### MATH325: Foundations of Geometry

Section 001: Monday and Wednesday, 1:50-3:05, DMF 440
Instructor: Heidi Burgiel, hburgiel@bridgew.edu
Tentative Office Hours: DMF 453. Monday 11:00-12:00, Tuesday 3:30-4:30, Thursday 9:30-10:30 and by appointment.
Required Materials bring to class daily:
• John Stillwell, The Four Pillars of Geometry. Springer Verlag, 2005.
• Patty Paper, graph paper.
• Ruler, compass, protractor, scissors
• Calculator (cell phone use prohibited on quizzes and exams)

Description: In this course, students will broaden their understanding of Euclidean geometry; study finite geometries, geometric transformations and non-Euclidean geometries; write geometric proofs; construction problems; and apply geometric concepts to real-world situations.

Objective: To instill in future teachers a profound understanding of the fundamental concepts of geometry.

Outcomes:

• Know Euclid's five axioms and, in particular, the implications of accepting, changing or omitting the fifth axiom.
• Observe and participate in the deduction of mathematical truths from axioms and definitions.
• Be able to follow or provide step by step instructions for geometric construction.
• Use tools from modern mathematics such as coordinate geometry, complex numbers, non-Euclidean geometries and linear algebra in the context of classical geometry.
• Attain a deep understanding of topics typically found in high school geometry.
• Work independently and with others to identify and communicate geometric truths.
Grades for the course will be recorded on the course web site and computed on a curve. The final grade will be determined as follows:
• Final exam: 20%
• Homework: 20%
• Project: 15%
• Quizzes: 15% (redo lowest)
• Group Participation: 5%
• Class participation: 5%
• Activators/TTL's: 20% (drop the lowest 3)

Final exam: Monday, May 9, 11:00 - 1:00, DMF 440

Quizzes: There will be a quiz on each chapter for a total of about 4 quizzes. This may mean that there is a quiz during the last week of class in addition to a cumulative final during the final exam period. Quizzes (especially quiz 2) may include group work.

There will be no make-up quizzes. Instead, you will have the option to rework the problems on and resubmit one quiz at the end of the semester. Students who miss more than one quiz should consider dropping the class or applying for a grade of incomplete.

Homework: Homework will be assigned every class, but will collected at most once a week. The purpose of the homework is to prepare you for work in class; if you have not completed the homework, you will be less able to aid your group in classwork and may receive a lower group participation grade.

Project: In the last third of the semester your group will be assigned a project to complete and turn in. Your grade may be affected by peer evaluations of your contributions to this project.

Group Participation: Much of the classwork will be done in groups; many of the students in this class are future teachers who will benefit from experiencing this model of instruction. You will be evaluated by your group mates based on a rubric posted on the course web site. The lowest of the three resulting grades will be dropped.

Class Participation: My goal in teaching this class is to engage students in thinking about geometry. You can help by asking questions, explaining things to your peers, and participating in discussions. Please use common courtesy: turn cell phones off, refrain from discussing subjects other than mathematics, and if you must leave early please notify me in advance and sit near an exit.

Activators and Tickets To Leave: These are daily mini-quizzes used to assess your understanding of the homework, set the stage for a day's work, or sum up what you've learned in class. They are leniently graded on a scale of 0 to 3. These cannot be made up, but at the end of the semester I drop the lowest 3 grades.

Office hours: I will be available in DMF 453 during these hours for consultation on a first-come-first-served basis. You do not need an appointment in advance. Please also feel free to email me, talk to me after class, or schedule an appointment outside of office hours.

Academic conduct: It is important to fairly recognize others' contributions to your work. Failure to properly cite your sources or other unethical behavior will be dealt with according to BSU's Academic Integrity and Classroom Conduct policy.

Students with Disabilities: The Disability Resoruces office is located on teh ground floor of Maxwell Library. If you have a diagnosed disability which will make it difficult for you to carry out the course work please contact me during the first two weeks of class to discuss reasonable accommodations.

Math Services: Math Services provides free tutoring on a walk-in basis. It is located on the ground floor of Maxwell Library.