Department of Mathematics Generic Syllabus
Boise State University Updated Spring 2002
MATH 311
Foundations of Geometry
3 semester credits
Catalog Description
MATH 311 FOUNDATIONS OF GEOMETRY (3-0-3)(S).
Euclidean, non-euclidean and projective geometries from an axiomatic
point of view. PREREQ: MATH 187 and MATH 175.
Prerequisites
MATH 187 and MATH 175 or permission of the instructor. Calculus is not
necessary except to ensure mathematical maturity. It is expected that
students will have had previous experience in writing proofs, as
obtained in MATH 187.
Jurisdiction
There is no committee that oversees this course. Selection of the
text and the format of the course are the prerogative of the instructor.
Learning Objectives
The objectives of Foundations of Geometry coincide with three of the
four departmental goals. MATH 311 does not stress the applications of
mathematics or the impact of technology, but it does stress the ideas
of abstraction, aesthetics, the development of mathematical tools and
the use of the language of mathematics.
This course is required of mathematics/secondary education majors, and
they usually account for the majority of the enrollment.
Upon completion of this course, students should:
- Appreciate the historical and cultural role that geometry has
played in the development of mathematics.
- Be able to give a coherent account of the rise of the axiomatic
viewpoint in geometry. The student will know both biographical
and chronological landmarks in this development.
- Be able to state the important definitions and theorems of neutral,
Euclidean, and hyperbolic geometry.
- Be able to write coherent and correct mathematical proofs.
- Have gained a perspective that mathematics is not dead, but alive
and evolving.
Assessment of Learning Objectives
Students will be assessed by evaluating their ability to do problems
based on the learning objectives. The problems will occur in several
contexts:
- Periodic problem sets for homework serve both as learning and as
assessment tools.
- Problems given on take-home exams are designed to evaluate a
student's ability to solve more complicated and time consuming
problems than can be reasonably completed on an in-class exam.
- Problems given on in-class exams are designed to see if
students can use the tools that have been developed to solve
straight forward problems in a limited amount of time.
- Students may also be expected to present solutions in class or
to work in small groups to solve problems. Both of these situations
permit the instructor to assess the student's ability to communicate
effectively using the language of mathematics.
Topics and Approximate Timeline
The following table is based on a typical semester schedule-45 class meetings
of 50 minutes each. The actual amount of time spent on each topic will vary
slightly from semester to semester and instructor to instructor.
|
|
| Number of |
| Topic | Meetings
|
| Introduction | 1
|
| Logic and Incidence Geometry | 8
|
| Neutral Geometry | 10
|
| Euclidean Geometry | 10
|
| Non-Euclidean Geometry | 10
|
| Summary | 2
|
| 3 Exams | 3 |
Text
Euclidean and Non-euclidean Geometries, Third Ed.,Marvin Jay Greenberg,
W. H. Freeman and Company, 1994
Format, Student Activities, and Grades
There is no standard format for this course. It is usually taught in a lecture
format, but it is occasionally taught using the Moore Method. The use of
powerful programs and machines is slowly being incorporated in the
course. It is usually expected, even in the lecture format, that there will be
occasional student presentations. The instructor chooses the exact
grading scheme, but a typical distribution would be:
|
|
| Homework (scaled to) | 200
|
| 2 Exams | 200
|
| Projects and Presentations | 100
|
| Final Exam | 200
|
| Total | 700
|
Letter grades are usually based on a standard scale in which 90% of the
total points guarantees an A, 80% a B, 70% a C, and 60% a D, with the
instructor having the discretion to lower these cut-offs if warranted.
File translated from TEX by TTH, version 1.56.