Are There Any Recommended Books for Undergraduate Math Competition Preparation?

[talisman2212]

Hi. I am from Greece and I am an undergraduate student at the University of Patra and I study pure Mathematics. I am interested in mathematical competitions a lot, but I have never gone before in a mathematical competition. I want to study so I can be able to take part in competitions for undergraduate students. Here in my university there isn't lot of advising and preparation for students who are willing to take part in mathematical contests.
Could you recommend some good books for preparation in mathematical competitions for undergraduate students? I am also interested in books for solving problems, could you suggest me some good books? Any suggestions would be really appreciated.

 

[mathwonk]

how hard an exam are you contemplating? the hardest one in the USA is probably the Putnam exam:

here is a link for old questions and answers:

http://www.math.niu.edu/~rusin/problems-math/

 

[talisman2212]

I am willing to prepare for very hard exams, I have heard about Putnam exam, but I didn't know that is the hardest.

 

[disregardthat]

Try "The art and craft of problem solving" of Paul Zeits, it has helped me and many of my friends in competition problem solving, national and international. I think the book is superb, and as the author advises I recommend you to try to solve a lot of problems. Putnam isn't the hardest contest, I believe IMO for high schoolers, and IMC for university students are much harder and more prestigious.

 

[Bill Simpson]

This book is a training manual for the math olympiad.
https://www.amazon.com/dp/0387982191/?tag=pfamazon01-20
I thought the olympiad was supposed to be much less difficult than the Putnam, maybe I am wrong, but this book might teach you some things you did not know. I am not trying to sell books for Amazon. You can even see small parts of this book using Google books.

I once listened to a lecture by a person who had been a grader for the Putnam for years.
He claimed that, at least at that time and maybe still now, most people either get small or zero credit for each Putnam problem or they get almost full credit, there is little middle ground. He tried to explain what you needed to do to get the higher credit but it has been too long for me to remember what he said.

I strongly recommend you find a professor who is an expert on the Putnam and have them tutor you on the kinds of things you need to know and how to write answers so that you will score as highly as you can.

 

[talisman2212]

I'll try "The art and craft of problem solving" and "Problem-Solving Strategies". In my school unfortunately none professor is expert in mathematics contests.