Instructor: Emily Cliff.
Lectures: MWF 2--2:50pm, 243 Altgeld Hall.
Office hours: Monday 3--3:50pm and Thursday 12--12:50pm, 165 Altgeld Hall (or by appointment).
is available here.
Wednesday, 12 December: Office hours tomorrow (Thursday) will be in Altgeld Hall 341, from 12--12:50 and 4--4:50.
Tuesday, 11 December: Note the sign change in homework 12, Q1. (It is possible to do the question with minus signs too, so don't worry if you've already finished; but if you haven't done it yet, it will be a bit more straight-forward this way.)
Sunday, 9 November: Solutions for Exam 3 are posted below, as is a summary sheet on Möbius transformations and isometries in the Poincaré model. (We will cover some of this material on Monday, so don't worry if it doesn't look familiar yet!) Remember that the last homework is due on Wednesday. We will have a review class on Wednesday, office hours on Thursday from 12--1 (as usual), and an extra set of office hours from 4--5. Check back for the location. The final exam is on Friday at 7pm.
Friday, 30 November: Exam 3 is next Wednesday (5 December). We will do a review session on Monday. In addition to the usual office hour time on Monday (3--3:50pm), there will be an extra session on Tuesday 10--10:50am. I have posted optional homework for you to practice this week's material before the exam. (If it was being graded, I couldn't post solutions before everyone had handed it in, and it's probably more helpful for you to look at solutions. But it's still a very good idea to do this homework, just don't worry about writing it up nicely.)
Wednesday, 7 November: Office hours tomorrow (Thursday) will be from 11:30 to 12:20 (instead of from 12 to 12:50). Please email me for an appointment if this time doesn't work for you.
Wednesday, 31 October: Extra office hours before midterm 2 will be held on Sunday, 4 November, from 3:30 to 5pm in Altgeld 347.
Wednesday, 31 October: Homework 8 updates: only the first two problems are required; the last problem is optional (but good practice)! You can hand in the homework in class on Friday (2 November) or in office hours on Sunday (5 November). The solutions will not be posted until after the deadline on Sunday, but if you have already handed in the homework and want to see solutions while you're studying, send me an email.
Thursday, 25 October: The second midterm exam will be on Monday, 5 November (at the usual class time and usual location). The exam will cover the material up to the lecture this Friday (October 26). There will be a homework due next Friday (November 2) on this material, we will do a review class on that Friday, and there will be extra office hours on Sunday afternoon (November 4) in Altgeld Hall.
Tuesday, 23 October: The schedule for office hours this week will be slightly different from usual: Wednesday 3:00--3:50 and Thursday 11:30--12:20. (Still in Altgeld 165! And also still other options available by appointment!)
Wednesday, 26 September: The grader has just returned Homework 3. If you'd like to see it before the midterm, come pick it up in office hours on Thursday (12--1pm).
Monday, 24 September: Midterm 1 is this Friday, September 28. There is no homework or project due this week. Instead, prepare for the exam by going over the weekly summary sheets (posted towards the bottom of the page), and making sure you understand the solutions to all homework and worksheet problems. During Wednesday's class, you will have a chance to ask questions and work on practice problems. You can also ask questions at office hours, or make an appointment.
Friday, 14 September: I will be away all of next week; a different professor will give the lectures and will collect the homework and projects on their due dates. The material covered in lectures will be examinable; remember that Midterm 1 is coming up on September 28! (I will post a practice exam and there will be a review session the class before the exam.) Please email me if you have questions, since office hours will be cancelled.
