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Book with undergrad-level olympiad type problems

  1. Sep 11, 2013 #1
    Hello everyone! My first post in this seemingly wonderful forum! Anyways, I an currently an undergrad and throughout my high-school career, I have honed my problem-solving skills very well. I have done very well on the olympiads, Putnam, IMC etc. Now that I am an undergrad, I still believe that solving problems is the best way to become better at problem solving. Can anyone recommend me math books with lots and lots of tough undergrad-level olympiad type problems, rather then just basic computational (plug-and-chug) exercises? Mainly for math, but physics/bio/chem/EECS would also be greatly appreciated. Thanks everyone!
  2. jcsd
  3. Sep 11, 2013 #2


    Staff: Mentor

    well there's always: Proofs from The Book

    with the best of the best proofs across a wide range of mathematical topics:


    and there's a recent book on Mistakes in Math:


    It doesn't have problems but it shows how errors creep into problems undiscovered until decades later.

    My favorite is: Mathematics 1001 by Elwes


    Again no explicit problems, but every topic can open up into a whole range of fun.

    For Physics perhaps the Arfken Weber Mathematical Methods for Physicists:


    Following each chapter, is a collection of problems in applied math/physics.
  4. Sep 11, 2013 #3
    Hi; the thing is I have done lots and lots of proof already. I was looking for a few textbooks like Rudin's Principles of Math Analysis which have lots of problems and theorems to proof. I went through the books in the "Math textbook listings" and spending some time with the list made me realize that I would need to complete most of the problems in most of those books! Also, thanks for replying!
    Last edited: Sep 11, 2013
  5. Sep 12, 2013 #4
    Also, I would prefer biology and chem books too.
  6. Sep 12, 2013 #5
    Try PUTNAM Problems available at MAA Web. if you like difficult undergrad math problems.
  7. Sep 13, 2013 #6
    I am looking for above-Putnam level. But thanks anyways!
  8. Sep 13, 2013 #7


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    Homework Helper

    Good luck getting an answer. Your best bet is to do what people have done in the past, apply your skills to a real problem, be it something medical or whatever.
  9. Sep 13, 2013 #8


    Staff: Mentor

    I agree, solve some interesting problems then solve some no one has solved.
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