There is about a month left before the Putnam Exam, and it will be the last one I could take. I have looked over several problems from previous exams, and done several dozen problems from Paul Zeitz's The Art and Craft of Problem Solving. I still believe I need more training, and so, I found a large collection of exercises at Northwestern University's math department website.
The authors of this problem set segregated the different exercises based on strategies, which I will list below. Due to schoolwork, I don't have the time to work through each one, so I thought about picking $4$ or $5$ topics and working through as many problems as I could within those problem sets.
I'm curious to hear what my fellow MSE users would choose if they were in my position today. Which 4-5 topics would you devote your time to, and how would you rank them?
In order to minimize the "opinion-based" nature of this question, I ask that people give some sort of justification.
If you'd like to see the link to the problem sets, it's here: http://www.math.northwestern.edu/putnam/training_problems-2014.pdf
Otherwise, here is the list:
- Number theory
- Complex numbers
- Generating functions
- Pigeonhole principle
- Combinatorics and probability