Numbers and Functions: Steps into Analysis 2nd Edition by R. P. Burn (PDF)

Description

The transition from studying calculus in high school to studying mathematical analysis in college is notoriously difficult. In this new edition of Numbers and Functions, Dr. Burn invites the student to tackle each of the key concepts, progressing from experience through a structured sequence of several hundred problems to concepts, definitions and proofs of classical real analysis. The problems, with all solutions supplied, draw readers into constructing definitions and theorems. This novel approach to rigorous analysis will enable students to grow in confidence and skill and thus overcome traditional difficulties in learning this subject.

User’s Reviews

Editorial Reviews: Review ‘ … an excellent guide through the basic course of mathematical analysis at university.’ EMS Book Description In this second edition of Numbers and Functions, the reader is invited to tackle each of the key concepts of mathematical analysis in turn.

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐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.

⭐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.

⭐Useful elementary guide for Analysis, including basic examples and tons of questions to help for those like myself who need to be questioned.

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