Problem-Solving Through Problems (Problem Books in Mathematics)

I'm a physics major and I bought this because I've been struggling in some of my math courses. The nice thing about this book is that it's not on its own a "contest practice" book, but rather a math book that is designed to hone your skill at doing math rather than your knowledge of a particular subject. It's very appropriate for upper-level math students in that it goes into some fairly advanced subjects, but most importantly it teaches you how to use your knowledge of those subjects. Interestingly enough, the skills I learned from this thing were very transferable. It wasn't just my math grades that improved, but also my scores in physics and computer science classes.

Finally, a book that develops problem solving techniques in a structured way for the Putnam. However, the techniques can be generally applicable to solve problems in many different areas. The power of using "first principles" to solve problems that at first sight seem almost impossible is brought out clearly. (Example, show that any sequence of consecutive integers is divisible by n!. Where does even start to solve such problems? The book shows you how.) You can read the book from the beginning to end, but a better way is to read it at random. Read the first chapter, though. It does a marvellous job of enumerating the different types of techniques. Enjoy this book. You'll be amazed at how simple ideas can lead to difficult problems.

I first read this book when I was in middle school. At the time I wanted a guide to solve mathematical puzzles and the pieces introduced herein has stuck with my all throughout my scientific career, whether in AI, genetics or medicine.

Great, challenging problems! Any upper level high school classroom should keep a copy on hand. Kids pull it off the shelf and wrestle with interesting problems during their down time and teachers find great , new ways to approach topics.

Came super fast and exactly what I wanted

This really is a great mathematics book. Before reading this, I read How to Solve It: A New Aspect of Mathematical Method by George Polya, another classic in math literature. This book takes the method of Polya's heuristics one step further by providing a wealth of examples in various disciplines including geometry, calculus, and abstract algebra. For anyone interested in developing problem solving skills, this book is a MUST! The only downside: no hints and solutions. Awesome book!!!!!

I would like to suggest that the audience for this book is somewhat broader than just the "all-star" math students. I will indeed use this book to help students preparing to take the Putnam exam this fall - it is the best book I have seen for this purpose. But in just the first two chapters, Larson presents strategies such as working backwards, modifying the problem, mathematical induction, and the pigeonhole principle, in a way which all math majors can benefit from. A graduating senior reported that once he started participating in math contests, his performance in ALL of his math classes improved. Problem solving unifies mathematical understanding. This student took the Putnam last fall (which, if you've got this far without knowing, is a six-hour national undergraduate mathematics competition taken by 3000 students in the US and Canada each year, approximately half of whom score zero) just to see what he could do, to gauge his improvement in mathematics. There isn't much more of a compliment a student could give me, intentional or otherwise. That can't all be attributed to this book, but it is that good. The presentation is unique; the organization - by strategy, rather than by year or whatever you see in other problem books - is illuminating by itself, and has improved my pedagogy; and he just makes hard problems look easy. Any student past the level of Linear Algebra who is up for a challenge will benefit from this book.

+ list of heuristics in chapter 1 + subchapter of the heuristic generalize - no solutions

In this book we find the polya's ideas working together to proof great an difficult problems, more of them belong to Putman so it could be a hard book to follow if you are not acquainted, but it worth to follow. This book help like in making you a best problem solver. I highly recommend this book, it is among the best problem solving books, together with problem solving strategies of Engel.

Entrega super rápida e o material em muita boa qualidade.