Customer Reviews

Numbers and Functions: Steps to Analysis

5 star:		(3)
4 star:		(1)
3 star:		(0)
2 star:		(1)
1 star:		(0)

 

 

I worked through this book several years ago and I remember enjoying its style of pointing out an interesting property of a particular function, and then showing, step by step, that a whole class of functions have that property; that is, the theorems are built up from examples, instead of the other way round. I also think each step was quite manageable - there were no big gaps where I was left scratching my head not knowing what to do. It is not meant as a reference book, as you're more likely to find sketches or hints to parts of proofs, rather than complete proofs. I don't know if it's ever been used as a text book, but if it were, students couldn't just sit back and absorb knowledge - they would have to figure things out (with the benefit of lots of pointers to tell them what needs figuring out, and hints about how to do it), which is just what the book is intended to encourage.

If you follow the study plan laid out in the preface of this book, you'll get a background in Calculus and Undergraduate Analysis second to none. After this truly thorough coarse of study, 'little Rudin' will present few difficulties and 'Big Rudin' will be much more approachable. Depending on your background, you may have to buy the references that are conveniently listed at the beginning of each chapter. But the effort and expense is well worth it. If you're just starting out or you're looking for an indepth review of Calculus and basic Analysis, this book is THE best. This book will also benefit those studying applied math and engineering because it provides the mathematical background for many of the more complicated functions and approximations used in mathematical applications.

The poor review found above is not reliable. There is abundant background material provided in the excellant (and mostly cheap) references. Each chapter ends with historical insights very helpful in comprehending the material. The whole approach is based the presentation of fundemental concepts and their origins and implications. The title is exactly right. This book combines problem solving with the historical sequence that led to the development of the major IDEAS behind the mathematics. Thus, each problem is a stepping stone to the next problem. Each section is a stepping stone to the next section and so on. Also, each problem is broken down into conceptual components that allow the student to understand not only the raw mathematics but also the strategy used to solve the problem. Each problem set is followed by an exposition of the big picture of just what concepts are being illucidated. I love the very well done and useful approach to teaching. If you have no or a weak background in the subject of Calculus or Analysis, you must do the preliminary reading indicated at the beginning of each chapter. For those with a stronger background the concurrent and further reading suggestions are very helpful though not necessary in all cases. Be patient and give yourself a chance, it's well worth it.

This beautiful book is by far the best undergraduate single variable real analysis text I have seen. It covers all the basic topics in impeccable detail. Each chapter opens by listing a few references, labelled "Preliminary", "Concurrent", and "Further" Reading. The main part of each chapter consists of "questions" which guide the student through a complete theoretical development of the material and which the student is invited to work through. This part of the chapter contains definitions, statements of theorems, and informal discussion. This section is followed by a brief summary, outlining the previous material. Next comes a "Historical Note" which is very illuminating and fun to read. The last part of the chapter contains a complete working out of all the "questions". At the end of the book is an extensive bibliography, containing all books mentioned at the beginning of the chapters and many others. There is also an accurate and detailed index.

All in all, the text contains an exhaustive and perspicuous treatment of material which often is presented in a less transparent way in other texts such as Rudin. I also prefer it by far to other excellent recent books such as those by Ross or Abbott. The format engages the reader in a unique way that other books don't. This book was developed for use in the math program at the University of Warwick and as far as I know, it is still in use there. Unfortunately, it is less well known in the US. I cannot recommend this book highly enough. Once you see a copy for yourself, I think you will understand why.

This book is incredible. It actually guides you through the development of analysis in single strokes. By the end of each chapter you will have developed some important results that most textbooks just throw at you and expect you to grasp immediately. In each chapter, the author refers you to multiple readings to assist you with the topics within. This can be helpful when you want to delve deeper into something of interest. I'm sure the structure of this book will look strange at first sight, but once you actually sit down and attempt each problem, you will feel like you're in control of a careful development of analysis. For the Math teacher who thought this book was awful, I hope s/he reconsiders what the intended purpose of this book is.

Please. As a Math teacher. WOW! I can NOT understand this book. If you are looking for a book to make things more clear and present a review to your current understanding then find another book! This one is way too difficult to read - unless I suppose all you can relate to is numbers and signs, not humans.