I am a student who is just starting high school and am very interested in taking part in the IMO (International Mathematical Olympiad). I am currently reading about inequalities. Having studied many of the classical inequalities, I have found that a good knowledge of functions and functional equations would be very beneficial. However, the books I have looked up seem very complicated and I have not found any book offering a friendly introduction into the subject for beginners. None of what I have looked up also relate to olympiad problems. Can anyone please recommend me a book that could help me get acquainted with the topic. Thanks.

  • $\begingroup$ You might find imomath.com/index.php?options=338 useful, but I almost always turn to eqworld.ipmnet.ru/en/solutions/fe.htm and especially eqworld.ipmnet.ru/en/solutions/fe/fe-toc3.htm $\endgroup$ – Henry Aug 31 '16 at 21:28
  • 1
    $\begingroup$ Related: math.stackexchange.com/questions/272591/… and math.stackexchange.com/questions/241445/… $\endgroup$ – Henry Aug 31 '16 at 21:31
  • $\begingroup$ @Henry I have checked the links, IMO math is providing problem-solving techniques (assuming you have prior knowledge). Also the other two links are giving more of a handout, listing and summing up the important parts. But I would like a good book to really understand the topic, and maybe also through exercises. I.e. I don't really know where all the equations in the last two links came from. I really need to understand the topic so that I could eventually solve problems, Olympiad level. I really appreciate your help but I just wanted to make it clear for anyone else who might want to answer. $\endgroup$ – Basem Fouda Aug 31 '16 at 21:35
  • $\begingroup$ Sorry, I didn't see the last comment. I think it would be helpful. $\endgroup$ – Basem Fouda Aug 31 '16 at 21:36
  • 1
    $\begingroup$ Functional Equations and how to solve them - Christopher G Small, is totally awesome. $\endgroup$ – gambler101 Aug 31 '16 at 23:05

Hint: Since you put the focus on inequalities I'd like to point to The Cauchy-Schwarz Master Class by J. Michael Steele. This book gives a comprehensive treatment of inequalities from many different perspectives. It is both, instructive and a pleasure to read. If you don't know it, it might provide you with a lot of nice gems.

A valuable, systematical primer into functional equations is Introduction to Functional Equations by Costas Efthimiou. It also provides IMO examples. Maybe it is even online available.

| cite | improve this answer | |

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.