Books Preparatory for Putnam Exam
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:
- https://www.math.hmc.edu/putnam/
- Studying for the Putnam Exam
- http://www.quora.com/What-is-the-best-way-to-prepare-for-the-Putnam-Competition
- http://web.unbc.ca/~bluskovi/teaching/putnam/putnam.html
- 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.)
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[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.
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[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.
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[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.
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[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.
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[Advanced] D.J. Newman, A problem seminar. A collection of 100+ carefully
selected--and quite challenging--problems, with hints and solutions.
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[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!