Math 130, Spring 2019

Information for students

Syllabus
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.

Textbook

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 lib.berkeley.edu). 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)


January 22: intro, Euclid's postulates
   Reading: Stillwell 1.1
   Handout: Euclid's Elements
      for the adventurous, here's a Greek version
January 24: Euclid's constructions; Thales' theorem
   Reading: Stillwell 1.1–1.3 / Hartshorne 1–2
   Random: story about Thales by Plutarch (starts at VI, goes onto page 419)
   Activity: Euclid: the game
   Activity: Play with Geogebra
January 29: arithmetic with Euclidean constructions
   Reading: Stillwell 1.3–1.4
   Review for Thursday: fields (16.1—2)
   Worksheet 1: click here
 * Homework 1: click here
January 31: square roots; parallel postulate
   Reading: Stillwell 1.5–2.2
   Reading: Critique of superposition, Hartshorne pp 31–34
February 5: area; Thales' theorem
   Reading: Stillwell 2.3–6 / Hartshorne 22
 * Homework 2: click here
February 7: equidecomposability
   Some resources: Hartshorne 22, Wikipedia, interactive demonstrations
   For fun: Hinged dissections
February 12: constructibility
   Reading: field extensions
   Reading: Constructible n-gons and field extensions (from Conjecture and Proof by M. Laczkovich)
   Reading: Hartshorne 28–29
   Video: Construction of 17-gon (other videos: 1 and 2)
February 14: more constructibility; impossible constructions
   Reading: see February 12
 * Homework 3: click here
February 19: constructibility of regular polygons; Gauss–Wantzel theorem
   Reading: Regular polygons (from Galois Theory by Ian Stewart)
February 21: Hilbert's axioms: incidence and betweenness
   Reading: Hartshorne 6–7
   Notes on the real projective plane: click here
 * Homework 4: click here
February 26: betweenness: plane/line separation; rays, angles, triangles
   Worksheet 2: click here
   Reading: Hartshorne 7
February 28: intro to project; more betweenness: crossbar theorem, "in between point"
   Reading: Hartshorne 7
March 5: Midterm (in class)
   Material: everything up to and including betweenness (Feb 26 class), all homework questions
             plane/line separation, angles, but no triangles, no crossbar theorem, no "in between point"
   You will be given a list of Hilbert's axioms
   You do not need to cite Euclid's axioms by number (you can assume unique lines); any construction will be "from the axioms" unless stated
   I will not ask you to reprove anything we did in class, but you might need to give definitions
March 7: congruence axioms
   Reading: Hartshorne 8–9
 * Homework 5: click here
March 12: finishing Hilbert's axioms; starting projective geometry
   Reading: Hartshorne 10, Stillwell 5.1–5.3
   Reading: How to Win the Lottery with Projective Geometry (from How Not To Be Wrong, by Jordan Ellenberg)
March 14: projective geometry
   Reading: Stillwell 5.1–5.5
 * Homework 6: click here
March 19: fractional linear transformations; invariants
   Reading: Stillwell 5.5–5.9
March 21: cross-ratio; other projective planes
   Reading: Stillwell 5.7–5.9
April 2: projective Pappus, Desargues; planar ternary rings
   Reading: Stillwell 6
   Worksheet 3: click here
 * Homework 7: click here
April 4: geometry via transformation groups
   Reading: Stillwell 7.1–7.3
April 9: Möbius transformations; hyperbolic lines; angles
   Reading: Stillwell 8.1–8.5
 * Homework 8: click here
April 10: angles; disc model; hyperbolic distance
   Reading: Stillwell 8.6–8.7
April 16: area on sphere and hyperbolic plane
   Reading: Stillwell 8.5
April 18: practice presentations
April 23, 35, 30, May 2: presentations
May 16: Final exam (in class, 8:10am–11am)
	Details on bCourses announcement

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