The glide reflections 'handout'.
The hyperbolic tape measure (what was going to be the last lecture of the course).
Moebius Transformations Revealed is a very pretty video of Moebius transformations (of the entire complex line), with a very nifty way of thinking about reflections across circles. A geometry video with 1,870,863 views is a really amazing accomplishment.
Symmetry Artist: a simple, user-friendly drawing tool for symmetric figures. You draw something with the mouse and it creates the specified reflections or rotations of your curve as you draw.
The linear algebra and geometry sections from the California math standards for K-12 teachers (officially "Mathematics Teacher Preparation in California: Standards of Quality and Effectiveness for Subject Matter Programs"), with particularly course-relevant topics highlighted.
Evaluations are now submitted through eCommons and clicking on the Evaluation System link in the sidebar. Math's evaluation window closes Monday, 4:00 AM (before the final, of course)
Practice final exam problems
Midterm solutions (in case you want them for review)
Cayley exercises solutions
INSTRUCTOR
Instructor: Debra Lewis
Office: 4122 McHenry
Phone: 459-2718
E-mail: lewis [add the usual address info]
TA: Wei Yuan
Office:
E-mail: wyuan2 [add the usual address info]
TIMES AND PLACES
Lecture: MWF 12:30PM-01:40 PM, Engineering 2 194
Sections: Monday 4:00-5:10 PM, 1279 McHenry, and
Friday 11:00-12:10 AM, 1257 McHenry
D.L.'s office hours: Monday, 11:00-12:00, Tuesday 12:00-1:30, Wednesday 2:00-3:00.
W.Y.'s office hours: Tuesday 2:00-3:00, Thursday 12:00-2:00
TEXT
The Four Pillars of Geometry, by John Stillwell. Springer, 2005.
FREE ONLINE GEOMETRY AND LINEAR ALGEBRA BOOKS
POSSIBLY USEFUL WEB SITES
The Mathematica Demonstrations
project has some interesting geometry demos.
Mathematica
notebook
for rectangle/parallelogram conversions and the Pythagorean theorem.
You will need to download and install
Mathematica Player
(it's free) to run this if you don't have Mathematica on your machine.
I haven't used Player before; let me know if you have problems with it.
MIT OpenCourseWare course on linear algebra, taught by Professor Gil Strang.
Perspective Geometry, a website/online journal edited by Tomás García-Salgado
SUPPLEMENTAL TEXTS AND RESEARCH PAPERS
Secret Knowledge, by David Hockney (the use of optics in Renaissance art). On reserve in the Science and Engineering library.
The Science of Art, by Martin Kemp (perspective drawing etc.). On reserve in the Science and Engineering library.
OPTIONAL EXTRA CREDIT PROJECT
TENTATIVE LECTURE SCHEDULE
| Monday | Wednesday | Friday |
| September 23: 1.1-2. Introduction, constructions | ||
| September 26: 1.3-4. More constructions, multiplication and division | September 28: 1.5. Similar triangles | September 30: 2.1-2. The parallel and congruence axioms |
| October 3: 2.3-4. Area | October 5: 2.5 Pythagorean theorem | October 7: 3.1-3. The line and plane, distance |
| October 10: 3.4-5. Intersections of lines and circles, angles | October 12: 3.6-7. Isometries | October 14: 4.1-2. Vectors and linear independence |
| October 17: 4.3-4. Midpoints and centroids, the inner product | October 19: 4.4-5. The inner product and cosine | October 21: 5.1-2. Perspective drawing |
| October 24: 5.3. Projective plane models and axioms | October 26: MIDTERM | October 28: 5.4. Homogeneous coordinates |
| October 31: 5.5. Projection | November 2: 5.6. Linear fractional functions | November 4: 5.6-7. The cross-ratio |
| November 7: 7.1. Isometries of the plane | November 9: 7.2. Vector transformations | November 11: HOLIDAY |
| November 14: 7.3. Transformations of the projective line | November 16: 7.4-5. Spherical geometry and rotations of the sphere | November 18: 8.1-2. Extending the projective line to a plane, complex conjugation |
| November 21: 8.2-3. Reflections and Mobius transformations | November 23: 8.4. Preserving non-Euclidean lines | November 25: HOLIDAY |
| November 28: 8.5. Preserving angle | November 30: 8.6. Non-Euclidean distance | December 2: 8.7. Non-Euclidean translations and rotations |
FINAL EXAM:
Monday, December 5, 8:00–11:00 AM.
GRADING
On the exams you'll be asked to do K out of N problems. You can do one or more of the remaining N—K problems for extra credit. Any points you earn on these problems will not be included in your exam score; at most, they will nudge a borderline grade or influence some of the wording in your narrative evaluation. You will be much better off doing K problems well than doing all N problems less impressively.
HOMEWORK POLICIES
Most exercises will be from the text, but some may be taken from other sources.
Late homework will be discounted and may not be accepted. I do not need to convince you that we are consistent with such decisions; don't count on the "well, you let him/her turn in last week's assignment late, so you have to let me turn this week's assignment in late" argument.
Your homework should be neatly written and well-organized, with the pages securely fastened together and your name on every page. Many of the exercises involve several nontrivial steps; make it clear to your readers (and yourself!) what it is you're doing at each step.
Clearly number the exercises and try to submit them in numerical order;
if any problems are out of sequence, indicate that at the beginning of
the assignment. (You don't need to solve them in order, just submit them
in order.)
We should not have to hunt through several pages to find a particular
problem.