2011 spring

Math 329, Geometry, Spring 2011

M 4:40 - 6:20 1S-107 (Section 6952)
W 4:40 - 6:20 1S-219 (Section 6952)

Instructor:	Joseph Maher
Office:	1S-222
Office hours:	M 2:30-4:30, W 3:30-4:30
Webpage:	http://www.math.csi.cuny.edu/~maher/teaching
Email:	joseph.maher@csi.cuny.edu
Phone:	(718) 982-3623

Required textbook: The Four Pillars of Geometry by John Stillwell. You must also buy an (inexpensive) compass and ruler.

Recommended additional textbook: The Shape of Space, Second Edition, by Jeff Weeks.

Goals: The primary goal of this course is to understand geometry from different viewpoints, both classical and modern. Another goal is to learn how to write concise but complete arguments.

Homework: Assignments will be announced in class, sometimes referring to this website. I highly recommend working jointly on homework problems with fellow students. You are expected to be familiar with high-school geometry; for review, see www.mathopenref.com, a free online math textbook for high-school geometry.

Grading: The course grade will be determined as follows: 10% Homework and quizzes, 25% Exam 1, 25% Exam 2, 40% Final Exam.

Help: My office hours are on Mondays 2:30-4:30pm and Wednesdays 3:30-4:30pm, in my office, 1S-222.

Optimal Method of Study: (1.) Come to class (attendance is mandatory). (2.) Read the relevant sections and websites after class. (3.) Do the homework. Leave time to think–do not put homework off until it is due! (4.) Compare your solutions with other students. (5.) Come to office hours with any questions.

Important Dates (http://www.csi.cuny.edu/currentstudents/academiccalendars/)

Date	Topic	Reading	Homework
Mon Jan 31	Euclidean constructions	1.1 - 1.3	1.2.1-1.2.3, 1.3.3-1.3.6
Wed Feb 2	Thales’ Theorem, similar triangles	1.4 - 1.5	1.4.1-1.4.4
Mon Feb 7	Parallel and congruence axioms	2.1 - 2.2, properties of quadrilaterals	2.1.1-2.1.5, 2.2.1-2.2.3
Wed Feb 9	Pythagorean Theorem	2.3 - 2.5, pythagorean triples	2.3.2-2.3.3, 2.4.1, 2.4.4, 2.5.1-2.5.5
Mon Feb 14	Proof of Thales’ Theorem, angles in a circle	2.6 - 2.7, another construction for squaring a rectangle	2.6.1, 2.7.1-2.7.5
Wed Feb 16	Pythagorean Theorem revisited, other proofs	2.8, cut-the-knot, gogeometry, Givental	2.8.1-2.8.3
Mon Feb 21	No class
Wed Feb 23	Coordinates	3.1 - 3.5	3.2.1-3.2.6, 3.3.1, 3.4.1-3.4.3
Mon Feb 28	Concurrence in triangles, chords arcs and angles in a circle	regentsprep and mathopenref	Regents Exam
Wed Mar 2	Geometry on NY Regents Exam	regentsprep and mathopenref
Mon Mar 7	Review
Wed Mar 9	Exam 1
Mon Mar 14	Isometries, Three Reflections Theorem	3.6 - 3.8	3.6.1-3.6.4, 3.7.1-3.7.3
Wed Mar 16	Classification of plane isometries, group of isometries	cut-the-knot, wikipedia, 7.1	7.1.1-7.1.3
Mon Mar 21	Vectors	4.1 - 4.2	4.1.3-4.1.4, 4.2.1-4.2.2
Wed Mar 23	Concurrence, inner product	4.3 - 4.6, cut-the-knot	4.3.2-4.3.5, 4.4.1-4.4.2, 4.5.1-4.5.3
Mon Mar 28	Matrices, transformations, isometries	4.7, 7.2	7.2.1-7.2.6
Wed Mar 30	Spherical geometry	7.4 - 7.5, Polking, Strogatz (NYT article)	7.4.1-7.4.5
Mon Apr 4	Spherical triangles and Girard’s Theorem	Shape of Space 9, Polking	Dimensions Lectures 1 and 9
Wed Apr 6	Review
Mon Apr 11	Exam 2
Wed Apr 13	Perspective drawing, projective plane, Desargues Theorem	5.1 - 5.3, 6.1 - 6.2	5.1.1-5.1.3, 5.2.2, 5.3.1-5.3.2
Mon Apr 18	Spring break
Wed Apr 20	Spring break
Mon Apr 25	Spring break
Wed Apr 27	Hyperbolic geometry introduction	8.1 - 8.9, Shape of Space 10, 15, Isometries of the hyperbolic plane	Escher’s hyperbolic plane, cut-the-knot1, cut-the-knot2
Mon May 2	Euler’s formula and regular polyhedra	Regular polyhedra classified using the Euler Characteristic	Euler’s formula (AMS feature column)
Wed May 4	Classification of surfaces	Shape of Space 1 - 6, 8, and Fiedorow	Online resources for Shape of Space
Mon May 9	Geometry on surfaces	Shape of Space 7, 11
Wed May 11	Gauss-Bonnet Theorem and Euler Characteristic	Shape of Space 12
Mon May 16	Review
Wed May 18	Review
Mon May 23	Final