| Instructor: | Jonathan Rogness | |
| Office: | Vincent Hall 7 | |
| Phone: | 612-625-2861 | |
| Email: | rogness@umn.edu (By far the best way to reach me!) | |
| Web Page: | http://www.math.umn.edu/~rogness/ | |
| Course Page: | http://www.math.umn.edu/~rogness/math5335/ |
The fastest, most reliable way to reach me is via email. Occasionally I get a deluge of email, but anything with "Math 5335" in the subject line will get tagged as a high priority message.
| Course Description: |
The first part of the semester will use vector techniques for advanced study of Euclidean geometry in the plane,
concentrating on figures such as polygons and circles. We will also study special functions called isometries, and
classify all possible isometries on the plane. The later part of the semester will focus on (1) showing that our
vector techniques are consistent with the "regular" geometry one might find in a high school classroom, and (2)
learning the basics of hyperbolic and elliptic geometry and how they compare to Euclidean geometry.
During class you should expect a mixture of lecture and problems for you to work on with your fellow students. |
| Prerequisites: |
[2243 or 2373 or 2573], & [2263 or 2374 or 2574]. Roughly this means a sophomore-level sequences in linear
algebra and multivariable calculus. Between the two, linear algebra will be more important; we'll work with vectors
throughout the course, and use linear transformations to classify isometries of the plane. I'll likely make use of
multivariable optimization only once throughout the semester. However, comfort with two-dimensional coordinates and
parametric curves will be important.
The ability to read, write, and understand proofs is important for success in this course. If you haven't previously taken such a course, pay careful attention to comments on your homework, and make use of office hours to ask me questions. |
| Textbook: | Required: Math 5335 Geometry booklet for Fall 2019, Fristedt & Baxter. Available at Alpha Print (1407 Fourth Street SE) in Dinkytown for about $29. Ask for it by course number. |
| Homework and Exams: |
You will generally have a homework assignment every week, depending on our pace, selection of material, scheduled
exams, etc. Some weeks you will have in-depth assignments with multiple written problems and proofs. During other
weeks you will have "lab assignments" using GeoGebra. These lab assignments
are generally shorter than the written assignments.
Assignments will be announced in class and placed online. Homework will not be accepted after an
announced due date unless you've made previous arrangements with me. Collaboration is highly encouraged --
please work with other students! However, your solutions need to be written in your own words, and your
homework should include a note saying whom you worked with. Occasionally (read: the day before Thanksgiving) I might give a special problem in class
which is not required, but might be worth some extra credit.
We'll have two midterms, tentatively scheduled for Wednesday 10/23 and Wednesday 12/4. Those dates will be confirmed at least a week before the actual exams. Our final exam is scheduled for 8:00 to 10:00 a.m., Tuesday, December 17, but we will have a take-home final instead, with details forthcoming later in the semester. Make-up exams will only be permitted in extraordinary situations. (Think "emergency surgery," not "oversleeping," although I will be impressed -- and envious -- if you manage to sleep through 12:20pm class. However, I have to assign grades based on your demonstrated knowledge of geometry, not your ability to sleep into the afternoon. That said, feel free to sleep in on December 17th, provided you have finished your take-home final, and are not missing another exam. |
| Grading Scheme: |
35% Homework 40% Midterms (20% each) 25% Final Exam Overall course grades will be at least this generous; I reserve the right to lower gradelines if a test or homework assignment turns out to be harder than intended.
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| Other Policies: | We will follow all University and CSE policies regarding academic honesty and other matters. The most common situation involves asking for a grade of incomplete. Incompletes are given only in extremely unusual circumstances, and only if you arrange it with me in advance. Incompletes are given only if you have completed most of the course material at a satisfactory level -- at least one midterms at a C level and a majority of the homework -- but some terrible, unexpected event prevents you from finishing the course. In particular, we cannot give you an incomplete if you simply fall behind in your work. |