PREREQUISITES: Math 2614 Calculus I
CATALOG DESCRIPTION OF COURSE: Elementary theory in foundations of geometry and logical systems; basic theory in the fields of Euclidean, non-Euclidean, and synthetic coordinate projective geometry, including homogeneous coordinates; selected topics from topology
COURSE PURPOSE: This course broadens the students' views of geometry to include finite and non-Euclidean geometry. The student will learn about the connections between algebra and geometry at a higher level, and refine their skills in problem solving and reasoning.
EXPECTED COURSE OUTCOMES: The student will be expected to achieve the following objectives:
1. Communicate with appropriate mathematical symbols, and in writing a term paper, will communicate in writing about the connections between mathematics and the world..
2. Demonstrate proficiency in problem solving and reasoning within several finite geometries..
3. Define and study transformations and relate the algebra of group theory to geometry.
4. Investigate fractional dimensions and various fractals.
5. Solve problems and answer questions about topics in topology such as simple closed curves, invariant points and networks, Euler's formula and the map coloring problem.
6. Write proofs in non-Euclidean geometry
INSTRUCTIONAL MATERIALS: (Required Textbook) Modern Geometries 5 ed., James R. Smart, Brooks/Cole Publishing Company, 1998
INSTRUCTIONAL PROCEDURES: The expected course outcomes will be realized through a variety of instructional strategies to aid the students' construction of cognitive schemas . Those strategies include, but are not limited to, the following: expository-discussion, demonstration, inquiry, and group activities. The instructor also will integrate appropriate multi-media technology and invite guest speakers, for the purpose of enriching the students total experience.
Fundamental Concepts of Geometry
I. Sets of Axioms and Finite Geometries
A. Introduction to Geometry
B. Development of Modern Geometries
C. Introduction to Finite Geometries
D. Four-Line and Four-Point Geometries
E. Finite Geometries of Fano and Young
F. Finite Geometries of Pappus and Desarques
II. Geometric Transformations
A. Groups of transformations
B. Euclidean Motions of the Plane
C. Sets of Equations for Motions of the Plane
D Applications of transformations to Computer Graphics.
E. Properties of the Group of Euclidean Motions
F. Similarity Transformations
G. Introduction to the Geometry of Fractals and Fractal Dimension.
III. Geometric Introduction to Topological Transformations
A. Topological transformations
B. Simple Closed Curves
C. Invariant Points and Networks
D. Introduction to the Topology of Surfaces
E. Euler's Formula and Map-Coloring Problem
IV. Non-Euclidean Geometries
A. Foundations of Euclidean and Non-Euclidean Geoemtries
B. Introduction to Hyperbolic Geometry
C. Ideal Points and Omega Triangles
D. Quadrilaterals/Triangles/Area/Pairs of Lines
E. Elliptic Geometry
F. Consistency
ADA COMPLIANCE: If any member of the class feels that he/she has a disability and needs special accommodations of any nature whatsoever, the instructor will work with you and the University's Office of Student Affairs to provide reasonable accommodations to ensure that you have a fair opportunity to perform in this class. Please advise the instructor of such disability and the desired accommodations at the first class attended.
INCLEMENT WEATHER / DISASTER POLICY: The following are basic premises for the inclement weather policy at Northeastern State University:
1. Classes are expected to be held if at all possible.
2. It is the student's responsibility to receive the information when weather is questionable.
3. Neither students nor faculty are expected to risk life or limb.
4. Faculty members are obligated to hold classes if the University is not closed, unless the faculty member is unable to get to campus.
Policy: During times of inclement weather, decisions concerning day classes will be made by 6:00 a.m. in order for the media to be notified and for students to receive the announcement before they leave home. Decisions concerning night classes will be made by 3:00 p.m.
The following media will be notified regarding closing of the campus:
Radio Stations: Television Stations:
KRMG 740 AM Tulsa KJRH Channel 2 Tulsa
KAYI 107 FM Tulsa KOTV Channel 6 Tulsa
KTLQ 1350 AM Tahlequah KTUL Channel 8 Tulsa
KEOK 102 FM Tahlequah KFSM Channel 5 Fort Smith
KBIX 1490 AM Muskogee Cable Channel 96 Tahlequah
KMMY 97 FM Muskogee
KVOO 1170 AM Tulsa
The automated attendant message on 918-456-5511 will be modified to include information concerning campus operations during inclement weather.