MATHS 345: Survey of Geometries (4)

Syllabus

1.  Prerequisites:         MATHS 166, MATHS 215, and MATHS 217

2.  Course Description:  A comparative study of Euclidean and non-Euclidean geometries, their respective histories and technologies, and their applications in mathematics, the sciences, and modern life.

3.  Course Objectives:  Students will compare and contrast the axiomatic bases for Euclidean and non-Euclidean geometries, investigate their features and solve problems using modern technologies, and explore their applications in mathematics, the sciences, and modern life.

4.  Course Rationale:  The audience for this course consists primarily of secondary mathematics education majors and other mathematics students who desire a broad foundation in geometry.  Students will develop an understanding of and appreciation for both Euclidean and non-Euclidean geometries, their histories and technologies, and applications in the modern world.

5.  Course Content:  Topics covered include Euclidean geometry, hyperbolic geometry, transformation geometry, and analytic geometry.  Additional topics may be chosen from projective geometry, differential geometry, spherical geometry, fractal geometry and chaos, finite geometry, neutral geometry, geometric topology, and geometric modeling tools such as Logo, the Geometers Sketchpad, NonEuclid, Mathematica, Matlab, and WWW-based computational resources.

6.  Course Format:  Methods of instruction include lecture, small group activities, and computer labs. Consistent with state and national recommendations, instruction will emphasize mathematical reasoning, problem-solving, communication, connections, and the use of modeling technologies to facilitate conceptual development and formulation and testing of mathematical conjectures.

7.  Methods of Evaluating Student Performance:   Course grades are determined principally by student performance on tests, quizzes, and projects.  At the instructor’s discretion, participation in daily activities and assignments may also be a factor. Certain performance assessments conducted to meet specific certification requirements related to this course may or may not be factored into the course grade, at the discretion of the instructor, but are required of all students pursuing teacher certification.

8.  Evaluation of the Course:  Instruction is assessed by departmental student and peer evaluations.  The course is periodically reviewed, evaluated, and revised by the Departmental Undergraduate Programs Committee.

M. Toda, J. Emert, D. Thomas  2/05/01

V. Mascioni  04/07/04

M. Begum, 10/17/05