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Course Information
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Course Description:
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A brief review of Euclidean geometry with further topics including the non-Euclidean and discrete geometries.
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Course Objectives:
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The aim of this course is to take students through the basic topics of Euclidean geometry from an advanced standpoint while 1) introducing the students to several of the post Greek techniques including inversion and homothety and 2) introducing the students to several non-Euclidean geometries with corresponding and contrasting proofs.
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Prerequisites and Corequisites:
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The student is expected to have mathematical power in advanced Euclidean geometry and a working knowledge of several of the non-Euclidean geometries.
PREREQUISITES: MATH 1910 (Calculus I), MATH 1920 (Calculus II), and MATH 2010 (Linear Algebra)
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Course Topics:
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Upon successful completion of Math 3810, the student will be able to:
I. Axiomatics:
1. determine what properties a set of axioms possesses (complete, consistent, independent, categorical, etc.)
2. construct a model for a set of axioms.
II. Complex numbers:
1. compute in
2. use Euler's Formula
3. construct the geometric interpretation.
III. Discrete geometry:
1. exhibit examples and model
2. prove theorems concerning
IV. Euclidean n - space:
1. compute "hyper areas" and "hyper volumes"
V. Fractal Geometry:
1. Construct examples of fractals
2. compute the dimension of a self similar fractal.
VI. Geodesics:
1. determine the geodesics on a general 2-dimensional manifold
VII. Hyperbolic Geometry:
l. define and use Ponicare's Model
2. compare and constract with elliptic and parabolic geometries
VI.II. Mobius transformations:
1. determine the image of a given set of point
2. graph the tranformation
IX. Post-euclidean techniques:
1. use the cross ratio, circle inversion , and homothetic transformations as proof tools.
X. Quaternions
1. define, compute in and solve equations in
2. use quatenions to model motion in 3-dimensiomal Euclidean space.
XI Symmetries
1. Determine the symmetries of patterns in 1, 2 and three dimensional Euclidean space.
XII. Synthetic geometry techniques:
1. use the axioms and theorems of classical Euclidean geometry as proof tools.
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Specific Course Requirements:
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Install free browser plugins, and install and use free downloadable mathematics software
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Textbooks, Supplementary Materials, Hardware and Software Requirements
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Required Textbooks:
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Supplementary Materials:
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It is optional for students to purchase a copy of Mathematica for Students Limited Edition.
This is not required.
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Hardware Requirements:
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Software Requirements:
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The minimum requirements can be found at http://www.rodp.org/students/hardware_software.htm. Specific hardware requirements for this course include...(A list of software the student is required to purchase or download for the course, Real Player, Media Player, Acrobat Reader, Microsoft Office, etc).
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Instructor Information
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Please see the separate page inside the course to find instructor contact information as well as a statement of virtual office hours and other communication information.
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Assessment and Grading
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Testing Procedures:
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Assigned Problems, Midterm and Final Exams will be given online.
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Grading Procedure:
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Assigned Problems are graded relative to the ingenuity and depth of the solution. Examinations are graded on a strictly right or wrong scale. (No partial credit will be given). The assigned problems constitute sixty (60) percent of the students' grade. The other remaining 40% will be divided between the Midterm and Final Exams.
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Grading Scale:
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90 - 100---A
80 - 89 ---B
70 - 79 ---C below that is NOT GOOD!
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Assignments and Participation
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Assignments and Projects:
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Homework will be assigned for each textbook section. These problems will usually consist of selected odd-numbered problems.
Ten Problems Sets; Midterm Examination; Final Exam; Term Project
The assignment points are noted below:
Term Project: 15%
Class Homework: 45%
Midterm: 20%
Final 20%
100%
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Class Participation:
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WEEKLY PARTICIPATION IS REQUIRED!!!!!!
For all courses offered through the Physics and Mathematics Department, any incidence of academic dishonesty carries a minimum penalty of a non removable zero for that work. Students must communicate with other students in the chat room, students are expected to communicate with the instructor as a learning resource, students must check the course bulletin board frequently for announcements, and students must actively participate in threaded discussion events.
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Quizzes, homework assignments, tests, and the final exam will all have specific deadlines. These graded activities must be completed by the due date and time. Make-up work will be accepted at instructor's discretion and only under documented extreme circumstances.
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Course Ground Rules
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Online math courses are not for everyone. But for those that approach their online math course with the correct attitude and diligence, the effort usually results in a much deeper understanding of the course material than that acquired in a traditional classroom. My advice would be to establish a study schedule and stick to it, study the examples online and within the text, use web resources especially to check answers.
Participation is required. You are expected to communicate with other students in team projects Learn must learn how to navigate in WebCT. You must eep abreast of course announcements. Do use the assigned college or university e-mail address as opposed to a personal e-mail address Address technical problems immediately. Always observe course netiquette at all times.
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Guidelines for Communications
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Email:
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- Always include a subject line.
- Remember without facial expressions some comments may be taken the wrong way. Be careful in wording your emails. Use of emoticons might be helpful in some cases.
- Use standard fonts.
- Do not send large attachments without permission.
- Special formatting such as centering, audio messages, tables, html, etc. should be avoided unless necessary to complete an assignment or other communication.
- Respect the privacy of other class members
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Discussion Groups:
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- Review the discussion threads thoroughly before entering the discussion. Be a lurker then a discussant.
- Try to maintain threads by using the "Reply" button rather starting a new topic.
- Do not make insulting or inflammatory statements to other members of the discussion group. Be respectful of other's ideas.
- Be patient and read the comments of other group members thoroughly before entering your remarks.
- Be cooperative with group leaders in completing assigned tasks.
- Be positive and constructive in group discussions.
- Respond in a thoughtful and timely manner.
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Chat:
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- Introduce yourself to the other learners in the chat session.
- Be polite. Choose your words carefully. Do not use derogatory statements.
- Be concise in responding to others in the chat session.
- Be prepared to open the chat session at the scheduled time.
- Be constructive in your comments and suggestion
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Web Resources:
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Library
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The Tennessee Virtual Library is available to all students enrolled in the Regents Degree Program. Links to library materials (such as electronic journals, databases, interlibrary loans, digital reserves, dictionaries, encyclopedias, maps, and librarian support) and Internet resources needed by learners to complete online assignments and as background reading must be included in all courses.
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Students With Disabilities
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Qualified students with disabilities will be provided reasonable and necessary academic accommodations if determined eligible by the appropriate disability services staff at their home institution. Prior to granting disability accommodations in this course, the instructor must receive written verification of a student's eligibility for specific accommodations from the disability services staff at the home institution. It is the student's responsibility to initiate contact with their home institution's disability services staff and to follow the established procedures for having the accommodation notice sent to the instructor.
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Syllabus Changes
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The instructor reserves the left to make changes as necessary to this syllabus. If changes are necessitated during the term of the course, the instructor will immediately notify students of such changes both by individual email communication and posting both notification and nature of change(s) on the course bulletin board.
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Technical Support
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Telephone Support:
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If you are having problems logging into your course,
timing out of your course, using your course web site tools, or other technical problems, please contact the AskRODP Help Desk by calling
1-866-550-7637 (toll free)
or go to the Ask RODP website at:
http://askrodp.custhelp.com
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