UNIVERSITY OF SAINT MARY
Course Syllabus
MA 455 Modern Geometries
Spring 2011
COURSE TITLE:
Ma 455 Modern Geometries
PREREQUISITES:
MA 221 (Calculus and Analytic Geometry I) and MA 270 (Introduction to
Proofs)
INSTRUCTOR:
Dr. Rick Silvey
OFFICE HOURS:
MTWThF
OFFICE:
Meige 102 A
PHONE:
Office
Home
913 6825151 x6405
816 5321542
EMAIL
Office
[email protected]
10:30 am – 11:30 am
University Goals and Outcomes
Mission Statement
The University of Saint Mary educates students of diverse backgrounds to realize their God-given potential and
prepares them for value-centered lives and careers that contribute to the well being of our global society.
Values Statement
The University of Saint Mary believes in the dignity of each person’s capacity to learn, to relate and to better our
diverse world. These values include community, respect, justice, and excellence.
University of Saint Mary Learning Goals
Participation in this course will advance University of Saint Mary goals by enabling students to engage the following
areas of investigation:
1.
2.
3.
4.
5.
the human imagination, expression in literature and the arts, and other artifacts of cultures;
inductive and deductive reasoning to model the natural, social, and technical world especially through
but not limited to mathematics, the natural sciences, the behavioral sciences, information systems and
technology;
the values, histories, and interactions of social and political systems across global cultures, with
emphasis on American democracy;
spirituality, faith, and wholeness of the human person, understanding interconnectedness of mind, heart,
and hand; and
ethical and moral dimensions of decisions and actions.
UNIVERSITY OF SAINT MARY LEARNING OUTCOMES (ULO):
Integrated through the areas of investigation (general education, content areas, majors, minors) University
of Saint Mary graduates will
I.
II.
Demonstrate ability to investigate and assess information to develop knowledge.
Demonstrate ability to use, integrate, analyze, and interpret complex information and connect
theory and practice to draw new and perceptive conclusions.
Demonstrate the ability to evaluate information from disparate sources, to transform
information into meaningful knowledge to solve or accept complex issues.
Demonstrate ability to use English language conventions accurately to construct coherent
written and oral arguments.
III.
IV.
MATHEMATICS PROGRAM LEARNING OUTCOMES (MPLO):
1. Develop problem solving and reasoning skills, and analyze conceptual relationships. ULO II
2. Apply disparate knowledge to solve complex problems in various disciplines, and interpret the
results in practical terms. ULO III
3. Use mathematical abstraction and symbolism to create generalizations from observed patterns, and
develop specific examples from general statements. ULO I
4. Read mathematical literature with increasing confidence, collaborate with others to solve problems,
and effectively communicate mathematical concepts and processes. ULO IV
5. Appropriately use technological tools, such as graphing calculators and computers, as aids in
solving problems, and correctly interpret the results that technology produces. ULO I
6. Develop quantitative literacy by collecting, organizing and interpreting data, and create models for
drawing trustworthy conclusions based on that data. ULOs I and II
COURSE GOALS:
On completion of Modern Geometry the student shall be able to
a.
b.
c.
d.
e.
f.
g.
h.
Use undefined terms, axioms, and definitions, to develop axiomatically and then use some major
results of absolute geometry 3, 6
Use undefined terms, axioms, and definitions, to develop axiomatically and then use some major
results of Euclidean geometry. 3, 6
Use the compass and straight edge and/or computer software to make basic geometric
constructions. 5
Use undefined terms, axioms, and definitions, to develop axiomatically and then use some major
results of Hyperbolic geometry. 3, 6
Identify and use transformations. 3, 6
Explore three-dimensional, including spherical, geometries. 1, 2
Contrast and compare the axioms and theorems of nonEuclidean geometries with those of
Euclidean geometry. 2, 4
Explore modern research in geometry. 4
COURSE DESCRIPTION:
Theory and applications of modern geometry, the role of axiomatics in developing a mathematical system,
various methods of proof, Euclidean geometry, hyperbolic geometry, transformational geometries, threedimensional geometries, and spherical geometry.
TEXTBOOK:
Kay, David, College Geometry a Discovery Approach, Addison Wesley, 2001.
SUPPLIES:
A compass and a graphing calculator and access to GeoGebra.
Course Policies
Academic Honesty:
Academic honesty is expected of all members of the University of Saint Mary community. It is an essential
component of higher education and is necessary for true academic growth. Christian tradition and
professional excellence demand that truth be valued in all of our interactions. Justice requires that we
possess the skills and learning that we profess to have. Academic honesty prohibits any form of cheating
whether in or out of classroom; the presenting of purchased or stolen papers, computer programs, reports,
etc., as one’s original work; failure to acknowledge the source of quotations, unique ideas, figures, tables,
charts, and diagrams when these are used in papers, reports, or formal presentation; and falsification of
information.
