - 6

We're using John M. Lee's Axiomatic Geometry, referred to below as AG. The textbook is absolutely necessary, both for the reading and in order to do the assignments.

You'll also need access to Book I of Euclid's Elements, available electronically here.

It's essential that you do the reading. I won't have time to go over every relevant example in class, and you'll need a good grasp of the material in order to do the homework. In fact, I encourage you to regard the reading as part of your homework.

Each reading assignment will be paired with a homework assignment so that they're numbered identically in the two tables. Unless I say otherwise, 'Chapter X' refers to the textbook, AG.

Due date Assignment Remarks
1 Wed, Jun 24 Chapter 1 of AG and Book I of Euclid's Elements You do not need to read the proofs of the theorems in Euclid's
Book I of the Elements, just the Definitions, Postulates, Common Notions,
and statements of the Propositions
2 Fri, Jun 26 Chapter 2 before the theorems on page 42
Appendix E
3 Mon, Jun 29 Rest of Chapter 2
Appendix F
4 Wed, Jul 01 Chapter 3 before 'Betweenness of Points' on page 59
Appendix G
5 Mon, Jul 06 Chapter 3 before 'Rays' on page 71
6 Wed, Jul 08 Rest of Chapter 3
Pages 83 and 84 of Chapter 4
7 Fri, Jul 10 Chapter 4, stopping after Corollary 4.24 (page 97)
8 Mon, Jul 13 Rest of Chapter 4
Pages 103 - 112 of Chapter 5, skipping the
'Intersections of Lines and Triangles' section
9 Wed, Jul 15 Rest of Chapter 5, including the bit you skipped for the previous assignment
If interpretations and models are a bit dim in your memory,
reread the first page and a half of Chapter 2
Remind yourself of the Cartesian Plane (pages 33, 34)
10 Fri, Jul 17 Chapter 6
11 Mon, Jul 20 Chapter 7 Last assignment of the term


I will list the problems from AG, as numbered there. The numerical part indicates the chapter, so say problem 1A is at the end of chapter 1 in AG, and so on.

There will be homework due every class, and you have to turn it in at the beginning, before the lecture. No late homework for any reason, but I will drop the two lowest scores.

Because of time constraints your TA will grade a couple of problems (tops) for correctness and the rest for completeness. I won't be telling you in advance which problems are graded for correctness though..

Due date Assignment Remarks
1 Wed, Jun 24 1A, 1B, 1C, 1D For 1C only do Propositions 6 and 9
and disregard the last bullet point.
2 Fri, Jun 26 2A, 2D, 2F, 2H, 2J
EA from Appendix E
For 2J don't do part (m).
3 Mon, Jun 29 2K, 2L, 2M, 2N
parts (a), (b) and (c) of EB and EC
Please do the 2-column-style proofs as well!
4 Wed, Jul 01 2O, 2Q, 2R, 2T, 2U
Again, please do the 2-column proofs for the Chapter 2 problems.
5 Mon, Jul 06 3B, 3C, 3D, 3E, 3F Do not turn in!
We're skipping this Monday's homework because I am away,
but do the suggested problems as exercises, for practice.
Do turn in the next two assignments this week though.
6 Wed, Jul 08 3G, 3I, 3J, 3K, 3L No need to do any 2-column proofs anymore.
7 Fri, Jul 10 4A, 4B, 4C, 4D, 4E, 4F 4A and 4B are analogous to 3.9 and 3.10 respectively;
your proofs should be very similar to those.
8 Mon, Jul 13 4G, 4H, 4I
5D, 5E
9 Wed, Jul 15 5B, 5C, 5F, 5G, 5H, 5I
10 Fri, Jul 17 6B, 6C, 6D, 6E, 6F
11 Mon, Jul 20 7A, 7B, 7C, 7E, 7F, 7I Last assignment of the term


These might happen on any lecture day at any time during class, but I'll let you know at least a day ahead of time. I am not sure how many we'll have, but probably at least one each week, and I'll bring them back with me on the following lecture day.

They'll be quick 10-minute affairs having to do mostly with matters of logic, short proofs, definitions, or other such things that you can answer quickly. Each quiz will probably consist of a single question / problem.

There are no make up quizzes, but I'll drop the lowest one.

Quiz 1 and answers.

Here's Quiz 2, with solutions.

I've now posted a solution for Quiz 3 as well.

Quiz 4 and solution.


It's going to be in class, on the last day of the term, at the usual time:

As mentioned above, we'll drop the two lowest homework scores as well as the lowest quiz.

"Overloading" means allowing more students in class than the limit (which in our case is 35). Because 35 is also our room limit, there will be no overloading.
Disability Resources

If you need special accomodations please go to DRS (Disability Resources for Students) for more information. You should meet with a DRS counselor and get a letter attesting your need for academic accomodations. Once you have such a letter, please see me so that we can arrange for those.
If you have any questions, don't hesitate to email me.

Back to homepage