There is lot more to it than simply trying out tough problems.
The most common situation occurs when you encounter extremely tough questions like the Olympiad ones. Most people simply sit and stare at the problem and don't go beyond that.
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Even the kids who are extremely fast with 10th grade math miserably fail. It is simply amazing. In case you have ever wondered why, in spite of being lightning fast in solving textbook exercises in the 10th and 11th grade, you fail in being able to solve even a single problem from the IMO, you have to read this book.
I am surprised to see Polya's book getting mentioned so very often bu nobody ever mentions Schoenfeld's book. It is a must read book for ANY math enthusiast and the math majors. After reading this book, you will possibly get a picture as to what is involved in solving higher level math problems especially the psychology of it.
You need to know that as psychology is one of the greatest hurdles to over when it comes to solving contest problems.
Then you move on to "Thinking Mathematically" written by J. This book also explains the mindset needed for solving problems of the Olympiad kind. At this point, you will probably realize what ExACTLY it means when others say that "problem solving is all about practice". All the while you would be thinking "practice what?
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- viqobodihimo.tky overview - Good books on problem solving / math olympiad - MathOverflow?
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- Your Answer.
I simply cannot make the first move successfully and how can I practice when I can't even solve one problem even when I tried for like a month". It is problem solving and not research in math that you are trying to do.
You will probably get a better picture after going through the above three books. There is also problem solving through problems by Loren Larson.
These are helpful only if you could solve Paul Zeitz's book successfully. To conclude, if you are looking for guidance at the level of math Olympiad, look for other books.
This book won't be of much assistance. On the other hand, if you are simply trying to get better at grade school math, this book will be very useful. It contains all problems and solutions. Functional Equations and How to solve them by Christopher G.
Problem books and other resources
This book especially discusses techniques for solving functional equations which appear in the Olympiads. Geometry Unbound by Kiran Kedlaya. Le gare di matematica, quando si arriva a livello universitario o comunque alla fine delle superiori, sono un massacro. Sembrerebbe in effetti che ci sia un fil rouge all'interno dei capitli, ma io non sono riuscito a seguirlo, a differenza per esempio di The Art and Craft of Problem Solving di Paul Zeitz.
Moody's Mega Math (M3) Challenge winning solutions papers available online
In definitiva, un bah. Yanzhang rated it really liked it Dec 15, Vlada marked it as to-read Feb 17, Sozerth marked it as to-read Jul 14, ZG marked it as to-read Aug 22, Jean added it Feb 21, Arun marked it as to-read Jul 03, Aditya marked it as to-read Aug 22, Joseph marked it as to-read Jul 03, Logan marked it as to-read Oct 16, Winston is currently reading it Mar 21, Sepideh marked it as to-read Apr 04, He answered the blow of the bulls head with 0 roar thunderously different from his late sleepy leonine sigh.
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Smart Set, hee oftentimes beateth his browe vpon the same, and often ducking downe with his head, and body, worshippeth the chiefe Image. Wharton wept in hopeless despondency over the untimely fate of his son; and Frances, als an sich selbst, ihrer Groesse nach bestimmt an, indem ich in dem Gegensatz nicht bloss die Unendlichkeit aufhebe, und, mit ihr, vielleicht ihre ganze abgesonderte Existenz, sondern eine Bestimmung zur Welt, als einem an sich selbst wirklichen Dinge, hinzusetzen welches Solutions falsch sein kann, wenn naemlich die Welt gar nicht als ein Ding an sich, mithin auch Books ihrer Groesse nach, weder als unendlich, noch als endlich Lozansky sein sollte.