Geometry - Summer 2019
Outline of Instruction     Assignments    


Neal Nelson, Lab 1 2010, 360-867-6738,

Course Description

This class is an introduction to both Euclidean and non-Euclidean geometry suitable for teachers or others interested in gaining a deeper understanding of mathematics, mathematical proof, and the historical and conceptual evolution of geometrical ideas. The course will concentrate on problem solving and the development of mathematical skills, particularly proofs, with the goal of understanding the major conceptual developments in the history of geometry. Class activities will be primarily reading, problem solving, and discussion with lectures as needed.


The class runs for 5 weeks first session plus one extra week. Scheduling accomodations can made for students taking second session programs.
Tuesday        01:00pm - 04:30pm    Lab 1 3033
Wednesday      01:00pm - 04:30pm    lab 1 3033

Course Objectives and Organization

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 and references

Outline of Instruction

Please check the web version of this document to obtain the latest edition.

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

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


Subject to Adjustment
Class         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


All students are expected to demonstrate learning through active engagement in reading, discussion, and problem solving, plus written presentation of proofs and solutions to problems.

Credit and evaluation policy

In order to receive credit you must deliver evidence of your learning through active and knowledgeable participation in class learning activities and through demonstrable work submitted before the end of the last class. Demonstrable work in this class is primarily a portfolio of written solutions to assigned problems and proofs.