Fundamentals of Modern Geometry – MATH 405

CG • Section 8WK • 07/01/2018 to 12/31/2199 • Modified 05/25/2022

Course Description

A treatment of the foundations of modern Euclidean geometry and an introduction to non-Euclidean geometries with emphasis on hyperbolic geometry. The course focuses on demonstrating and explaining geometric concepts through axiomatic methods.

For information regarding prerequisites for this course, please refer to the Academic Course Catalog.


This course provides an introduction to modern axiomatic geometry with an emphasis on presentation of proofs. The geometry of Euclid is approached through axioms of incidence, betweenness, congruence, continuity, and parallelism. A great deal of emphasis is placed on the development of Plane, Neutral and Euclidean geometry, and also includes basic theorems of non-Euclidean geometry.

Course Assignment

Textbook readings, presentations, and documents

Course Requirements Checklist

After reading the Course Syllabus and Student Expectations, the student will complete the related checklist found in the Course Overview.

Discussions (2)

Discussions are collaborative learning experiences. Therefore, the student will create a thread in response to the provided prompt for each discussion. Each thread must demonstrate course-related knowledge and include proper APA citation when applicable. In addition to the thread, the student is required to reply to 2 classmates’ threads.

Video Demonstration Assignment

The student will create a video of the proof provided in the assignment instructions.

The Video Demonstration must be concise, precise, and well-practiced before taping. The video must include an introduction in which the student visually introduces himself or herself and what is being demonstrated. While the style and method of presentation can (and probably should) vary depending on the student, the demonstration must be logically sound and organized with reasons provided as steps are undertaken. Demonstrations must be less than 6 minutes long, and points will be deducted for videos over 6 minutes long. 

Homework Assignments (4)

Homework will be assigned each Module: Week and will be submitted bi-Module: Week.

Project Assignments (2)

There will be two individual projects. These projects will apply directly to the educational/instructional aspect of geometry.

Quizzes (4)

Each quiz will be timed, open-book/open-notes, and cover the Learn material for the assigned Modules: Weeks.

Quiz: Midterm Exam

The test will be timed, open-book/open-notes, and cover the material assigned for Module 1: Week 1 — Module 4: Week 4.

Quiz: Final Exam

The Final Exam will be timed, open-book/open-notes, and cover the material for Module 5: Week 5 — Module 8: Week 8.