MODERN GEOMETRY

MATH W310A- Spring 2008

Benedictine University

Contents:

Basic Information:

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Course Description:

Geometry is a very exciting area of current mathematics.  In this course, we begin with some explorations of our intuition of Euclidean geometry and use these as a springboard to consider other important geometrical systems that occur in modern mathematics.  In particular, we will consider spherical geometry and hyperbolic geometry--arguably the most rich and beautiful non-Euclidean geometry. 

This course is a problem-based course in which we will explore, discover, and develop concepts through experimentation and discussion.  Your tools for discovery may include paper, pencil, pen, colored markers, string, modeling clay, scissors, compass, ruler, yarn, and dynamic geometry software such as Cinderella or The Geometer’s Sketchpad.

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Course Objectives:

By the end of this course, you should be expected to understand and appreciate different geometrical systems, develop the ability to understand and construct a correct geometric argument, and develop an appreciation of how geometry relates to other areas in mathematics and in other disciplines. Success in this course will be dependent upon your ability to communicate your technical understanding of course material to your peers as well as to the instructor. You will also be expected to successfully work collaboratively with others.

ISBE Math Content Area Standards: 1C, 2A, 2B, 2C, 3A, 3B, 3C, 4D, 4E, 4F, 4G, 5A, 5B, 5C, 5D, 9B, 9C2, 9C3, 9E4, 9E8

IDEA Objectives:

1. Learning fundamental principles, generalizations, or theories. (Essential)
2. Learning to apply course material (to improve thinking, problem solving, and decisions). (Essential)

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Expectations:

You are expected to work on each problem until you obtain a complete solution.  This may require several revisions of your work.  Please expect some frustration as you proceed through the course but even greater satisfaction once you have correctly completed and understood a particular problem.  You will need to spend six hours per week outside of class on this course.  You are encouraged to work with other class members, but you should submit your own work. Please give credit to anyone you use as a resource.  Ask questions!  If there is material with which you are not fully comfortable, you are expected to ask questions either during class or during office hours.  . Ask questions!  If there is material with which you are not fully comfortable, you are expected to ask questions either during class, online, or during office hours. 

We are a community of learners working together to achieve our course goals. As such, it is incumbent upon all class members to show appropriate respect for each other. Each class member has something important to contribute to the class and should feel comfortable sharing with the class. Cell phones and pagers must be turned off. Inappropriate and disrespectful behavior including cell phone usage will result in dismissal from the class for the remainder of the class period.

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Technology Requirement:

Students are expected to use WebCT/Blackboard for all course communications, accessing notes and course information, and the completion of certain assignments as indicated in this syllabus. Students will be introduced to the dynamic geometry software programs The Geometer's Sketchpad and Cinderella. These programs will be used in class for demonstrations Students will use these programs for the homework and course projects as needed, Mathematical typesetting software such as Mathtype, Latex, Scientific Word, or Microsoft Word with the Microsoft Equation Editor is strongly encouraged for homework submissions and is required for the written paper.

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Writing Intensive Requirement:

This course is a Writing Intensive course. The requirements for a Writing Intensive course include at least twelve written pages and the submission of rough drafts, for which comments will be provided for revision. There will also be an opportunity for peer review as well. This twelve page minimum will be achieved through the written paper and regular homework submissions.

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Evaluation:

The grading scale is 90% for A, 80% for B, 70% for C, and 60% for a D.  It is the student’s responsibility to seek clarification of the course requirements and evaluation policy.

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Homework:

There will be no exams in this course. You will be evaluated primarily on the quality and correctness of your homework solutions.  You will have the opportunity to resubmit homework until the instructor is satisfied with the quality, clarity, and correctness of the solution.  By the nature of the problem, you may not have a chance to complete work on or address all problems or questions posed in class. In order to earn ANY credit on a particular homework assignment, you first submission must be submitted within two weeks of the date listed on the syllabus. Submissions later than two weeks past the date listed on the syllabus will not be read by the instructor and will receive no credit. All submissions and revisions will be submitted to the instructor by 1:35 pm. Friday, 5/2/08.

You will be regularly revising your homework submissions to improve the mathematical accuracy and writing style of your arguments. You are strongly encouraged to prepare your homework in an editable electronic file so that you do not need to rewrite all of an argument upon resubmssion. You are strongly encouraged to use appropriate mathematical typesetting software such as Mathtype, Latex, Scientific Word, or Microsoft Word with the Microsoft Equation Editor. Figures from The Geometer's Sketchpad, Cinderella, or Derive should be included as needed. Unstapled or illegible work will not be read by the instructor.

