The main focus of the course will be to solve interesting, challeging mathematics problems. Another objective is to help you develop good habits of mathematics communication (see below).
Here is one of the problems from the 2013 competition:
| Recall that a regular icosahedron is a convex polyhedron having 12 vertices and 20 faces; the faces are congruent equilateral triangles. On each face of a regular icosahedron is written a nonnegative integer such that the sum of all 20 integers is 39. Show that there are two faces that share a vertex and have the same integer written on them. |
The following notes serve as the main text for this course.
I'd suggest that you download a copy of this. HOWEVER, your grade will be partially determined on your activity in annotating a copy of this document that is posted on Perusall. So most of your reading should be done on Perusall. You'll be able to access Persuall through Blackboard, or you can create a free account at Perusall.com to access the course once the semester starts.
In addition, there are many resources, including free online ones. Here is a partial list.
Kiran S. Kedlaya, Bjorn Poonen, Ravi Vakil, The William Lowell Putnam Mathematical Competition 1985-2000: Problems, Solutions, and Commentary (MAA Problem Book Series), 2002, ISBN: 088385807X
To earn a grade in this course you will need to do the following:
For each class there is a main topic (e. g., Calculus, Probability, Geometry,...). About a week before each class, you will be given a reading assignment on Perusall. It will consist of some notes on the main topic and a list of problems. I'll expect you to post comments and/or questions on the reading on Perusall. Part of your grade will be based on your engagement in this activity. The problems in the reading assignment will be the ones we will work on in the class meeting for that topic. As part of the reading assignment activity, you can ask questions about the problems. Another way to engage in the this activity is to answer your classmate's questions. I'll answer some, but often I'll hold off answering if I think it's reasonable to expect the answer to come from the class.
If you have a solution to a problem in a reading assignment (partial or complete), you can post a hint or general outline of you solution. In addition, I'll encourage you to be prepared to share the solution in our meeting. We will have document camera in the class, so having the solution on paper would be a quick way to share it. Depending on how much board space we have, you could also write the solution on the board before the class.
Don't worry if you don't have a solution in every class. Many of the problems are difficult, but I've tried to include a few relatively easy problems in each week. I'm not telling you which problem is easy. Also, what is easy to one person isn't necessary easy to someone else. I understand that there are some topics that you might have less familiarity with than others.
After some classes I may assign a problem for the class to turn in using Gradescope.
The first class meeting is not typical. Since there is no required reading assignment although there are notes on Perusall you should take a look at. Feel free to comment on them.
I won't require that you use LaTeX in the course, but I'd like you to give it a try. There will be one assignment that will require using it. Even if you don't get in the habit of using it for full documents, you should be comfortable writing mathematical expressions with it since it's the standard way to do so on sites like Perusall.
One of the objectives of this course is to help you develop your mathematical communications skills. The following are a list of the things you should keep in mind for this course. I'll be looking for you to attempt to follow these guidelines.
Source: Richard Wong, UCLA, Active Learning Exchange on MAA Connect
All students are advised that there is a University policy regarding academic integrity. It is the students' responsibility to familiarize themselves with these policies. Students are responsible for the honest completion and representation of their work. Link to the Academic Integrity Policy
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