| ||||||||||||||||||
 Trade In this Item for up to £6.05
Get an extra £5 when you trade in books worth £10 or more until June 30, 2012. Trade in Numbers and Functions: Steps to Analysis for an Amazon.co.uk gift card of up to £6.05, which you can then spend on millions of items across the site. Trade-in values may vary (terms apply). Find more products eligible for trade-in.
|
Frequently Bought Together
Product details
|
More About the Author
Product Description
Review
' … an excellent guide through the basic course of mathematical analysis at university.' EMS
Product Description
The transition from studying calculus in schools to studying mathematical analysis at university is notoriously difficult. In this new edition of Numbers and Functions, Dr Burn invites the student reader to tackle each of the key concepts in turn, progressing from experience through a structured sequence of several hundred problems to concepts, definitions and proofs of classical real analysis. The sequence of problems, which all have solutions supplied, draws students into constructing definitions and theorems for themselves. This natural development is informed and complemented by historical insight. The novel approach to rigorous analysis offered here is designed to enable students to grow in confidence and skill and thus overcome the traditional difficulties.
Inside This Book
(Learn More)
First Sentence
The set of all whole numbers {1,2,3,...) is often denoted by N. Read the first page
Front Cover | Copyright | Table of Contents | Excerpt | Index | Back Cover
The set of all whole numbers {1,2,3,...) is often denoted by N. Read the first page
Explore More
Concordance
Browse Sample PagesConcordance
Front Cover | Copyright | Table of Contents | Excerpt | Index | Back Cover
Suggested Tags from Similar Products(What's this?)Be the first one to add a relevant tag (keyword that's strongly related to this product)
|
Sell a Digital Version of This Book in the Kindle Store
If you are a publisher or author and hold the digital rights to a book, you can sell a digital version of it in our Kindle Store.
Learn more
What Other Items Do Customers Buy After Viewing This Item?
Customer Reviews
Most Helpful Customer Reviews
13 of 14 people found the following review helpful
Format:Paperback
I found this book very helpful in my first year reading maths, and it is recommended by all of our lecturers. It guides you through step - by - step and even has the answers to the questions in the back so you can work out where you are going wrong / need more practice. Also included are some charts of prime factors etc. which came in handy for other courses. Overall I would say that this book was the best that I found for a comprehensible and user - friendly approach to numerical analysis.
Format:Paperback
This book is very different to all other books on analysis that I've seen, there are no massive definitions and theorems and proofs. Everything is taught via questions and so there are lots of examples of sequences and functions which is helpful for understanding the ideas. There are also fairly complete answers to all the questions which are often lacking in other books. All the definitions are worked through before hand to show not what they are but why they are too which makes all the pretty obscure definitions a lot simpler to understand. At the end of each main idea there are summaries too so it's a good reference. I would definitely reccommend this if you find the usual analysis books dry and hard to get into as this is so much easier and actually leaves you feeling like you understand the material.
Most Helpful Customer Reviews on Amazon.com (beta)
Amazon.com:
5 reviews
17 of 17 people found the following review helpful
Interesting and refreshing approach
6 May 2000
Format:Paperback
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.
16 of 16 people found the following review helpful
Numbers and Functions, Steps into Analysis
28 Feb 2005
Format:Hardcover
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.
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.
11 of 11 people found the following review helpful
Best Undergraduate Single Variable Real Analysis Text by Far
22 Dec 2005
Format:Paperback
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.
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.
Were these reviews helpful?
Let us know
Listmania!
Look for similar items by category
- Books > Science & Nature > Mathematics > Calculus & Mathematical Analysis > Functional Analysis
- Books > Science & Nature > Mathematics > Education > Higher Education
- Books > Science & Nature > Mathematics > Geometry & Topology
- Books > Science & Nature > Mathematics > Probability & Statistics
- Books > Science & Nature > Popular Science > Maths
- Books > Scientific, Technical & Medical > Mathematics > Applied Mathematics > Statistics & Probability
- Books > Scientific, Technical & Medical > Mathematics > Calculus & Mathematical Analysis
Look for similar items by subject
Feedback
- Would you like to update product info or give feedback on images?
- I am the Author, and I want to comment on my book.
- I am the Publisher, and I want to comment on this book.
|