Studying mathematics is a social process. Much benefit can be gained by sharing insights and by struggling through problems with your peers.  Learn to work with each other and learn from each other. Some activities may require follow-up work and re-writing outside of class.   You are strongly encouraged to study and work with other class members.  You are also strongly encouraged to consult Dr. Comar outside of the class periods during office hours, at the course web site, or via e-mail at tcomar@ben.edu.

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Oral Presentation:

This assignment is designed to encourage you to explore a geometric or topological topic that is not addressed directly by the class discussion.  You may explore how geometry may be used outside the classroom, create an interactive demonstration or activity using dynamic geometry software, or study a geometric topic in greater depth. This could be the start of work that could lead to independent study, research, graduate school! Enjoy! You will present your work in a fifteen-minute oral presentation in class. You are required to present your work externally. The preferred venue is the Annual ISMAA Meeting, at Eastern Illinois University, April 4-5, 2008.

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Written Paper:

This assignment is the written portion of the project which you present to the class in your oral presentation. This will be collected at the beginning of the final exam period for this course at 10:15 a.m. on Friday, May 9. 2008. The rough draft will be due in class on Monday, April 9, 2008 and will be returned to you with comments. You will be expected to write rigorous mathematical arguments and provide further details and background that can be expected in the fifteen-minute presentation. Your paper should be written using appropriate mathematical typesetting software such as Mathtype, Latex, Scientific Word, or Microsoft Word with the Microsoft Equation Editor. Figures from The Geometer's Sketchpad, Cinderella, or Derive should be included as needed. Topics for this paper include topics in the texts not otherwise addressed in class and other topics from geometry, differential geometry, and topology.

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Absence and Tardiness:

Absence due to documented illness, participation in Benedictine University athletic activities, religious observance, or other extenuating circumstances will be excused.  It is your responsibility to inform Dr. Comar in the event of such absences.  Class attendance is very important.  Others will depend on you to be to participate in group exercises. It is incumbent upon you to obtain class notes and updated assignments for missed classes. Tardiness will interfere with your time to complete homework quizzes and exams.  No student shall be admitted fifteen minutes after the scheduled classtime.

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Academic Honesty:

The search for truth and the dissemination of knowledge are the central missions of a university. Benedictine University pursues these missions in an environment guided by our Roman Catholic tradition and our Benedictine heritage. Integrity and honesty are therefore expected of all members of the University community, including students, faculty members, administration, and staff. Actions such as cheating, plagiarism, collusion, fabrication, forgery, falsification, destruction, multiple submission, solicitation, and misrepresentation, are violations of these expectations and constitute unacceptable behavior in the University community. The penalties for such actions can range from a private verbal warning, all the way to expulsion from the University. The University's Academic Honesty Policy is available at http://www.ben.edu/AHP , and students are expected to read it. Acts of any sort of academic dishonesty will not be tolerated.  All instances will be pursued.  The first case of any academic dishonesty will result in a grade of zero for the assignment.  A second case will result in failure of the course. Any incident of academic honesty on the final exam will result in failure of the course.

Your name should appear on all of your submissions of your work.  If collaboration is allowed, you must state with whom you have collaborated. You are responsible for understanding any authorized collaboriation policies on specific assignments. You must also properly reference any other print, electronic, or human resource that you consult.

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Academic Accommodations For Religious Obligations (AAFRO)

A student whose religious obligation conflicts with a course requirement may request an academic accommodation from the instructor. Students must make such requests in writing by the end of the first week of the class.

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Electronic Devices Policy

One aspect of being a member of a community of scholars is to show respect for others by the way you behave. One way of showing respect for others in the educational community is to do your part to create or maintain an environment that is conducive to learning. That being said, allowing your cell phone to ring in class is completely inappropriate because it distracts your classmates and thus degrades their overall classroom experience. For the sake of your classmates, you are expected to turn off your cell phone or set it to mute/silence BEFORE you enter class-every class. Furthermore, if you use your cell phone in any manner during class (e.g. text messaging, games, etc.), you will be dismissed from class and will forfeit any points you might have earned in the remainder of the period. If you use your cell phone in any manner during a test or quiz, you will receive a zero for that test or quiz. (This policy also applies to pagers, iPODs, BlackBerrys, PDAs, Treos, MP3 players and all other electronic communication and/or data storage devices.)

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Other Information:

If you have a documented learning, psychological or physical disability, you may be eligible for reasonable academic accommodations or services. To request accommodations or services, please contact Tina Sonderby in the Academic Resource Center, 249 Kindlon Hall, 630-829-6512. All students are expected to fulfill essential course requirements. The University will not waive any essential skill or requirement of a course or degree program.

Final Drop Date:April 13, 2008.

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This syllabus is subject to change. Any changes will be communicated to all class members electronically.

Contact Dr. Comar: tcomar@ben.edu

 Dr. Tim Comar's Homepage 

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