A First Course in Real Analysis (Undergraduate Texts in Mathematics) 2nd Edition by Murray H. Protter (PDF)

Description

Many changes have been made in this second edition of A First Course in Real Analysis. The most noticeable is the addition of many problems and the inclusion of answers to most of the odd-numbered exercises. The book’s readability has also been improved by the further clarification of many of the proofs, additional explanatory remarks, and clearer notation.

User’s Reviews

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

⭐My appreciation for this book grew with time. At first you may not like it very much because it can be very rigorous at times. There are great topics in the text that you will not find in others. After using and understanding this book, your level of mathematical maturity should be raised.

⭐The book arrived three days after I ordered it! It was in great condition with only markings it from a sticker on a the cover. Great price for a used book, barely used even it had a “good” rating.

⭐I don’t have words to describe this book, it is very comprehensive on the topic of analysis and the proofs are very understandalbe. Please note this book is an analysis book not a calculus one, this means you will find a lot of profs, theorems and definitions but not many exercises to learn to make calculations.

⭐a book that helped a lot in the course of the analysis I UNPRG Peru. The theory and the presentation of it is done in didactic way.

⭐Many definitions in the book are unclear. Proofs are unnecessary complicated while there is a simple straightforward proof. The problems really are too straight forward that I do not get practice at all. I would suggest to buy the other book to get a better basics in real analysis

⭐Good comprehensive book

⭐great

⭐First off, this is not a text dedicated to Functional Analysis and, I assume, anyone capable of reading the title would know that. If you are encountering, for the first time, the world of abstract mathematics by way of some class in Real Analysis, then this text is a nice and almost comfortable place to start. This text is not overwhelming terse and lacking in examples like, say Lang’s text, and, conversely, this text does not baby you and waste your time with verbose explanations and or proof like, say Strichartz’s text. Instead, I would say that this text stands above middle of the road beginning analysis texts and, in general, contains ample exercises as well as examples. Through out the entire text, the authors do an excellent job of not loosing sight of the fact that mathematics is about rigor, about intuitive understanding of abstract theoretical concepts. Remember, this text falls into a class of texts, such as Herstein’s, whose purpose (not necessarily primary) is to introduce the reader/student to elegant and more abstract concepts and not to assume that you are inherently gifted with the ability to quickly absorb these new abstract ideas and methods. That is, and with respect to students, this text is for persons with either very limited exposure to analysis or for those who are meeting analysis for the first time. Whereas, the existence of such nice and well thought-out examples make this book a must have as a reference. Especially for those engaged in more abstract higher analysis since the examples that have been given provide an excellent reminder that mathematics is built from the ground up, like a growing pyramid, and highlights the necessary role of abstraction. Finally, this text is thick and covers alot of material. Do not let this fact overwhelm you and in turn persuade you to not engage in reading it. Just take your time and suffer through it like all good mathematicians.

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