"Problems from the book" by Dr. Andreescu and Dospinescu

[chungaops]

(Someone might have asked the question already. However, I could not find it by search.)

Can someones share their opinions about the book "Problems from the Book" by Andreescu and Dospinescu. Is it just another collections of competition problems or present systematic approaches how to solve the problems or else? I have been searching for the website trying to know how those who had the book thought about the book. Unfortunately, I could not find one.

Can anyone help? Many thanks.

Chin Hong

[Γιώργος]

[grfield]

A request to people who have seen this book : Can you please let me know how much do the contents of this book overlap the contents of other books by Andreescu or other sources? Basically, I am trying to figure out whether to spend the money on this. Is bulk of the content of this book already available elsewhere or does it have useful stuff that is not easily available elsewhere?

Thanks.

[PowerOfPi]

http://www.artofproblemsolving.com/Forum/index.php?f=584

[grfield]

Thanks. I had seen that. But, as I understand, those are only the unsolved problems from that book and might occupy just 30-40 pages in that book?

[fwolth]

PftB revolutionized my entire view of existence. Gazing back on empty, forsaken days before my enlightenment in the core of its pages, I wonder, a little wistfully, and not without astonishment, however I ever lived, how I ever trudged my way through the dreariness of every day life before my soul was set aflame with this masterpiece.

Anyways. Essentially, PftB is divided into chapters, each containing a few techniques in a fairly constrained field such as use of linear algebra in combinatorics, formal series, complex colorings, polynomial irreducibility, ordered based on the level of the mathematics contained within. For example, the first chapter is only a few trick algebraic substitutions for inequalities with constraints, while a chapter near the end might use in combination theorems from linear algebra, real analysis, as well as results like Alon's combinatorial nullstellensatz (which is one of the techniques covered in the last chapter).

It certainly is not just "another collection of competition problems". It does indeed contain "systematic" methods to solve the problems contained (each chapter has several problems of varying difficulties with fully written-out solutions to explain the concepts and then a section of problems based on the concepts at the end), assuming that by "systematic" you mean "methods which could be applied to make some progress on a wide variety of problems" - direct applications of a technique are generally only contained in a few introductory examples.