Spring 2013, 12:30 M,T,Th,F, Olin 329
Text: Geometry with Geometry Explorer,
Phone: 933-7480 by Michael Hvidsten, McGraw-Hill (2005)
Office Hours: 2:30-4:30 Mon,Thurs 2:30-4:00 Tues
and by appointment
Class Email Alias: email@example.com
The study of geometry is an ancient and noble practice begun by Greek mathematician- philosophers. The most influential of these was Euclid, whose system of axioms and theorems has come to be known as Euclidean Geometry.
In this course we will see that Euclid's axiomatic system is not the only logically consistent geometric system. We will investigate non-Euclidean geometries such as finite, hyperbolic, and elliptic geometries, as well as fractal geometry. Of course we will also review Euclidean geometry.
Throughout the course we will focus on three different geometric viewpoints: the synthetic, analytic, and transformational. The synthetic perspective is to study geometric figures directly, without any reference to coordinate systems or algebraic descriptions. This is the foundational, axiomatic perspective of Euclid. In analytic geometry we reason from coordinate-based descriptions of geometric objects. This viewpoint was the grand achievement of Descartes and others in the early 1600's and directly led to the invention of calculus in the late 1600's. The transformational view of geometry is the most modern of the three perspectives and arises from the work of Felix Klein in the late 1800's. In transformational geometry we study how geometric objects change (or don't change) under transformations such as rotations, translations, scalings, and other geometric operations. The transformational perspective is used widely today in the area of computer graphics.
MCS 303 is a writing course and thus there will be frequent writing assignments during the semester. These will be of three types. First, homework assignments will require written proofs of theorems. Second, computer lab projects will require written reports. Lastly, there will be a final research paper for the course.
MCS 303 will have a significant computer laboratory component. We will be using the software package Geometry Explorer to help visualize and understand classroom concepts. All labs will take place in the 3rd floor computer lab. There will be approximately one lab a week. There will also be several in-class mini-projects. These are group projects designed to be done during a class period.
Assignments: We will have frequent homework assignments which will normally involve the writing of proofs. Also, there will be weekly lab projects and a final research paper. There will be two hour exams, but no final exam. The final research paper will include an in-class presentation.
Homework and Labs 400 pts
Final Paper/Project 200 pts
The grading scale used for the course will be essentially a flat 90-80-70-60 scale.
Honor Policy: Students are expected to abide by the college's Academic Homesty Policy. I will typically not proctor exams, but will have students sign an honor pledge for each examination. Students are encouraged to discuss with one another topics from the course. However, the work done in the homework assignments, on lab projects, and on the research paper should be individual work unless otherwise specified. If you are having difficulty with an assignment you may ask fellow students for assistance in understanding the assignment, but not for assistance in doing the assignment. Feel free to ask me for assistance at any time.
Disability Services: Gustavus Adolphus College is committed to ensuring the full participation of all students in its programs. If you have a documented disability (or you think you may have a disability of any nature) and, as a result, need reasonable academic accommodation to participate in class, take tests or benefit from the College’s services, then you should speak with the Disability Services Coordinator, for a confidential discussion of your needs and appropriate plans. Course requirements cannot be waived, but reasonable accommodations may be provided based on disability documentation and course outcomes. Accommodations cannot be made retroactively; therefore, to maximize your academic success at Gustavus, please contact Disability Services as early as possible. Disability Services is located in the Advising and Counseling Center.
Course Web Site: http://www.gac.edu/~hvidsten/courses/MC303