Any form of cheating or plagiarism (misrepresenting material written or prepared by someone else as one’s
own work) is clearly understood to be grounds for disciplinary action. The student may receive a failing
grade on the project in question and may even fail the course. The individual instructor will ordinarily
handle the situation. If an instructor fails a student in a course or significantly lowers the final grade
because of academic dishonesty, he/she will file a written report with the Academic Vice President. A
student who has serious reasons to challenge a judgment of cheating or plagiarism may use the standard
appeal process.
Attendance and Participation:
Prompt attendance at academic appointments (classes, lectures, or conferences) is an essential part of
academic work. It is expected that students will keep all academic appointments.
Excessive absences (four or more) will be reported the Academic Vice President and/or the Athletic
department. Such attendance policy recognizes the validity of required college-sponsored activities. The
responsibility for work missed because of absence, regardless of the reason, rests upon the student.
Excessive absences may result in grade adjustments, recommended withdrawal from the course, or failure.
Course Evaluation and Grading
HOMEWORK: ULO 1, 2
A list of homework exercises to be completed and submitted will be given for each section. These
exercises should be completed neatly, in pencil, and wellorganized in a notebook. In addition to
exercises, selected theorems may also be required. Late assignments will not be accepted unless approved
by the instructor.
PROJECTS:
ULO 2, 4
Individual or group projects will be assigned. These projects may include: exercises from the text,
computer activities, short essay items, critiques of articles, review of pertinent literature, or personal
reflection essays.
RESEARCH PAPER:
ULO 2, 4
One paper, 8-10 pages in length is required. The paper, and accompanying presentation, will focus on a
topic in modern geometry. More information about the paper will be given later.
PRESENTATION:
ULO 1
Two oral presentations are required. One of these presentations will cover topics or exercises not
presented by the instructor. The second presentation will be in conjunction with the final paper. More
information about the presentations will be given later.
GRADING:
The final grade will be assessed according to points obtained from the
following:
homework
200 points
33%
projects
200 points
33%
paper
100 points
17%
presentations
100 points
17%
total
600 points
100%
GRADING SCALE:
Final grades will be assigned according to the following ranges:
540 – 600 points
90%  100%
A
480 – 539 points
80%  89%
B
420 – 489 points
70%  79%
C
360 – 419 points
60%  69%
D
0 – 359 points
0%  59%
F
SPECIAL NEEDS:
If you have a physical condition that might prevent you from carrying out classroom assignments, please
inform the instructor as soon as possible. An effort will be made to make special arrangements so that the
assignments can be completed.
RESOURCES:
1.
2.
See me during my office hours or call me.
Form a study group with the members of your class.
BIBLIOGRAPHY:
Baragar, Arthur. A Survey of Classical and Modern Geometries. Prentice Hall. 2001.
Dresslar, Isidore. Geometry Review Guide. Amsco School Publications. 1973
Musser, Gary and Trimpe, Lynn. College Geometry. Prentice Hall 1994.
Posamentier, Alfred. Advanced Eudlidean Geometry. Key Publishing. 2002.
COMMENTS:
I hope you find the course enjoyable and rewarding. Your progress in the course will be greatly influenced
by how well you manage your time. Please be reasonable in setting aside time for your homework,
reading, and test preparation.
Date
T January 18
Introduction
Section
Th January 20
2.3 Incidence Axioms for Geometry
2.4 Distance, Ruler Postulate, Segments, Rays, and Angles
T January 25
Th January 27
2.5 Angle Measure and the Protractor
3.1 Triangles, Congruence Relations, SAS Hypothesis
T February 1
Th Febuary 3
3.3 SAS, ASA, SSS, Congruence, and Perpendicular Bisectors
3.4 Exterior Angle Inequality
T February 8
3.5 The Inequality Theorems
Th February 10
3.6 Additional Congruence Criteria
T February 15
Th February 17
3.7 Quadrilaterals
3.8 Circles
T February 22
Th February 24
4.1 Euclidean Parallelism, Existence of Rectangles
4.2 Parallelograms and Trapezoids: Parallel Projection
T March 1
Th March 3
4.3 Similar Triangles, Pythagorean Theorem, Trigonometry
4.4 Regular Polygons and Tiling
T March 8
Th March 10
4.5 The Circle Theorems
Presentations
T March 22
Th March 24
5.2 Reflections: Building Blocks for Isometries
5.3 Translations, Rotations, and other Isometries
T March 29
Th March 31
5.4 Other Linear Transformations
5.5 Coordinate Characterizations
T April5
Th April 7
5.5 Coordinate Characterizations
6.2 An Improbable Case
No Class
T April 12
Th April 14
6.3 Hyperbolic Geometry: Angle Sum Theorem
6.4 Two Models for Hypberbolic Geometry
T April 19
Th April 21
6.5 Circular Inversion
7.2 Parallelism in Space: Prisms, Pyramids, and Platonic Solids
T April 26
Th April 28
SMURF
7.4 Volume in E3
T May 3
Th May 5
7.6 Spherical Geometry
Optional
Th May 12
Final: 10:00 am – 11:50am