Math 409 (Geometry for Secondary and Middle School Teachers)
Spring 2009

End-of-semester schedule

• Review session: Monday 5/11, 3:30-5:00, Snow 152
• Office hours: Tuesday 5/12, 1:00-3:00, Snow 541
• Final exam: Wednesday 5/13, 1:30-4:00, Snow 152

Basic Information | Required Materials | Homework Problems | Midterm and Final Exam Information | More Resources | Links

All students enrolled in Math 409 should also be enrolled simultaneously in Math 410 (Mathematics History for Secondary and Middle School Teachers).

• KU course line number: 59445
• Instructor: Prof. Jeremy Martin
  
  541 Snow, 864-7114
• Office hours: Monday 1--2, Thursday 11--12, or by appointment
  
• Syllabus (1/15/09, 11:00 AM)
• Meeting times: Tue/Thu, 1:00-1:50 PM, 152 Snow
• Prerequisites: Math 122
• Complete list of homework problems (4/30/09)

Software

Each student should purchase a copy of The Geometer's Sketchpad (student edition), available from Key Curriculum Press for approximately $40. You may also want to try Amazon or other online vendors.

Textbook

The main textbook (which we won't follow too closely) is Euclid +/- by Saul Stahl. Thanks to Prof. Stahl, the book is available for free download as a set of PDF files.

• Table of contents, and introductory material
• Chapter 1 (Other Geometries: A Computational Introduction)
• Chapter 2 (The Neutral Geometry of the Triangle)
• Chapter 3 (Non-Neutral Geometry)
• Chapter 4 (Circles and Regular Polygons)
• Chapter 5 (Towards Projective Geometry)
• Chapter 6 (Planar Symmetries)
• Chapter 7 (Inversions)
• Chapter 8 (Symmetry in Space)
• Appendix A (Introduction to Geometer's Sketchpad)
• Appendix B (Summary of Propositions)
• Appendix F (Permutations)
• Appendix G (Modular Arithmetic)
• Bibliography

The midterm exam was given on Thursday, March 12. Here is some review information.

The final exam will be given on Wednesday, May 13, from 1:30 - 4:00 PM in Snow 152. Here is some review information.

• Introduction to Geometer's Sketchpad (adapted from Prof. Judy Roitman)
• List of axioms, definitions and theorems for Euclidean geometry (with proofs and comments); updated 3/9/09
• List of axioms, definitions and theorems for Euclidean geometry (no proofs, just statements -- this version may be easier to cite when writing proofs); updated 3/9/09
• Notes on transformational geometry (adapted from Prof. Judy Roitman); updated 4/17/09
• Notes on polyhedra (adapted from Prof. Judy Roitman); updated 4/30/09

Here is the master problem list (last updated 4/30/09). I'll assign some of these as homework, and you'll work on some of them in groups in class. You can use the other ones for review. I will be adding problems to the list as the semester progresses.

Homework is due every Tuesday at 5:00 PM. No late homework will be accepted. If you have a conflict which prevents you from turning the homework in on time, let me know before the deadline.

Written assignments should be submitted to me in class, left in my mailbox in the Math Department office (405 Snow) or brought to my office (541 Snow).

Sketchpad assignments should be e-mailed to me as attachments. If you submit them early, I will try to respond as quickly as possible so that you can fix mistakes. You can keep re-submitting sketches until the weekly deadline of Tuesday at 5 PM. Here is my grading scale for Sketchpad assignments:

• 5/5: Construction works, and I can't mess it up no matter how hard I try
• 4/5: Construction works in most cases, but after some effort, I found a way to mess it up
• 3/5: Construction works in some cases, but I found an easy way to mess it up
• 2/5: Construction doesn't work, but I think you've made partial progress toward a solution
• 1/5: Construction doesn't work, and I don't see any partial progress
• 0/5: No construction submitted

Re-submitting a sketch (before the deadline) can only increase your grade on it.

Homework #1 (due Tuesday, January 27):

• Written problems: EG 3, EG 9, EG 10. Each construction should be accompanied by an explanation of the steps you have taken and why the construction works.
• Sketchpad problems: SA 2, SA 3, SA 4. For SA 2 and SA 3, use only the Point, Circle and Line tools---do not use any of the shortcuts from the Construct menu.
• Answers to EG 3 and EG 9

Homework #2 (due Tuesday, February 3):

• Reading: These notes on axiom systems, and section 2.1 of Stahl's textbook
• Written problems: EG 11.
• Sketchpad problems: SA 6, SA 7, SA 8.

Homework #3 (due Tuesday, February 10):

• Written problems: EG 19, EG 21, EG 22. When you write your proofs in problems 19 and 21, you should refer to the master list of axioms, definitions and theorems, and cite (by number) every fact or definition that you use.
• Sketchpad problems: SA 14, SA 15.

Homework #4 (due Tuesday, February 17):

• Written problems: EG 17, EG 23. Again, you should refer to the master list of axioms, definitions and theorems as needed.
• Sketchpad problems: SA 16, SA 17.

Homework #5 (due Tuesday, February 24):

• Written problems: EG 26, EG 27. Also, read this note (revised 3/1/09) and then redo problem EG 22.
• Sketchpad problems: SA 18, SA 19.

Homework #6 (due Tuesday, March 3):

• Written problems: EG 28, EG 29.
• Sketchpad problems: SA 21, SA 23.

Homework #7 (due Tuesday, March 31):

• Written problems: TG 1, TG 2, TG 3, TG 4, TG 5. It may help to refer to the notes on transformational geometry. For TG 3 and TG 4, your answer should use the notation in the table on p.4 of the notes.

Homework #8 (due Tuesday, April 7):

• Written problems: TG 7, TG 8, TG 10.
• Sketchpad problem: TG 9. For this problem, start with this sketch.
• Answer to TG 10

Homework #9 (due Tuesday, April 14):

• Written problems: TG 12, TG 14, TG 15.

Homework #10 (due Thursday, April 23):

• Written problems: TG 17, TG 19, TG 20.

Homework #11 (due Thursday, April 30):

• Written problems: PH 1, PH 2, PH 3.

Homework #12 (due Thursday, April 30):

• Written problem: PH 4.
  
• Prize problem: EG 30. Whoever submits the best solution to this problem, as judged by me, will receive a free copy of Prof. Saul Stahl's book A Gateway To Modern Geometry (which will be the textbook for Math 559 this fall). Correct solutions may also receive extra credit at my discretion.

Mathematics links

• Math 410

Mathematical and technical writing information

The book "How to Read and Do Proofs" by Daniel Solow is a great place to get started.

• Writing in the Sciences (UNC Chapel Hill Writing Center)
• A Guide to Writing Mathematics and Mathematical Writing Checklist (Prof. Kevin Lee, Purdue)

KU links

• Jeremy Martin's home page
• KU Mathematics Department
• KU Registrar
• KU Bookstore
• KU policies on academic honesty
• KU Office of Disability Resources

Outside KU

• Get Acrobat Reader (free software, necessary to read PDF files on this page)