Customer Reviews

A Friendly Introduction to Analysis

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

 

 

The appeal this text has to readers is that it is approachable, readable, and thorough. Among the topics included are proof techniques, sequences, limits, and single and multi variable calculus.

In comparison to other books I have studied concerning this material, this text has been written with students making the transition from computational mathematics (calculus sequence, linear, DEs) to analytical, theorem proving mathematics in mind. There is a strong emphasis on conceptual understanding and on how the topics are related to one another, with motivation provided for the study of each topic. Theorems are presented in a logical sequence, a large number are proved, and the discussions are very useful in pointing out important aspects of theorems and special cases to consider.

Concerning exercises, one nice thing I have come to appreciate is that, while being an analysis text, computational exercises are provided to ensure that the concepts are fully understood. Following these exercises, the numerous examples will help when completing the requested proofs.

The second edition is noticeably slimmer than the first. This is mainly due to a change in typesetting (which is better, in my opinion; the text is closer together so the pages look more full). There was one chapter removed on Fourier Series, but this can now be downloaded from Dr. Kosmala's web site. Aside from this one removal, there is more material presented in the second edition to go along with the corrections and rearrangements to the first.

Analysis can be a difficult subject to grasp, so I highly recommend this text for (as the preface says) its "clarity, readability, and friendliness."

This is a wonderful book for all of you out there that are struggling with analysis because your professor has chosen a traditional analysis text that is very terse like Rudin. The problem with so many of the traditional analysis textbooks is that you need a professor by your side guiding you, and without that type of help a student beginning analysis would be completley lost.

So to remedy that situation I strongly recommend all of you future analysis students to first take a look at this book. I think one of the main problems with students taking analysis is that it overwhelms them at first because it is nothing like the rest of the undergraduate curriculum in school. The math programs at most universities ignore analysis until the senior year. Typically before that students are in math courses that are purely computational. Usually learning calculus out of Stewart or something and never really touching on the theoretical aspects of calculus.

So of course when a student hits analysis its going to be mind boggling. That is why this book is so wonderful. It is sort of bridge from computational calculus to advanced calculus. It is not intimidating like so many of the analysis books. It approaches each subject matter in a very clear fashion. It has many examples which is rare for an analysis book.

I found chapter 8 to be a wonderful treatment of sequences and series of functions. I think many students would agree that concepts such as uniform convergence can be confusing but the author does a great job illustrating this somewhat complex topic.

All I can say is I wish when I was taking analysis I had access to this book. I think this book is great for an undergraduate analysis class as well as a first year graduate level class.

I think also if you are doing self study to prepare for examinations I think this is a great reference book. I really appreciate the author's efforts to write an analysis textbook that is so easy to read.

I selected this text for my undergraduate analysis class. It was a big mistake

it starts out nice and chatty and "friendly" but the author soon buries the

material in detailed tangential remarks. Particularly annoying is

his comparing exercises to many previous ( and future!!) problems in

the text. Togetherbwith the remarks the text grinds to a halt trying

to leaf back and forth to reference them. My students found this book

to be very difficult. Even simple things to prove he sometimes refers

the reader to previous material. My students need help on simple

things involving series say. He includes so many different ratio tests

for example and then has few straightforward probs for them to do.

It was an ordeal selecting problemsfor them to do.

Many of the easy ones he refers them to previous probs in

the text so the student refers back to the earlier solution instead

of proving it himself. A really bad experience!

This book is required for a 2 semester course that began fall 2010. I bought it from Amazon.com.

The first problem is the content layout. The author has you jumping forward and backward through the chapters while explaining the current chapter. This is not an occasional thing. It's extremely frustrating and totally unnecessary. The author does a decent job of explaining things and if the book was organized better, it might be a decent textbook.

The second problem is that this book, published by Pearson Prentice Hall began falling apart within a couple weeks of my purchase. By the end of the semester, it was in two parts and now individual pages in each part are begining to come apart. I don't know when Prentice Hall became "Pearson Prentice Hall" but I have text from Prentice Hall that have held up well for a couple decades and have been used during this time. At some point, they started putting out very poor quality books and this is one.

If you have a choice, I'd suggest finding another text. If you are a instructor, please don't choose this text and force students to waste their money. While the book is cheaper than many others, if it falls apart, it is still a bad deal overall.

Bunch of lies the two reviewers gave. I bought the book, tried to learn from it, and ended up hating the book. I realized pretty fast that the book is like any ordinary real analysis book: routine restated theorems, routine common simple problems, routine impossibly hard exercises, and routinely almost zero help from the back of the book. Sure, sure...I needed help from this book for a class using a different book while that book is presented exactly the same way as this book. I know for sure that this book or any book on real analysis anywhere is set out to doom my head to never ending death of my desire in mathematics. Can't anybody publish a book called "Real Analysis for Dummies"? Cause I surely need to buy that book.

The idea of this book is great - you are sitting in front of Rudin, you have no idea what to do and all of a sudden you open this book and things become clear! Umm, not quite. First, this book has had problems with a multitude of typos (see the author's web site). Second, the title is stupid. There is no such thing as a 'friendly introduction to analysis'. That's an oxymoron if ever there was one. This book is very good at explaining basic ideas and giving you some insights BUT IT STILL AIN'T RUDIN (and its discussion/proofs of convergence tests is weak since they all link back to geometric sums and that is not mentioned here). If you want to study analysis you eventually have to make large pot of coffee, put butt in chair, take out pencil and a raft of paper and start working - without tv, ipod, music, dog, wife, etc. Will this book help some? Sure, it is a nice reference. Will it teach you enough to say you know analysis. No.