MAT 360-01

Foundations of Geometry

Syllabus

Textbook

Description

Prerequisites

Grading

Homework Expectations

Projects

Sources of Help

Important Dates

Handouts

Axioms

Definitions

Propositions

Models and Interpretations of Incidence Geometry

 

Course Related Links

Euclid's Elements web site developed by E.E.Joyce of Clark University.

Non-Euclid web site developed by Joel Castellanos, Joe Dan Austin, and Ervan Darnell of Rice University.

The Lobachevskian Plane web site developed by Kerry E. Grant of Southern Connecticut State University.

The Geometry Site of the Cut the Knot web site developed by A. Bogomolny of CTK Software, Inc.

 

TEXTBOOK:

Euclidean and Non-Euclidean Geometries: Development and History by Marvin Jay Greenberg, W.H. Freeman and Company, 4th edition

DESCRIPTION:

Introduction to the geometries of Bolyai-Lobachesky and Riemann and their mathematical significance, critique of Euclid's axiomatic approach to geometry with modern standards of rigor, introduction to metamathematics.

PREREQUISITES:

A grade of C- or better in MAT 250 & High School Euclidean Geometry.

GRADING:

Your grade will be based on 5 exams (50 points each), a project (50 points), and an oral final exam. Make-up exams will be given in case of illness or emergency. Imminent failure is not an emergency! If you miss an exam due to illness or emergency, you must contact me on or before the day of the exam. Based on the five written exams, and the project, you will receive a range of letter grades. Based on your performance on the oral final exam, you will receive a final grade in your specific range. While partial credit will be given on all proofs on the written exams, only complete proofs will count on the final oral exam. In order for a proof to be considered, you should be able to justify all the steps in your proof, and be able to state all the axioms and definitions used in your proof. (No made up axioms or pseudodefinitions will be accepted! There is no such thing as a half proof!) The following table shows the grade expected based on the average before the final exam and the number of correct proofs (out of 4) on the final exam:

 

Average before final exam

Number of correct proofs on the final exam

 

0

1

2

3

4

93-100

A (waiver from the final exam)*

90-92

A-

A-

A-

A

A*

87-89

B+

B+

A-

A-

A*

83-86

B

B+

A-

A-

A*

80-82

B-

B

B+

A-

A

77-79

C+

B-

B

B+

A-

73-76

C

C+

B-

B

B+

70-72

C-

C

C+

B-

B

67-69

D+

C-

C

C+

B-

63-66

D

D+

C-

C

C+

60-62

D-

D

D+

C-

C

55-59

F

D-

D

D+

C-

50-54

F

F

D-

D

D+

45-49

F

F

F

D-

D

40-44

F

F

F

F

D-

0-39

F  (no final exam offered)

* if your average is  93 or higher, or between 83 and 92 and you can complete all 4 proofs on the final exam, you are eligible for the A+ challenge! (one additional proof for a grade of A+)

March 28 is the last day for course withdrawals for Spring 2007. Course withdrawals must be completed in person in the Registrar’s Office. Late course withdrawals, and incompletes will be given only in the most extreme circumstances, beyond a student’s control. (such circumstances usually require students to withdraw from all their classes, and not just this particular class!)

HOMEWORK EXPECTATIONS:

To succeed in this course, it is essential that you solve a lot of problems, and that you understand each step involved in solving problems! I will suggest homework problems in class. These problems will not be collected, but doing them will help you prepare for quizzes and exams. In order to succeed in this course, you should sacrifice at least 6 hours a week solving problems.

SOURCES OF HELP:

Many students experience difficulties understanding some of the material in a mathematics class. If this should happen to you, please seek extra help immediately. Office hours are scheduled so that you can get individual help if the need arises or if you feel you need to talk to me for any reason. If there is a conflict between my office hours and your schedule, please bring me a copy of your schedule, and we will make an appointment.

IMPORTANT DATES:

January 31

Last day to add or drop courses.

February 18-21

Presidents’ Birthdays - no classes.

March 20

Midterm grades available.

March 21-26

Spring Break – no classes.

March 28

Last day to withdraw from a course.

May 12-13

Reading Days.

May 19

Final Exam (tentative day)