Mathematics 467, Section 900, Fall 2021

Modern Geometry

Announcements (reverse chronological order)

• 6 Dec: New items added below:
  • final exam preview
  • proof of Uniformity Theorem
  • Final exam key from Spring '21
• 30 Oct:
  1. An old solution to [the ancestor of] the angle-ordering questions is now posted below.
  2. The discussion topics for the Chapter 4 group work now exist in Canvas.
• 27 Oct: Revisions of the midterm test essay are due Monday, 1 November.
• 22 Oct: Revisions of Paper 1 are due Friday, 5 November (2 weeks from today).
• 13 Oct: Math Club meeting Tuesday, 19 October
• 19 Sep: I will be unable to hold the office hour on Wednesday, 22 September. It is quite likely that I will be late for the office hour on Thursday, too.

Course procedures and resources

• Course handout (syllabus) in PDF (please read).
• Chapter 1 exercises (in case your book arrives late)
• Instructor: S. A. Fulling
  Office: Blocker 620H (but I'm often not there during the pandemic)
  ZOOM office hours: 957 9632 7828 ._. T 2-3, W 3-4, R 2:45-3:45 (subject to change)
  The passcode will be announced in class.
• Please see my home page for up-to-date office hours.
• Canvas (Submit group work and read that of others; check your grades.)
• Weekly schedule of topics
• Summary of axioms, definitions, and theorems ._. misprints
• Review exercises for Chapter 2 (a correction to the textbook)
• Policies about term papers (subject to change) ._._. Guidelines for authors ._._. MAA Reference Guide
• Help from ITS about how to put math content into a wiki, or attach a file to it.
• Information from University Writing Center
• Proof of Proposition 3.13
• Solution to Exercises 4 and 5 of the 4th homework (angle ordering)
• Preview of midterm exam.
• Preview of final exam.
• Excerpt from Halsted's report on Dehn's models (G. B. Halsted, Science 14 (1901) 705-717). The missing words at the beginning are
  • Manning says, p. 27: "The three hypotheses give rise to three systems of geom-"
• Outline of proof of uniformity theorem ._. file 1 ._. file 2

Old class home pages

• Spring 2021
• Fall 2020
• Spring 2019
• Fall 2017
• Spring 2017
• Fall 2016
• Fall 2015
• Fall 2014
• Fall 2013
• Spring 2013
• Spring 2011
• Fall 2010
• Fall 2009
• Spring 2009 ._. Note that the point value of the final exam was larger that time.

Lecture notes

Printer version

• Chapter 1
• Chapter 2
• Chapter 3
• Chapter 4
• Chapters 5 and 6
• Interlude: Arc Length and Riemannian Metric Geometry
• Chapter 7

Projector version

• Chapter 1
• Chapter 2
• Chapter 3
• Chapter 4
• Chapters 5 and 6
• Interlude
• Chapter 7

Weekly instructions

• Week 1 (Introduction and Chapter 1)
• Weeks 2 and 3 (Chapter 2)
• Weeks 4 and 5 (Chapter 3, betweenness part (and Chapter 8))
• Weeks 6 and 7 (Chapter 3, remainder)
• Weeks 8 and 9 (Chapter 4)
• Weeks 10 and 11 (Chapters 5 and 6)
• Weeks 12 and 13 (Chapter 7)
• Week 14 (Appendix A (and Chapter 8))

Test solutions

• Midterm
• Last semester's final (missing from Calclab)
• Final

External resources

• MacTutor History of Mathematics Archive (University of St. Andrews)
• Evans Library mathematics course guide and mathematics subject guide
• University Writing Center
• Maurits Escher's visions of the Poincare disc
• David Borthwick's lecture on hyperbolic surfaces
• Example of reductio ad absurdum combined with reasoning by cases (A. J. Lerner, F. Loewe, R. Goulet): Google "If ever I would leave you (lyrics)"

Go to home pages: Fulling ._._. Fulling on people ._._. Math Dept ._._. University

e-mail: fulling@math.tamu.edu