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Homework 1
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due Wednesday, January 16
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Reading: [AG] Chapter 1; Euclid Elements
Book1
[AG] Chapter 2 (up to page 36)
Writing: [AG] 1A, 1B, 1C (for 1C,
rewrite Prop. 3, 6, 9, 10, 27 from Euclid’s Book I)
Bonus: replace any one of the
problems above with 1D
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Additional homework for Week 1
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Make a reference list for yourself which includes
Euclid’s ``logical definitions” (from the first 23), 5
Postulates and 5 Common notions. Bring it to class.
Discussion board: post an entry
describing why you are taking the class; due Wednesday, January 9th,
by midnight
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Homework 2
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due Wednesday, January 23
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Reading: Appendix E, Appendix F, rest of Chapter 2
Writing: EA, EB, EC; 2B, 2D, 2E, 2F, 2G, 2H, 2I
Bonus: Prove
that Axiom 2 holds for the Poincare half plane model (you may use all the
“standard high school geometry” facts)
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Homework 3
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due Wednesday, January 30
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Reading: Appendix G, Appendix H
Writing: 2N, 2O, 2Q, 2T, 2U, GC(a, d, e, l, m, n, o), GD
Notes on writing proofs for Ch. 2: 1) It’s ok to
do only the “paragraph style proof” but make sure everything is
justified! 2) You can refer to the preceding theorems.
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Homework 4
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due Wednesday, February 6
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Reading: Chapter 3
Writing: 3A, 3B, 3C
Bonus: Prove that there exists a bijective function f:R→R2
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Homework 5
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due Wednesday, February 13
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Reading: Chapter 3
Writing: 3D, 3F, 3G, 3H, 3J
Complete the statement of Theorem 3.22 (Euclid’s
common notions) in your notes and add the proof; add statements of 3.23 and
3.32 and the proof of 3.23 (only!) to your notes – by Friday, Feb 8,
in class.
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Homework 6
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due Wednesday, February 20
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No homework due
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Homework 7
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due Wednesday, February 27
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Reading: finish chapter 3. Work through the proof of
Theorem 3.50
Writing: Homework 7
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Homework 8
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Due Wednesday, March 6
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Reading: Chapter 4
Special assignment: add formulation of Theorem 4.11
(Euclid’s common notions for angles) to your notes
Writing:4A, 4C, 4D, 4E, 4F
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Homework 9
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Due Wednesday, March 13
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Reading Finish chapter 4
Writing: 4H, 5B, 5C, 5D, 5F
Additional problem (assigned for
everyone) Let S,
T, U, V be four convex sets on the plane such that any three of them have a
non-trivial intersection. Prove that all four sets share a common point.
Bonus problem (last chance
to get bonus points to improve your hw score). Let S1, S2, ..., Sn be convex
sets on the plane such that any three of them have a non-trivial
intersection. Prove that all n sets share a common point.
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Homework 9
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Additional
homework for Week 9
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Read and understand the Pappus’ proof of the Isosceles triangle theorem; then write it
in your notes
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