Saint Joseph's College
Mth 333 Geometry 3 credit hrs.
M.W.F. 2 p.m.. McHale 300 Sem: 122
Instructor: P.F. Gilbert, C.PP.S.
Office: McHale 303; Tel: 6180 Office hours: M-Th 1 p.m. and by appointment
Text: "Modern Geometries" 5th ed., James R. Smart; Brooks/Cole Publ 1997
Computer software available to the student: “The Geometer’s SketchPad”
This course is a critical examination of the foundations of plane geometry, using an axiomatic approach. It includes the study of both Euclidean and non-Euclidean geometries. Proofs are emphasized as well as student presentations using a modern computer based utility.
Purpose and Goals
This course considers geometry, or more properly, geometries, from a viewpoint of axioms, which are assumptions of “truth” necessary to begin discussing the subject (much like the rules of a game). The Euclidean geometry studied in high school used a particular set of axioms. Varying these axioms produces other geometries, some of which, e.g., hyperbolic geometry have applications to the intrinsic structure of the universe, whereas others like the finite geometries (that require only a finite set of points) are of mostly pedagogical interest because of their simplicity.
Understanding proofs is a fundamental, and perhaps – along with student oral/written presentations -- the most important, purpose of the course. The student will learn to proceed, using rules of logical inference (deductive reasoning), from axioms and definitions and previously established results (theorems, propositions, lemmas), to prove further results.
Chapter 1: Axioms and finite geometries – (also appendix 1: logic)
Chapter 2: Geometric Transformations – many of the concepts considered here
overlap with Modern (or Abstract) Algebra.
Chapter 3 and 4: Convexity and some modern Euclidean geometry
Chapter 6 and 7: Inversion and Projective Geometry
Chapter 9: Non-Euclidean geometries – checking the
postulate” is negated.
Chapter 5: Constructions
Assignments and Tests:
Four in-class examinations will be given throughout the semester. The fourth – a comprehensive exam -- is during the “finals week.” Weekly problem assignments will be made on a regular basis. Some oral/written presentations will also be assigned. One major presentation (the oral portion to be 10-15 minutes in length) is to be done toward the end of the semester. Several quizzes will also be given throughout the semester
You will be graded on the results of the four tests as well as your quizzes, problem assignments, and written/oral presentations. The examinations will count 40% toward your semester grade, your homework 40%, the quizzes 5%, and your written/oral presentations 15%. Your home assignments are to manifest discipline. Points will be lost for slovenly work.
Grading scale for all work, including final grade:
93-100 90 – 92 87- 89 83 - 86 80-82 77 - 79 73 – 76 70 – 72 67 - 69 60-66 0 - 59
A A- B+ B B- C+ C C- D+ D F
If you are a student with a disability, meet with your instructor as soon as possible to discuss the accommodations you will need during class activity, and out of class assignments, in order to participate fully and demonstrate your abilities.
The student is expected to do his/her own work. Attempted plagiarism will not only be handled by your instructor, they may also be reported to the office of the Vice President for Academic Affairs. Due process will be initiated, if warranted. See the "Academic Honesty" section of the 2012-2013 academic catalog of the college, pp. 57-58
Class participation, "excused" absences, and late assignments:
We all acknowledge that there are times when attendance at class might be preempted by more pressing duties. The obligation of participation remains, however, as does the requirement of turning in all assignments on time.
Active participation is expected when another student is making a presentation to the class. One or the other can be delayed to a later time if necessary, but this should be a rare occurrence.
The student is to notify the instructor ahead of time, if possible, of an impending absence. The instructor is the judge of the appropriateness of the excuse for the absence.
An assignment turned in late will result in loss of points for the lateness. An in-class quiz or an examination that is missed may only be made up if the absence was "excused" and unavoidable. The request to make up a quiz must be made on or before the first day the student returns to class.