Straight From the Book Titu Andreescu Gabriel Dospinescu Books
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This book is a compilation of many suggestions, much advice, and even more hard work. Its main objective is to provide solutions to the problems which were originally proposed in the first 12 chapters of "Problems from the Book". The volume is far more than a collection of solutions. The solutions are used as motivation for the introduction of some very clear expositions of mathematics. And this is modern, current, up-to-the-minute mathematics. This is absolutely state-of-the-art material. Everyone who loves mathematics and mathematical thinking should acquire this book.
Straight From the Book Titu Andreescu Gabriel Dospinescu Books
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Straight From the Book Titu Andreescu Gabriel Dospinescu Books Reviews
Great book!
Remaining current in the ever-changing world of competitive mathematics is a must! If you are a student or mathematician who enjoys mathematical thinking and problem-solving, this is the book for you. Straight from the Book contains many of the solutions to problems proposed in Problems from the Book. The insights garnered from the authors that can be used to enhance your mathematical toolbox are invaluable, and at over 500 pages, the book is a treasure for honing your skills and truly appreciating beautiful problems.
Straight from the book deserves to be a great book based on its presentation of solutions for problems in Problems from the Book, but goes above and beyond to include more chapters of higher level topics, which presents key theorems and problem solving techniques that are not covered in any high school or most undergraduate courses. If you wish to understand and learn the tools of most advanced mathematics besides analysis, this book gives you a taste.
This is another mathematical pearl by Prof. Andreescu and his colleagues.
This is a sequel of the book "Problems from the Book" and a part of it
contains solutions (sometimes, several various solutions) to the first 12
chapters of "Problems from the Book", but there does also exist much much more
many other interesting topics and the following amazing addendums
2.A. Cauchy-Schwarz in Number Theory
3.A. Classical Estimates on Prime Numbers
3.B. An Introduction to p-adic Numbers
5.A. Hölder's Inequality in Action
6.A. Some Pearls of Extremal Graph Theory
6.B. Probabilities in Combinatorics
7.A. Finite Fourier Analysis
8.A. Lagrange's Inversion Theorem
9.A. Equations over Finite Fields
9.B. A Glimpse of Algebraic Number Theory
I do highly recommend this book and all other books of Prof. Andreescu to all mathematics lovers.
I love the way this book is written. The exposition of a new topic is always clear and concisely covers all the necessary theory. The problems (with their origin always mentioned) are intriguing and undoubtedly hard. The proofs, however, are written in such a way that all the steps are very natural and very easy to comprehend. As a conequence, after reading a proof one is not only persuaded that the result is true but somehow "sees" it has to be so. Finally, the addendums show the applications of the ideas behind these problems in more advanced branches of mathematics.
This book is a natural bridge between elementary "high school olympiad" mathematics and "serious university" mathematics.
This book does far more than just list the solutions to the PftB problems, even if you throw out the ten wonderfully written addendums. The "solutions" portions have actually been re-arranged so that problems with similar solution ideas are sorted into the same sub-sections (rather than in the order they appear in the exercises) written. That even makes it possible to read this like an independent text. (It also throws off the problem numbering with respect to the original, but hey, if you just wanted solutions you already had the MathLinks forum.)
Once again, the solutions and addendums are written in the same instructive tone as in PftB ("this is not really what we want to prove, but it shows that we are on the right track", "the miracle is that if this fails, then we can apply T2's lemma...", and so on), where the solutions and their motivations are really explained, rather than just a "proof for the sake of a proof" which is so common in many other math textbooks.
Anyone who enjoyed Problems from the Book would enjoy this book, too. Cannot wait to see something like this come out for the second half of PftB.
Accroding to the writers there are two obectives for writing this book
1) Providing a solution to the problems that orginally proposed on the first 12 chapters of "Problems from the book" and could not be included in the book due to lack of space.
2) Correcting mistakes in the statements of the proposed problems.
In order to hear variety of ideas the authors used a well known forum for problem-solving, mathlinks.ro, in which anyone could discuss and contribute to the solution. The final product is one of the finest problem solving book - mostly short and lucid solution which ensures the understanding of the reader.
In addition the authors also include in the book 10 addendums, mostly on advanced topics
1) Cauchy-Schwarz in Number Theory
2) Classical Estimates on Prime Numbers
3) An introduction to p-adic Numbers
4) Holder's Inequality in Action
5) Some Pearls of Extermal Graph Theory
6) Probability in Combinatorics
7) Finite Fourier Analysis
8) Lagrange's Inversion Theorem
9) Equations over Finite Fields
10) A Glimpse of Algebraic Number Theory
Each one of these addendums discusses the key theorems (along with their proof) on the subject.
This book came with missing pages and contrary order.
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