Get the Best MATH 405 Fundamentals of Modern Geometry
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 the prerequisites for this course, please refer to the Academic Course Catalog.
This course provides an introduction to modern axiomatic geometry with an emphasis on the 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.
Measurable Learning Outcomes
Upon successful completion of this course, the student will be able to:
- Distinguish between undefined terms, definitions, axioms, and theorems.
- Demonstrate the logical structure of a mathematical argument by way of a geometric proof.
- Explain why a false argument is not valid.
- Outline a proof, indicating the basic steps used when provided with valid proof.
- Prove classical theorems (of Incidence, Neutral, Euclidean, and Hyperbolic Geometry).
- Demonstrate through proof the differences that assuming the parallel postulate makes in a geometric system.
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 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 citations 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.
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.
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