**Textbook:**
Philippe Tondeur, *Vectors and transformations in plane geometry*.

**Class time and location:** MWF 11:00am-11:50am, 445 Altgeld Hall.

**Professor:** Igor Mineyev, 243 Illini Hall.
Email is not very efficient for discussions.
Please talk to me before/during/after classes and come to office hours.

**Office hours:** Monday and Wednesday 2:00pm-2:50pm.

Homework will be posted here. If a newer version does not show up, restart your browser. We will roughly follow the textbook.

**Exams and grades.**
Do not miss the exams. There will be three midterm exams at the regular class time:

- Exam 1, Friday, February 15, 2019. Before the curve, the median score for exam 1 was 74.5, the mean was 72.0, and the standard deviation was 16.1.
- Exam 2, Friday, March 15, 2019.
- Exam 3, Friday, April 19, 2019.
- The final exam is at 7:00-10:00 p.m., Thursday, May 9, 2019, in the regular classroom, as required by the Final Exam Schedule.

**The project.**
The students will be randomly split into groups to work on a project, to write a report, and to present
it to the class in the second half of the semester. Select the topic of your project early,
and start working on it now. Take initiative, discuss it with me and others, if you have any questions.
The main requirements for the project:

- Most importantly, it must be interesting. Figure out what interests you, and make it interesting to others.
- It should be generally related to the course, for example, some part of general geometry, group theory, topology, etc.
- It should be something that you did not know before taking this course.
- The presentation should have mathematical content: concepts, statements, proofs.
- Type it up, or write neatly, provide pictures, diagrams, graphs, formulas, etc, whichever is needed. Include participant names, title. Hand the project to me. It also might be a good idea to provide copies to other students in the class during your presentation.
- Organize your thoughts and ideas in advance in order to present the project in class, since the time will be limited. It is a good idea to run a practice presentation with your group in advance to check how much time it takes. Consider making the presentation interesting and inspiring.

Interesting links related to geometry.

- Illinois Geometry Lab here at UIUC. The earlier you start doing research in math, the longer you will do it. :)
- Mathematical origami.
- Origami in math.
- Moebius transformations video. How transformations of the plane are related to transformations of the sphere, and to Moebius transformations, and the related article.