Saint Joseph's College
Syllabus
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”
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Course
Description
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
results when
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
Grading:
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
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Special
Needs:
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.
Plagiarism:
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.