THE NEWMAN SCHOOL
GEOMETRY
Course Syllabus for 2011-2012
Mr. McCallum Room 33
COURSE DESCRIPTION:
The course begins with a discussion of the axiomatic method and the related concept of deductive proof. All high school geometry today is based on Euclid's Elements, and is usually presented as a hybrid of ancient Greek methods and the more modern analytic geometry. We'll roughly follow the historical development of the subject, beginning with a guided reading of the relevant parts of Elements and gradually introducing algebraic techniques and the Cartesian coordinate system (although a few exceptions will be made for some of the most useful modern methods, which will be introduced as soon as possible). This way the student gets an idea of how the subject changed over time and hopefully has a better appreciation of the power of modern techniques. While studying Euclid, straightedge and compass constructions will occasionally be considered when they provide worthwhile practice with proofs, but they will not be a major consideration throughout the course.
After our work with Euclid, we'll introduce the Cartesian coordinate system, which unites geometry and algebra to their mutual benefit and can justly be called one of the most important developments in mathematics. We'll use this new tool to describe curves algebraically and plot their graphs, with a special focus on linear functions. Finally, we'll study some basic three dimensional geometry and end the course with a discussion of volumes of solids.
TEXTBOOKS:
1) Elements, Euclid
Note: The online bookstore lists the Dover edition. If you get this edition, only get volumes 1
and 2. We won't need volume 3. Another option is the Green Lion edition, whose ISBN-13 is
978-1888009194. The text is also free online and can be viewed at
http://aleph0.clarku.edu/~djoyce/java/elements/elements.html
or downloaded as a PDF from
http://farside.ph.utexas.edu/euclid/Elements.pdf.
These versions may be slightly different from the Dover and Green Lion editions but they should
be close enough to use as a source. If you do use one of these free editions, you must print out
the necessary pages beforehand and bring them to class with you (no laptops, phones, or ipads are allowed in class).
2) Geometry, Larson, Boswell, Stiff. 2004
OTHER RESOURCES:
1) GeoGebra is freeware that allows you to carry out geometric constructions and also functions as a powerful graphing calculator. I'll make frequent use of it in class and it will be helpful to have, but it's optional: http://www.geogebra.org/cms
2) A scientific calculator will come in handy. There's no need for a graphing calculator in this course.
GRADING:
Quizzes: 50%
Homework: 30%
Participation and effort: 20%
Homework will be collected at the start of each class. Any student with incomplete homework will be assigned to tutorial to make it up. Quizzes will be announced at least three days in advance and must be made up on the first day back in case of absence. Each semester comprises two quarters and the semester grade will be the average of the two quarterly grades.