Wednesday, 12 September: Homework 1 was returned today. The solutions are posted below. Make sure that you understand how to solve all of the questions, and that you understand where you made mistakes. Come to office hours or make an appointment if you have questions!
in reverse chronological order
| Date | Material covered; homework due |
|---|---|
| Wednesday, 12 December. |
Homework due! Last one! Solve these problems and turn them in. |
| Wednesday, 12 December. |
Review class. Here are some practice problems. In exercise 3, the final area should be 180. |
| Monday, 10 December. |
Reading. Section 8.2 (Poincaré isometries). |
| Friday, 7 December. |
Reading. Section 8.1 (Möbius transformations). |
| Wed., 5 December. |
Midterm 3. Here are the solutions. |
| Monday, 3 December. |
Review class. Look at this optional homework assignment before the review class! (Here is question 1---it had too many figures for me to type.) Solutions will be posted after class on Monday, so try to do as much as you can before then to practice the material fromt the last three lectures. Here is are the practice problems we discussed in the review class; and here are the answers to the true/false portion. |
| Monday, 3 December. |
Project due. Chapter 7.7. (You may wish to read section 6.4 on Euclidean tilings before beginning your study of hyperbolic tilings. You may also wish to do the computer constructions in Chapter 6.5---don't worry about the exercises, but the constructions might be fun.) |
| Friday, 30 November. |
Homework due. Solve these problems and turn them in. |
| Friday, 30 November. |
Reading. Sections 3.5, 8.1. |
| Wed., 28 November. |
Reading. Section 6.4.2 (tiling the Euclidean plane), section 3.5 (complex numbers). |
| Monday, 26 November. |
Reading. Section 7.6 (area in hyperbolic geometry). |
| Monday, 26 November. |
Project due. Chapter 7.4 (Saccheri quadrilaterals). Hand in a report containing: the definition of a Saccheri quadrilateral; the solution to Exercise 7.4.1; a proof of the claim below; and the solution to Exercise 7.4.2. In your solution to Exercise 7.4.2, rewrite the entire proof given in the book, with the gaps filled in as you're instructed to do. Include pictures as relevant.
The claim you must prove is the following: Let ABCD be a Saccheri quadrilateral with base AB as in the book. Let M be the midpoint of side CD and let N be the midpoint of side AB. Use congruent triangle arguments to prove that the line through M and N is perpendicular to both AB and CD. |
| Friday, 16 November. |
Homework due. Solve these problems and turn them in. |
| Friday, 16 November. |
Reading. Section 7.5 (Lambert quadrilaterals and triangles). |
| Wed., 14 November. |
Reading for worksheet. Section 7.3.2 (omega triangles). |
| Monday, 12 November. |
Reading. Section 7.3.2 (omega points and omega triangles). |
| Friday, 9 November. |
Reading. Section 7.3.1 (limiting parallels). |
| Wed., 7 November. |
Reading. Section 7.3.1 (limiting parallels). |
| Monday, 5 November. |
Midterm 2. Here are the solutions. Make sure you understand them. |
| Friday, 2 November. |
Review class. We worked on review questions. Here are the answers. |
| Friday, 2 November. |
Homework due. Solve these problems and turn them in. You only need to hand in the first two problems; the last problem is optional (but highly recommended for practice when studying!). You can hand in the homework in class on Friday, or in office hours on Sunday. |
| Wed., 31 October. |
Reading. Section 6.1 (finite plane symmetry groups); review models of hyperbolic geometry. |
| Monday, 29 October. |
Reading. Section 6.1 (finite plane symmetry groups). |
| Friday, 26 October. |
Homework due. Solve these problems and turn them in. |
| Friday, 26 October. |
Reading. Sections 5.2.2, 5.3.1, 5.4.1, 5.6.1 (symmetries). |
| Wed., 24 October. |
Reading. Chapter 5.7.2 (compositions of reflections and translations). |
| Monday, 22 October. |
Reading for Worksheet 5. Chapter 5.7 (matrix form of isometries). |
| Friday, 19 October. |
