Course Description: The main focus of this class is on engaging in mathematical exploration from various perspectives that have been employed throughout the development of geometry. At the end of the semester you will be familiar with the numerous traditions expressed in school geometry texts, be able to identify the tools, strengths, and weaknesses of those traditions, understand how these ideas are developed in conteporary mathematics and applied and theoretical science, and be able to draw connections between different approaches for solving problems or preparing instructional materials with a coherent focus. To accomplish this, we will explore important geometric structures from each perspective, identify the most interesting ones and give them names, develop our intuitions and abilities to argue about their properties and relationships, then look for what implications they have and ways in which they can be generalized and compare our results to those obtained historically. You will mostly work in groups, argue, present ideas to each other, and hold each other accountable to rigorous standards of reasoning. My main role will be to help you become better at all of these things by listening to what you say and helping to steer your investigation. On a regular basis, we will also take classroom time and use homework to explore additional topics related to the content from the text. Notably, we will regularly explore ideas in the field of differential geometry using basic multi-variable calculus. Depending on interest, additional topics may include definitions of volume, area and length, the Banach-Tarski paradox, Euler's formula (V-E+F=2) and its connection to curvature and vector fields, mappings of the earth and Thale's measurement of the earth's circumference, Foucault pendulums, astronomical coordinate systems, special and general relativity, the geometry of the universe, the shape of SO₃ and other interesting 3-dimensional spaces, and 4-dimensional spaces.

Class Participation: I expect everyone in the class to contribute constructively to the class and group discussions. This can take several forms from clearly articulating points of confusion to uncovering problems with previous lines of reasoning to providing key ideas and breakthroughs. If your entire group is stuck and/or confused (there is something wrong if this doesn't happen on a regular basis), you should not give up and wait for me to come around, but you should be resourceful in trying to find new ways to attack the problem. Also, you should look for ways to draw other students into the conversation - since much of what you need to learn is how to listen and evaluate. You are not participating fully if you are at either extreme: either never talking or doing all of the talking.

Quizzes: Unannounced quizzes will be given during class on a regular basis. These will cover key points from readings, discussions, and homework. I will drop your lowest two quiz scores to allow for reasonable absences, thus no make-up quizzes will be allowed under any circumstances.

Homework:  Written homework assignments will be based on classroom discussion covered each week and collected the following week at the beginning of class on Thursday. If you forget to bring your homework, you may submit it up to 24 hours later with a 20% penalty. No homework will be accepted later than this under any circumstances. I will drop your lowest two homework grades. Due dates for all homework will be listed on the homework page. You are responsible for checking the homework page regularly and keeping track of due dates for all assignments. Type or write legibly all of your work on 8½"×11" paper with at least one-inch margins on all sides free of writing except your name, date, and assignment number. For each homework assignment, you may place a star or asterisk next to the solution which you feel represents your best work, and while I may grade any of your responses, over the semester I will generally focus on the ones you mark. Getting a good grade on an assignment may be independent of solving the problems. A correct solution that is unclear or provides little understanding will not receive credit. A good discussion of the issues with strong reasoning, without finding a solution to a challenging problem may often receive full credit. In general, assigned questions will require significant depth in your responses. In order to earn an A or B for the course, I anticipate that most people will need to spend approximately six to eight hours per week outside of class on homework, reading, and studying.

Midterms:  Two midterm exams will be taken at the Testing Center (PSA 21). These exams will assess your understandings of the mathematical content covered in the course, and before each exam, I will provide an overview of what will be covered. The Testing Center is open M-Th 9:00am-8:00pm (with latest entry at 6:30pm) and Friday 9:00am-5:00pm (with latest entry at 3:30pm). In order to be admitted to the testing center, you must present a valid ASU "Sun Card". Your calculator program memory may be randomly viewed during any exam and will be cleared if anything suspicious is written therein.

Final Exam: The final exam will be comprehensive and administered in class on Tuesday, December 15 from 12:10pm - 2:00pm. The Department of Mathematics follows Arizona Board of Regents policy, which states that all final examinations shall be administered at their officially scheduled times. A final exam schedule appears in the Fall Bulletin of classes and on the Web at http://students.asu.edu/final-exam-schedule. Requests to take the final examination at a time other than the published time will not be granted except in cases of conflict with the scheduled exam time for another course, having more than three exams scheduled in one day, personal emergencies, or for reasons of religious practice. The Department of Mathematics reserves the right to require written documentation to substantiate any claim of hardship. In particular, nonrefundable plane tickets, weddings, work schedules, and the like are not acceptable reasons for rescheduling final examinations. Please keep this policy in mind when making end-of-semester plans.

Graduate Credit: Students enrolled in MTE 585 will complete an additional project. Additional meeting times may be substituted for the regular class to support work on these projects. The project may consist of an in-depth paper on some area of geometry not covered in the class or a small teaching experiment with some classroom materials that you develop with a subsequent write-up. Project proposals must be approved by me no later than Wednesday, February 8.

 
Academic Dishonesty: In the “Student Academic Integrity Policy” manual, ASU defines “Plagiarism [as] using another's words, ideas, materials or work without properly acknowledging and documenting the source.” Students are responsible for knowing the rules governing the use of another's work or materials and for acknowledging and documenting the source appropriately.” You can find this definition at: http://www.asu.edu/studentaffairs/studentlife/judicial/academic_integrity.htm#definitions. Academic dishonesty, including inappropriate collaboration, will not be tolerated. There are severe sanctions for cheating, plagiarizing and any other form of dishonesty.