I am extremely interested in the Putnam competition. Given that I am currently in 11th grade (so I have 12th grade and half my freshman year to study (plus summers and vacations, etc..)), what resources would you recommend to me?

I have done some research and found the following books. Is it advisable to use them to study for Putnam?

  • Principles of Mathematical Analysis -- Rudin
  • Real Mathematical Analysis -- Charles Pugh
  • Problem Solving Strategies -- Arthur Engel
  • Putnam and Beyond -- Andreescu
  • Calculus -- Spivak

Take a look at the following links:

  1. https://www.math.hmc.edu/putnam/
  2. Studying for the Putnam Exam
  3. http://www.quora.com/What-is-the-best-way-to-prepare-for-the-Putnam-Competition
  4. http://web.unbc.ca/~bluskovi/teaching/putnam/putnam.html
  5. https://answers.yahoo.com/question/index?qid=20100424024154AAxsocy

You can find good books scattered throughout the links. For a link which lists out the best references there without any clutter, click here: http://www.math.illinois.edu/~hildebr/putnam/resources.html

To relay a part of the content of the above link:-

[Beginner] A. Gardiner, The Mathematical Olympiad Handbook. The first part 
of this book contains a brief, but very handy collection of useful tools from 
algebra, geometry, number theory, and other areas. (The "Beginner" rating 
applies to this part. The second part, containing problems from the British     
Mathematical Olympiad, is much more challenging.)
[Beginner-Intermediate] E. Lozansky and C. Rousseau, Winning solutions, A good 
introduction to some useful background material from number theory, algebra, 
and combinatorics, and to problem-solving techniques.
[Beginner-Advanced] Arthur Engel, Problem solving strategies, A huge (1300+)  
collection of problems, with solutions, grouped by subject and proof technique.
The problems range from easy to extremely challenging.
[Intermediate-Advanced] Loren Larson, Problem solving through problems, A 
systematic treatment of problem-solving techniques, illustrated by Putnam level 
problems. Considerably more advanced than Lozansky/Rousseau, with the main
focus on techniques rather than theorems.
[Intermediate-Advanced] Paul Zeitz, The Art and Craft of Problem Solving.,
An excellent book for self-study for more advanced students. Problems are  
grouped by technique and by subject.
[Advanced] D.J. Newman, A problem seminar. A collection of 100+ carefully  
selected--and quite challenging--problems, with hints and solutions.
[Advanced] R. Gelca and T. Andreescu, Putnam and Beyond. At 800 pages, 
with 1100 problems, all with complete solutions, this is by far the largest
and most comprehensive Putnam training book. The level is fairly advanced 
and probably too much for all but the most experienced Putnam students.

Also, a personal recommendation includes http://www.amazon.com/The-Art-Problem-Solving-Vol/dp/0977304582, which, as a tenth grader, I find very interesting to solve problems from {Just got Principles of Mathematical Analysis today myself!).

Finally, I would like to say please have a look at problems scattered throughout the internet in sites like AOPS and MSE. Wishing you all the best for your studies; hope you have fun!

  • $\begingroup$ A problem seminar is a very strange book. Lots to learn in it, but badly exposed $\endgroup$ Mar 5 '15 at 19:37
  • $\begingroup$ ^I don't think it's too bad, some really good concepts are there immersed in this book. But yea...One could probably say his (Newman) exposition was a bit too rushed in some places. $\endgroup$
    – Kugelblitz
    Mar 6 '15 at 2:24
  • $\begingroup$ Good job listing all these references. Thank you very much! :) $\endgroup$
    – user62029
    Mar 6 '15 at 16:41
  • $\begingroup$ Your welcome @user62029 ! $\endgroup$
    – Kugelblitz
    Mar 7 '15 at 1:06

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