Handout on matrix groups, and Cayley transform mini-project description.
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.
INSTRUCTOR
Instructor: Debra Lewis
Office: 359B Baskin Engineering
Phone: 459-2718
E-mail: lewis at ucsc dot edu
(checked more often than voicemail or gmail)
and/or DebraKLewis at gmail dot com
TA: Min (Jimmy) Xue
Office: 356 Baskin Engineering
E-mail: mxue at ucsc dot edu
TIMES AND PLACES
Lecture: MWF 11:00-12:10, Earth & Marine Sciences B214
Sections: M 3:30-4:40, Th 12:00-1:10, both in Baskin Engineering 273
D.L.'s office hours: W 5:30-7:00 PM, Th 2:30-4:00
M.X.'s office hours: T 9:00-10:30, F 2:00-3:30
TEXT
The Four Pillars of Geometry, by John Stillwell. Springer, 2005.
SUPPLEMENTAL TEXTS
Euclid's Elements, by Euclid. (NSS)
The UBC Euclid's Elements
of Geometry website
has an integrated version of three different English translations: the 'classic' translation
by Thomas Heath, a vintage (1847) visuals-based translation by Oliver Byrne, and a
modern, Java-based translation by David Joyce; they also have a link to an online version of
the original Greek. A very reasonably priced hardcopy version of the
Heath translation is available.
RELATED RECREATIONAL READING
Mason & Dixon, by Thomas Pynchon. 1997.
'Pure' science, technology, and politics; some very complex geometry. (novel)
The Mathematica Demonstrations
project has some interesting geometry demos.
TENTATIVE LECTURE SCHEDULE
| Monday | Wednesday | Friday |
| September 25: 1.1-2. Introduction, constructions | ||
| September 28: 1.3-4. More constructions, multiplication and division | September 30: 1.5. Similar triangles | October 2: 2.1-2. The parallel and congruence axioms |
| October 5: 2.3-4. Area | October 7: 2.5 Pythagorean theorem | October 9: 3.1-3. The line and plane, distance |
| October 12: 3.4-5. Intersections of lines and circles, angles | October 14: 3.6-7. Isometries | October 16: 4.1-2. Vectors and linear independence |
| October 19: 4.3-4. Midpoints and centroids, the inner product | October 21: 4.4-5. The inner product and cosine | October 23: 5.1-2. Perspective drawing |
| October 26: 5.3. Projective plane models and axioms | October 28: MIDTERM | October 30: 5.4. Homogeneous coordinates |
| November 2: 5.5. Projection | November 4: 5.6. Linear fractional functions | November 6: 5.6-7. The cross-ratio |
| November 9: 7.1. Isometries of the plane | November 11: HOLIDAY | November 13: 7.2. Vector transformations |
| November 16: 7.3. Transformations of the projective line | November 18: 7.4-5. Spherical geometry and rotations of the sphere | November 20: 8.1-2. Extending the projective line to a plane, complex conjugation |
| November 23: 8.2-3. Reflections and Mobius transformations | November 25: 8.4. Preserving non-Euclidean lines | November 27: HOLIDAY |
| November 30: 8.5. Preserving angle | December 2: 8.6. Non-Euclidean distance | December 4: 8.7. Non-Euclidean translations and rotations |
FINAL EXAM:
Thursday, December 10, 12:00—3:00 PM.
GRADING
EXTRA CREDIT:
You may do an optional extra credit presentation or paper. Extra credit projects
will not be factored into your overall course score. A weak project won't influence
your grade for better or worse; a so-so project could nudge a borderline grade in the
right direction; a really nice project could improve your grade by half a grade.
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.