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. Only selected homework problems will be graded. You are expected to be familiar with high-school geometry; for review, see regentsprep.
Grading: The course grade will be determined as follows: 10% HW and participation + 25% Exam 1 + 25% 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 to improve what you hand in. (5.) Come to office hours with any remaining questions.
| Date | Topic | Reading | HW | |
| 1 | 26-Jan | Euclidean constructions | 1.1 - 1.3 | 1.2.1-1.2.3, 1.3.3-1.3.6 |
| 2 | 28-Jan | Thales' Theorem, similar triangles | 1.4 - 1.5 | 1.4.1-1.4.4 |
| 3 | 2-Feb | Parallel and congruence axioms | 2.1 - 2.2, Properties of quadrilaterals. | 2.1.1-2.1.5, 2.2.1-2.2.3 |
| 4 | 4-Feb | 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 | 9-Feb | 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 | 11-Feb | Pythagorean Theorem revisited, other proofs | 2.8, cut-the-knot, gogeometry, Givental | 2.8.1-2.8.3 |
| 7 | 18-Feb | Coordinates | 3.1 - 3.5 | 3.2.1-3.2.6, 3.3.1, 3.4.1-3.4.3 |
| 8 | 23-Feb | Concurrence in triangles Chords, arcs and angles in a circle |
regentsprep | Regents Exam |
| 9 | 25-Feb | Geometry on NY Regents Exam | regentsprep | |
| 10 | 2-Mar | Review | F07 Exam 1 | |
| 11 | 4-Mar | Exam 1 | S09 Exam 1 | |
| 12 | 9-Mar | Isometries, Three Reflections Theorem | 3.6 - 3.8 | 3.6.1-3.6.4, 3.7.1-3.7.3 |
| 13 | 11-Mar | Classification of plane isometries | cut-the-knot, wikipedia | |
| 14 | 16-Mar | Group of isometries, vectors | 7.1, 4.1 - 4.2 | 7.1.1-7.1.3, 4.1.3-4.1.4, 4.2.1-4.2.2 |
| 15 | 18-Mar | Concurrence, inner product | 4.3 - 4.6 | 4.3.2-4.3.5, 4.4.1-4.4.2, 4.5.1-4.5.3 |
| 16 | 23-Mar | Matrices, transformations, isometries | 4.7, 7.2 | 7.2.1-7.2.6 |
| 17 | 25-Mar | Spherical geometry | 7.4 - 7.5, Polking | 7.4.1-7.4.5 |
| 18 | 30-Mar | Review | Review Problems for Exam 2 | |
| 19 | 1-Apr | Exam 2 | Exam 2 solutions | |
| 20 | 6-Apr | Perspective drawing, projective plane | 5.1 - 5.3 | 5.1.1-5.1.3, 5.2.2, 5.3.1-5.3.2 |
| 21 | 20-Apr | Desargues Thm, linear fractional functions, cross-ratio | 6.1 - 6.2, 5.5 - 5.8 | |
| 22 | 22-Apr | Hyperbolic geometry introduction | 8.1 - 8.9 | |
| 23 | 27-Apr | Classification of surfaces | Shape of Space 1 - 6, 8, and Fiedorow | Online resources for Shape of Space |
| 24 | 29-Apr | Geometry on surfaces | Shape of Space 7, 10, 11 | |
| 25 | 4-May | Gauss-Bonnet Theorem and Euler Characteristic | Shape of Space 9, 12 | |
| 26 | 6-May | Euler Characteristic and regular polyhedra | Regular polyhedra classified using the Euler Characteristic | |
| 27 | 11-May | Review | ||
| 28 | 13-May | Review |
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