A Friendly Introduction to Analysis, Second Edition

Rating:
Summary: Great book for learning, reference, and review.
Review: 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."

Rating:
Summary: Having problems with analysis? GET THIS BOOK!
Review: 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.