Geometry - Summer 2019

http://ada.evergreen.edu/geometry

Outline of Instruction
Assignments

Tuesday 01:00pm - 04:30pm Lab 1 3033 Wednesday 01:00pm - 04:30pm lab 1 3033

The goal of this course is to give students a sound mathematical introduction to geometry together with an overview of the conceptual evolution of major geometrical ideas. Study begins with a look at the geometry of Euclid's Elements and then follows the development of the logical foundations of reasoning and numbers that led to both non-Euclidean geometry and modern analytical geometry. No specific mathematical prerequisites are required, but facility and comfort with reading and studying mathematics will be necessary. Upper division credit is possible for students who have completed one year of calculus. This is a great course to learn and improve on mathematical proofs. Additional options are available for continued work in non-Euclidean geometry for more advanced students.

Class time will consist of some mixture of (a) lecture and discussion on the weekly reading, (b) individual and group problem solving, and (c) presentation and discussion of problem solutions.

**Textbook:***Foundations of Geometry*, 2nd Edition by Gerard A. Venema, Pearson, 2011 ISBN: 978 0136020585*Geometry Connections: Mathematics for Middle School Teachers*, John K. Beem (not required, supplementary for teachers)-
*Euclid's Elements*by D. E. Joyce, 1998 (requires Java to be enabled for the drawings) -
*Euclid's Elements*- an alternate site - Non-Euclid program for visualizing the hyperbolic plane
- A fun model of Hyperbolic Geometry
- Supplementary handouts from:
*Plane Geometry*, by Morgan & Breckenridge

We'll go through the first 6 chapters and touch on chapter 10 of the textbook covering the following topics.

Readings are due for discussion at the beginning of the class in which they are listed in the table (except class 1 of course).Chapters 1,2 Mathematical Preliminaries Chapter 3 Axioms Chapter 4 Neutral Geometry Chapter 5 Euclidean Geometry Chapter 6 Hyperbolic Geometry Chapter 10 Transformations

Subject to AdjustmentClass Topic Textbook Chapters Lecture Notes ----- ----- ----------------- ------------- 1 Jun 25 Euclid's Elements Ch 1 Venema Ch 1 2 Jun 26 Incidence Geometry & Models Ch 2.1 - 2.4 Venema Ch2a 3 Jul 02 Logic and Proofs Ch 2.5 - 2.6 Venema Ch 2b 4 Jul 03 Numbers and Proofs Ch 2.6 and Apx E Venema Apx E Portfolio Check Ch 1-2 5 Jul 09 Plane Geometry Ch 3.1 - 3.3 Venema Ch 3a 6 Jul 10 Plane Geometry Ch 3.4 - 3.7 Venema Ch 3b 7 Jul 16 Portfolio Due Ch 1-3 8 Jul 17 Neutral Geometry Ch 4.1 - 4.4 Venema Ch 4a 9 Jul 23 Neutral Geometry Ch 4.5 - 4.9 Venema Ch 4b Portfolio Check Ch 1-4 10 Jul 24 Euclidean Geometry Ch 5.1 - 5.4 Venema Ch 5 11 Jul 30 Hyperbolic Geometry Ch 6.1 - 6.3, 6.6, 6.9 Venema Ch 6 12 Jul 31 Transformations Ch 10.1-10.5 Venema Ch 10 Aug 01 Portfolios Due Ch 1-6