Math 130, Fall 2016

Information for students

bCourses Site
DSP students should speak to the instructor as soon as possible, even if you don't have a letter yet.
Guidelines on what to do if you think you may have a conflict between this class and your extracurricular activities. In particular, you must speak to the instructor before the end of the second week of classes.
Academic honesty in mathematics courses: A statement on cheating and plagiarism, courtesy of Michael Hutchings.
How to get an A in this class, courtesy of Kathryn Mann.


The required text for this course is The Four Pillars of Geometry by John Stillwell. You can download a copy of this book for free on campus through the UC library (if that link doesn't work, just search for the book at This book is a wonderful introduction, but a little too easy for us, so there will be lots of required supplementary readings supplied by the instructor. We will also use some excerpts from Hartshorne's Geometry: Euclid and Beyond Euclid. I recommend this to students wishing to go further. It can also be downloaded on campus.

Homework, Readings, etc.

(will be updated throughout the course)

Week 1 --- Thursday, August 24: Introduction to the Class Reading: Believe It, Then Don't: Toward a Pedagogy of Discomfort
Week 2 --- August 30 and September 1: Stillwell, Chapters 1 and 2 Handout: Euclid's Elements (for the adventurous, here's a Greek version) Activity: Euclid: the game Homework (due Tuesday, September 6): Click here
Week 3 --- September 6 and 8: Stillwell, Chapter 2 Reading: Critique of the method of superposition, from Hartshorne Proofs of the Pythagorean Theorem: Click here For fun: Hinged dissections Homework (due Tuesday, September 13): Click here
Week 4 -- September 13 and 15: Constructibility Reading: Constructible n-gons and field extensions (from Conjecture and Proof by M. Laczkovich) Video: Construction of 17-gon (other videos: 1 and 2) Homework (due Tuesday, September 20): Click here
Week 5 -- September 20 and 22: Hilbert's Axioms Reading: Sections 2.6 and 2.7 in Hartshorne Homework (due Tuesday, September 27): Click here
Week 6 -- September 27 and 29: Hilbert's Axioms and Intro to Projective Geometry Reading: Sections 2.8, 2.9, and 2.10 in Hartshorne Reading: How to Win the Lottery with Projective Geometry (from How Not To Be Wrong, by Jordan Ellenberg) Homework: Prepare for Midterm
Week 7 -- October 4 and 6: Midterm and Projective Geometry Cumulative Midterm: Tuesday, October 4 covering: up to and including Hilbert's Axioms (the axioms will be provided on the midterm) Independent Project: Description, Topic Suggestions, and Grading Scheme Homework (due Tuesday, October 11): Click here
Week 8 -- October 11 and 13: Stillwell, Chapters 5 & 6 Homework (due Thursday, October 20): Click here
Week 9 -- October 18 and 20: Last week of Projective Geometry No class on October 18 Reading: Wikipedia page on planar ternary rings Reading: Planar ternary rings (see Appendix I) and projective plane --> p.t.r. (see pages 127-8)
Week 10 -- October 25 and 27: Stillwell Chapters 7 & 8 Homework (due Tuesday, November 1): Click here Reading: Wikipedia pages on quaternions and on quaternions for rotations
Week 11 -- November 1 and 3: Stillwell Chapter 8 Homework (due Tuesday, November 8): Click here More on quaternions and 4-dimensional geometry: Hypernom the game, explained here Möbius transformations: video by Douglas Arnold and Jonathan Rogness, with explanation, and an interactive applet by Terry Tao.
Week 12 -- November 8 and 10: Stillwell Chapter 8 Reading: Stillwell 8.6, hyperbolic distances Optional Reading (sec. 5 on): ignore the differential geometry; "Lobachevsky" = "hyperbolic"; for us, a is always 1 Homework (due Tuesday, November 15): Click here Tilings of hyperbolic space by Jos Leys Movies of hyperbolic isometries by Goodman-Strauss
Week 13 -- November 15 and 17: Geometry on Surfaces Reading: Here (ignore the "3-manifold" parts) and here Optional Reading: The Shape of Space (by Jeff Weeks) -- chapters 1-5 Homework (due Tuesday, November 22): Click here (triangle paper)