Homework due. Solve these problems and turn them in. |
| Friday, 19 October. |
Reading. Chapter 5.6 (glide reflections). |
| Wed. 17 October. |
Project due. Chapter 5.5 (Project 7: Quilts and Transformations.) Follow the instructions. Include solutions to exercises 5.5.1--5.5.4, including explicit descriptions of what transformations you used. |
| Wed., 10 October. |
Reading. Chapter 5.4 (rotations). |
| Monday, 15 October. |
Reading. Chapter 5.3 (translations). |
| Friday, 12 October. |
Homework due. Solve these problems and turn them in. |
| Friday, 12 October. |
Reading for Worksheet. Read about reflections in Chapter 5.2. |
| Wed., 10 October. |
Reading. Chapter 5.2 (reflections). |
| Monday, 8 October. |
Reading. Chapter 5.2 (reflections). |
| Friday, 5 October. |
Homework due. Solve these problems and turn them in. |
| Friday, 5 October. |
Reading. Chapter 7.2.2 (the Klein model) and Chapter 5.1 (Euclidean isometries). |
| Wed., 3 October. |
Project due. Finish up the part of Project 2.7 about orthogonal circles. You don't need to hand anything in. |
| Wed., 3 October. |
Reading for Worksheet. Read about the Klein model in section 7.2.2. The worksheet was too long, so you only have to do the first two questions---we'll talk about Q3 in class on Friday. |
| Monday, 1 October. |
Reading. Chapter 7.1 (hyperbolic geometry), Chapter 7.2.1 (the Poincaré model). |
| Friday, 28 September. |
Midterm 1. Here are the solutions. Make sure you understand them. |
| Wed., 26 September. |
Review class. We worked on review questions. Here are the answers. Make sure you understand the reasons for each answer! |
| Monday, 24 September. |
Reading. Chapter 2.7.1 (orthogonal circles), Chapter 3.2 (vectors). |
| Friday, 21 September. |
Reading. Chapter 3.1, 3.4 (coordinate geometry). |
| Friday, 21 September. |
Homework due. Solve these problems and turn them in. |
| Wed., 19 September. |
Reading. Chapter 2.6 (circle geometry). |
| Wed., 19 September. |
Project due. Chapter 2.7. (Only do the project up to Exercise 2.7.3---the last part, on orthogonal circles, will be for next week. Your report should include: a screenshot and definition for each of the concepts ``the power of a point'' and ``the inverse of a point''; and solutions to exercises 2.7.1, 2.7.2, 2.7.3. Hint for exercise 2.7.1: Look up and use Corollary 2.32 about inscribed angles, even if it hasn't been proved in class yet.) |
| Monday, 17 September. |
Reading. Chapter 2.6 (circle geometry). |
| Friday, 14 September. |
Homework due. Solve these problems and turn them in. |
| Friday, 14 September. |
Reading for Worksheet. Make sure you are comfortable with triangle similarity and triangle congruence results. |
| Wednesday, 12 September. |
Project due. Chapter 1.7. (Your report should include: a screenshot and a statement about each of Euclid's Axioms 1--5 in this system; and a response to Exercise 1.7.1, which may involve screenshots showing in each case whether the property holds or not.) |
| Wednesday, 12 September. |
Reading. Review: 2.5 (Similar triangles) and 2.1 (Playfair's postulate and the Parallel Postulate). Look at the material on Area in 2.4. |
| Monday, 10 September. |
Reading. Section 2.5: Similar triangles. |
| Friday, 7 September. |
Homework due. Solve these problems and turn them in. |
| Friday, 7 September. |
Reading. Check out the statements of Theorems 2.6, 2.7, 2.8, 2.9 and 2.14 (in sections 2.1 and 2.2.). |
| Wednesday, 5 September. |
Project due. Chapter 1.3. Here is a description of the expectations for your "report". |
| Wednesday, 5 September. |
Reading for Worksheet 1. 2.2: Pasch's axiom; plane separation properties. |
| Monday, 3 September. |
Labour Day: No class. |
| Friday, 31 August. |
Reading. 1.6, 2.1, Appendix D: Using Euclid's axioms; Hilbert's axiomatic system. |
| Wednesday, 29 August. |
Reading. 1.4, 1.5, Appendix A: Axiomatic systems and examples. |
| Monday, 27 August. |
Introduction to the course. Before next class: download the textbook and install Geometry Explorer. |
October 29--31, November 7--9.