MATH 335: Foundations of Geometry
Prerequisites: MATH 235 or permission of instructor
Credit hours (3)
The course presents a formal axiomatic development of Euclidean geometry with an emphasis on valid arguments. Development of spatial visualization and geometric modeling to explore and analyze geometric shapes, structures, and their properties from both formal and informal perspectives is an important part of the course. The content is presented as a sequence of theorems, each rigorously proven using axioms and earlier theorems. The goal is to develop students’ deeper understanding of geometric content and their ability to think critically. Some attention is also given to non-Euclidean geometry.
Detailed Description of Course
Course content includes the following geometric topics and corresponding axioms, lemmas, corollaries, and theorems:
1) Axiomatic Systems
2) Selected Topics in Non-Euclidian Geometry
3) Geometric Constructions
5) Parallel and Perpendicular Lines
7) Circles and their properties
9) Trigonometric relationships
10)Measurement in 1-D; 2-D; 3-D
Detailed Description of Conduct of Course
Course instructors will focus on assisting students to develop a deeper understanding of geometry presented in this class, as well as to develop reasoning skills. Instruction will include cooperative/group learning and projects, student presentations, small group and whole class discussions and questioning, and student explorations of geometric concepts using manipulatives and technology. Diverse assessments will be used, including formative assessments where students monitor their own learning which helps to guide instructional
Goals and Objectives of the Course
The primary goal is to prepare students to think critically and creatively about ideas, issues, problems, and texts both within and across academic disciplines. Upon successful completion of this course, students will be able to:
1) Write formal and informal/outlined geometric proofs,
2) Conjecture and perform individual and/or group mathematical investigations in a shared process of inquiry and problem-solving.
3) Perform constructions of visualizations using appropriate technology and/or physical models
4) Deeply understand the connections among course concepts, procedures, and applications while also developing proficiency with
geometric skills, including constructing logical and persuasive arguments.
5) Understand axiomatic reasoning and the role it has played in the development of mathematics.
Graded tasks may include homework, quizzes, and written exams. They may also include writing assignments, self or peer assessments, individual or group projects or presentations, and class participation.
Other Course Information
Review and Approval
November 7, 2017
October 14, 2016
June 15, 2015