# Math 351, College Geometry, Fall 2017

## MWF 8:30 a.m. – 9:20 a.m., 3128 Schaap

Instructor: Aaron Cinzori
Office: 216 VanderWerf
Office Hours: Monday and Wednesday, 2:00-2:50 p.m.; Friday, 9:30-10:20 a.m. These are times when I will be in my office and available to help you. You may drop in at these times without an appointment. I am also available at many other times by appointment. You may set up an appointment by phone, email, or in person. Finally, if you see me in my office, feel free to pop in. I'll be happy to help you if I can or schedule a mutually agreeable meeting time. Email: cinzori@hope.edu
Phone: 395-7528 (my office), 395-7530 (math department)

All page references are for Roads to Geometry, 3rd ed. by Wallace and West.

Sunday, August 27:

• Read and understand the Preface and pages 1-5 (section 1.1).
• Be prepared to present solutions to problems 1, 2, 5, 8, and 10 from pages 5-7.

Wednesday, August 30:

• Read and understand pages 8-16 (section 1.2).
• Be prepared to present solutions to problems 8 and 10 in section 1.1 from pages 6-7 and problems 1-9 and 12 in section 1.2 from page 17.
• On Friday, hand in your solution to problem 5 on page 6 (section 1.1).

Friday, September 1:

• Be prepared to present solutions to problems 1-9 and 12 in section 1.2 from page 17.

Monday, September 4:

• Be prepared to present solutions to problems 5-9, 12, and 14-16 in section 1.2 from pages 17-18.
• On FridayWednesday, hand in your solution to problem 2 on page 17 (section 1.2).

Wednesday, September 6:

• Read and understand pages 19-21 (Four-Point Geometry in section 1.3).
• Be prepared to present solutions to problems 9, 12, 16, 20, 21, and 24 in section 1.2 from page 18 and problems 1-11 in section 1.3 from pages 24-25.
• On Friday, hand in your solution to problems 14 and 15 on page 18 (section 1.2).

Friday, September 8:

• Read and understand pages 21-24 (Geometries of Fano and Young in section 1.3).
• Be prepared to present solutions to problems 20, 21, and 24 in section 1.2 from page 18 and problems 1-11 and 14-17 in section 1.3 from pages 24-26.

Monday, September 11:

• Be prepared to present solutions to problems 6-11, 14-17, and 22-27 in section 1.3 from pages 25-26.
• On Wednesday, hand in your solutions to problems 24 on page 18 (section 1.2) and 5 on page 25 (section 1.3).

Wednesday, September 13:

• Be prepared to present solutions to problems 14-17, and 22-27 in section 1.3 from pages 25-26.
• On Friday, hand in your solution to problem 15 on page 25 (section 1.3).

Friday, September 15:

• Read and understand pages 28-30 (section 1.4).
• Be prepared to present solutions to problems 2-4 and 5 section 1.4 from page 31.
• On Monday, hand in your solution to problem 26 on page 26 (section 1.3).

Monday, September 18:

• Be prepared to present solutions to problems 3-5 and 7-9 in section 1.4 from pages 31-32. Problems 7-9 in particular are going to take some work, so make sure to spend some time with them.
• Note the bit of vocabulary in problem 6 on page 32.

Wednesday, September 20:

• Be prepared to present solutions to problems 7-9 in section 1.4 from pages 31-32.

Friday, September 22:

• On Monday, hand in your solution to the following problem (which is a special case of problem 7 on page 32): Prove that, in a finite, affine geometry, if $$\ell_1$$ and $$\ell_2$$ are intersecting lines for which $$\ell_1$$ has exactly 3 points and $$\ell_2$$ has at least 2 points, then $$\ell_2$$ must have 3 points.
• Try to complete the version of the above problem in which $$\ell_1$$ and $$\ell_2$$ are parallel rather than intersecting.
• Now solve the full problem 7 starting with one line with $$n$$ points and another line with $$n+1$$ points (in both the intersecting and parallel cases).
• Be prepared to present solutions to problems 7-9 in section 1.4 from pages 31-32.

Monday, September 25:

• On Wednesday, hand in your solution to the part of (the full general) problem 7 on page 32 in which the initial two lines are parallel.
• Be prepared to present solutions to problems 9 and 14 in section 1.4 from pages 32-33.

Friday, October 6:

• Read and understand pages 35-49 (sections 2.1-2.3). Pay particular attention to the different interpretations and development of the parallel postulate.
• Be prepared to present solutions to problems 2, 4 and 13 on pages 45-47 (section 2.2) and problems 1-7 and 9-10 on pages 49-51 (section 2.3).

Wednesday, October 11:

• Read and understand pages 65-80 (sections 2.6-2.7). You can ignore references to Hilbert's geometry and Birkhoff's geometry.
• Be prepared to present solutions to problems 9-10 on pages 50-51 (section 2.3), problems 2-4, 6, 7, 10, and 11 on pages 71-72 (section 2.6), and problems 1-3, 5, and 6 on pages 80-81 (section 2.7).
• On Friday, hand in your solutions to problems 3-7 on page 50 (section 2.3).

Friday, October 13:

• Read and understand pages 82-88 (sections 3.1-3.2).
• Be prepared to present solutions to problems 1-3, 5, and 6 on pages 80-81 (section 2.7) and problems 1 and 4-13 on pages 88-89 (section 3.2). I'll assign presenters to the 3.2 problems via email because they're a bit longer.

Friday, October 20:

• Read and understand pages 89-93 (section 3.3).
• Be prepared to present solutions to problems 11-13 on pages 88-89 (section 3.2) and problems 1-2, 4-8, and 10 on page 94 (section 3.3). I'll assign presenters to the 3.3 problems via email because they're a bit longer.

Monday, October 23:

• On Wednesday, hand in your solution to problem 13 on page 89.
• Be prepared to present solutions to problems 1-2, 4-8, and 10 on page 94 (section 3.3).

Wednesday, October 25:

• Be prepared to present solutions to problems 2, 4-8, and 10 on page 94 (section 3.3).
• On Friday, hand in your solution to problem 1 on page 94 (section 3.3).

Friday, October 27:

• Write up careful solutions to problems 4 and 5 in section 3.3.

Monday, October 30:

• Read and understand pages 94-101 (section 3.4). You may want to collect somewhere in your notes a list of all the things that are equivalent to the Euclidean Parallel Postulate. Also, spend some time with the proof of Theorem 3.4.9; there's a lot going on there.
• Prepare solutions to problems 1, 2, and 4.
• Be prepared to present solutions to problems 3, 5-8, and 10-12 on page 101-102 (section 3.4). I'll assign presenters for these by email.

Monday, November 13:

• Read and understand pages 102-115 (sections 3.5 and 3.6).

Wednesday, November 22:

• Be prepared to present solutions to problems 1-16, 18-21, 24-26, and 28-32 on pages 115-119 (section 3.6). I'll assign presenters for some of these by email.