MATH.5200-201 Mathematical Problem Solving

**This will be a virtual class, which means that you will be expected to attend a Zoom meeting each week.** The class will meet online on __Tuesdays__, 3:30 - 6:15 PM, but **
if you take this course,
you must also be available from 10AM to 6 PM on Saturday December 5, 2020** to compete in the William Lowell Putnam Mathematical Competition - this will be your final exam for the course.

**It is unclear what effect the Covid-19 pandemic will have on this year's Putnam. If it is cancelled, an alternative UML competition will be arranged.**

The main focus of the course will be to solve interesting, challeging mathematics problems. 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 Putnam Archive
- This is the third in a series of Putnam problem books published by the Mathematical Association of America.
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 - Michael Penn (Randolph College) had posted many excellent (and entertaining) videos at https://www.youtube.com/c/MichaelPennMath/. Lots of them are Putnam problems or problems from similar competitions.
- The Art of Problem Solving Community is a site devoted to problem solving at all levels, but has some specific resources relating to the Putnam.

To earn a grade in this course you will need to do the following:

**Attend classes.**Unless you have valid medical or legal excuse for missing a class, you will be considered absent. You get one free absence, and then your starting grade will be moved down the list {A, A-, B+, B, B-,...}. Your starting grade will then be the highest possible grade you can earn in the course, assuming you do "A" work for everything.**Participate.**40% of your grade will be based on your participation and effort both inside and outside of the class. This includes engagement in discussions on the course's Piazza page.**Work independently on problems.**There will be problems assigned for work outside of class. Your work on them will represent 30% of the final grade.**Compete**. You must compete in the William Lowell Putnam Mathematical Competition on December 2. Competing is 20% of the grade. We will meet on Wednesday, December 11 to "debrief."**Reflect**. The final requirement for the course will be to write up a reflection on the course and the competition. In this 3-5 page paper, you can describe your efforts, preferably highlighting one of the Putnam problems. In addition, you can comment on what you've learned about mathematics and the problem solving process. This will count for 10% of the course and will be due Monday, December 16 at noon.