How to Solve It

Course Description and Grading Breakdown

The William Lowell Putnam Mathematics Competition is the most prestigious annual contest for college students. While the problems only employ machinery from the standard undergraduate curriculum, the ability to solve them requires a great deal of ingenuity. This can be developed through systematic and specific training, and it is this class' aim to assist the interested students in the preparation for the Putnam exam. Beyond the competition itself, problem solving is an essential skill in every discipline, so at the same time we will use the contest as an excuse to develop this ability through challenging (but fun) problems. These problems will generally come from mathematical competitions, but the syllabus will be constructed around carefully-selected topics which simultaneously develop problem solving techniques and inspire discussions about more advanced mathematics. Our aim is to use the competition problems to provide a tour through many interesting topics, and to expose a bridge to higher mathematics.  

Grading will be based on attendance and weekly homework. Caltech students who are not officially enrolled are welcome to participate, but should not hand in homework.

Course Meeting Time and Location
Tuesday
7:00 - 8:55 pm
103 Downs Physics Laboratory (DWN)

Course Instructor Contact Information and Office Hours
111 Math Building (Building 15)

210-I Math Building (Building 15)


Office Hours
TBD


Contest and Course Schedule

The Seventy Eight Putnam Examination will be held on Saturday, December 2nd, 2017It will consist of two sessions of three hours each. Also, do not forget to register. You can do that by sending an e-mail to Meagan Heirwegh. The deadline is Monday October 9th at noon. See the flyer at the bottom of the page for more details.

The rough schedule for the quarter below.

 DateTopic 
      09/26 
      10/3 
     10/10 
     10/17 
     10/24 
     10/31 
     11/7 
     11/14 
     11/21 
     11/28 
     12/02       Putnam exam


Course Policies

You are expected to attend class and submit homework every week. You should hand in carefully written solutions to exactly three problems for each assignment. Problem sets will usually contain six problems on the week's topic, together maybe with some supplementary ones, which can be tangential. You are encouraged to work on more than three for your own enjoyment, but they will not be graded. For each homework, you are also encouraged to submit partial progress for one of the questions marked as difficult instead of a full proof for an easier question. You will receive credit as for a full proof if you show work.

Your goal in this class should be to learn the largely individual skill of problem-solving, so collaboration on the homework (before having solved three problems independently), while not forbidden, is rather discouraged. You should spend a significant amount of time tackling a problem on your own before you ask a friend or consult the internet. 

Assignments

 Date PostedAssignment Due Date 
   
   


Resources

I will send frequent e-mails with various reading recommendations based on the topics we will be discussing. In addition to these, you are also encouraged to consult:

Putnam archive by Kiran Kedlaya. This page contains all the problems and solutions from the recent Putnam exams.
Putnam and Beyond by Titu Andreescu and Razvan Gelca. This book is available electronically via the Caltech library.