MATH 403
FOUNDATIONS OF GEOMETRY
- Catalog Entry
MATH 403. Foundations of Geometry
Three hours lecture (3).
Prerequisite: MATH 200
Systems of postulates in a comparison of Euclidean and non-Euclidean geometries; geometric structures such as incidence geometry and transformational geometries are developed.
- Detailed Description of Content of Course
The following is an outline of the mathematical content:
(a) Neutral Geometry
The basic theorems of Euclid's geometry before the introduction of a parallel postulate are developed.
(b) Lobachevskian Geometry
As an alternative to Euclid's parallel postulate, the parallel postulate of Lobachevskian geometry is considered with the resulting effects. Models are used to demonstrate relative consistency.
(c) Theory of Incidence and Models.
An axiomatic approach is used to develop the incidence properties and models of this geometry are considered.
(d) Transformational Geometry
Euclidean geometry is developed from an abstract algebra point of view by using transformational geometry. The historical developments in geometry will be used as a basis for the course. Neutral geometry, with its origins in Euclid and its extension with Saccheri’s work, to the more recent development in transformational geometry will be reviewed from a historical perspective.
The history of the main results of the course will also be discussed.
- Detailed Description of Conduct of Course
Instruction will take place in a variety of modes. The instructor will lecture. The students will work to solve problems in cooperative groups. Students will be assigned homework problems which will be done on an individual basis.
- Goals and Objectives of the Course
This course is intended for mathematics majors who plan to teach mathematics at the secondary level. Students are expected to develop the skills necessary to successfully address geometric problems in a variety of settings.
- Assessment Measures
Tests, homework assignments, class attendance and participation will be used to determine grades.
- Other Course Information
Only mathematics majors who plan to teach at the secondary level will be encouraged to take this course.
- Review and Approval
DATE ACTION APPROVED BY
Sept. 2001 Review Stephen Corwin, Chair |