Prof. Ilya Kofman
Email: ikofman
math.csi.cuny.edu
Website: http://www.math.csi.cuny.edu/~ikofman/
| Course Time and Place: |
Mondays: 4:40pm - 6:20pm in 1S-107 Wednesdays: 4:40pm - 6:20pm in 1S-219 |
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: 30% Exam 1 + 30% Exam 2 + 40% Final Exam.
Help: My office hours are on Mondays 1:30-3:00pm and Wednesdays 3:30-4:30pm, in my office, 1S-209.
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.
| Date | Topic | Reading | HW | |
| 1 | Feb 1 | Euclidean constructions | 1.1 - 1.3 | 1.2.1-1.2.3, 1.3.3-1.3.6 |
| 2 | Feb 3 | Thales' Theorem, similar triangles | 1.4 - 1.5 | 1.4.1-1.4.4 |
| 3 | Feb 8 | Parallel and congruence axioms | 2.1 - 2.2, Properties of quadrilaterals. | 2.1.1-2.1.5, 2.2.1-2.2.3 |
| 4 | Feb 10 | 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 |
| 5 | Feb 17 | 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 |
| 6 | Feb 18 | Pythagorean Theorem revisited, other proofs | 2.8, cut-the-knot, gogeometry, Givental | 2.8.1-2.8.3 |
| 7 | Feb 22 | Coordinates | 3.1 - 3.5 | 3.2.1-3.2.6, 3.3.1, 3.4.1-3.4.3 |
| 8 | Feb 24 | Concurrence in triangles Chords, arcs and angles in a circle |
regentsprep and mathopenref | Regents Exam |
| 9 | Mar 1 | Geometry on NY Regents Exam | regentsprep and mathopenref | |
| 10 | Mar 3 | Review | F07 Exam 1, S09 Exam 1 | |
| 11 | Mar 8 | Exam 1 | S10 Exam 1 | |
| 12 | Mar 10 | Isometries, Three Reflections Theorem | 3.6 - 3.8 | 3.6.1-3.6.4, 3.7.1-3.7.3 |
| 13 | Mar 15 | Classification of plane isometries, group of isometries | cut-the-knot, wikipedia, 7.1 | 7.1.1-7.1.3 |
| 14 | Mar 17 | Vectors | 4.1 - 4.2 | 4.1.3-4.1.4, 4.2.1-4.2.2 |
| 15 | Mar 22 | 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 |
| 16 | Mar 24 | Matrices, transformations, isometries | 4.7, 7.2 | 7.2.1-7.2.6 |
| 17 | Apr 7 | Spherical geometry | 7.4 - 7.5, Polking, Strogatz (NYT article) | 7.4.1-7.4.5 |
| 18 | Apr 12 | Spherical triangles and Girard's Theorem | Shape of Space 9, Polking | Dimensions Lectures 1 and 9 |
| 19 | Apr 14 | Review | Review Problems for Exam 2 | |
| 20 | Apr 19 | Exam 2 | S10 Exam 2 | S09 Exam 2, S09 Exam 2 solutions |
| 21 | Apr 21 | 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 |
| 22 | Apr 26 | Hyperbolic geometry introduction | 8.1 - 8.9, Shape of Space 10, 15, Isometries of hyperbolic plane | Escher's hyperbolic plane, cut-the-knot1, cut-the-knot2 |
| 23 | Apr 28 | Euler's formula and regular polyhedra | Regular polyhedra classified using the Euler Characteristic | Euler's formula (AMS feature column) |
| 24 | May 3 | Classification of surfaces | Shape of Space 1 - 6, 8, and Fiedorow | Online resources for Shape of Space |
| 25 | May 5 | Geometry on surfaces | Shape of Space 7, 11 | |
| 26 | May 10 | Gauss-Bonnet Theorem and Euler Characteristic | Shape of Space 12 | |
| 27 | May 12 | Review | ||
| 28 | May 17 | Review |
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