Real Analysis 1st Edition by N. L. Carothers (PDF)

Description

This is a course in real analysis directed at advanced undergraduates and beginning graduate students in mathematics and related fields. Presupposing only a modest background in real analysis or advanced calculus, the book offers something to specialists and non-specialists. The course consists of three major topics: metric and normed linear spaces, function spaces, and Lebesgue measure and integration on the line. In an informal style, the author gives motivation and overview of new ideas, while supplying full details and proofs. He includes historical commentary, recommends articles for specialists and non-specialists, and provides exercises and suggestions for further study. This text for a first graduate course in real analysis was written to accommodate the heterogeneous audiences found at the masters level: students interested in pure and applied mathematics, statistics, education, engineering, and economics.

User’s Reviews

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

⭐In the author’s preface, he states that the prerequisites are “one semester of advanced calculus or real analysis at the undergraduate level”. So, this book cannot be judged as an ‘intro to real analysis’.I just want to comment on how I have experienced this book. Let me mention that I am using this for self-study after completing a course using Rudin’s Principles of Mathematical Analysis (we covered every chapter except Ch. 10 on integration in R^n). I picked this up to review analysis with the goal of covering function spaces and measure theory with more emphasis that Rudin. This book does just that! But, I also wanted a book that stays in R for the Lebesgue measure. Having read the first 3 chapters of Folland, I didn’t really think I ‘understood’ the material even though I could do the exercises (but not without a lot of sweat and coffee). (At one point I felt I became a function: [input] facts, assumptions then [output] proofs, ie hw exercises.) Folland does everything for abstract measures and treats the Lebesgue measure as a corollary.Having said that, this books hits the spot.A previous reviewer said this book was informal, unprofessional, and chatty. I do agree with him on that the book is very informal in the exposition and is chatty. I feel that this might be very distracting for those who do not wish to be specialists in analysis, or to those who are seeing analysis for the first time. However, for someone who has finished, say Baby Rudin, this book IS AMAZING. His chatty ‘foreshadowing’ is the best part, since by now you are trying to see the ‘big picture’. In this respect, the chattiness tells of the shortcomings of the previous theory and points one to the right questions to ask.I think this book shines for the purpose of an intermediate course between Baby Rudin and graduate real analysis ala Folland. As such, the exercises are at the perfect level and include standard, important, and interesting results and extensions. I don’t think this book is rigorous enough for a real course at the graduate level, however.A final note, the editorial (why?)’s placed throughout do get annoying but I feel they make sure you do not take results for granted, an all too common habit when reading advanced math.

⭐I’ve gone through 1 term of this book and it’s been a horrible experience. Before I continue, I should say that I have gone through an entire semester of analysis at the undergraduate level. This book is used in the honors course at the university I attend. The text isn’t difficult to read in the sense of writing style, but it is difficult to understand. Indeed, the material isn’t beyond all abstractness; rather it is made more difficult by how the material is presented. As advertised, it is written in a more conversational manner, but in many instances it is often too brief. At times, there are gaps or jumps in explanations. Carothers often lacks explanation where it is needed most. A comprehensive book will explain clearly the concepts as well as the fine detail that many undergraduates get caught up in (e.g. – algebraic manipulations, alternative uses of definitions, etc.). Instead of going through the trouble of explaining why, he simply states “Why?” And will often not go on to explain why. I understand this is to make the reader think and wrestle with the material, but if one truly cannot understand the material, there’s really no where else to go but to ask the professor or TA. In my view, the idea of a textbook is to teach and present the material clearly, THEN challenge the reader by the exercises (after she at least understands the main concepts). If you end up being challenged so often in the readings, you end up on wikipedia more than you do the text. It would also be nice to see more pictures. Yes, pictures. As elementary or low-level as that may sound, pictures are absolutely necessary in explaining ideas. I bet there isn’t a single professor of any level that will teach topology effectively without drawing pictures. Just because they can be a hassle to insert with LaTeX doesn’t mean they should be avoided.What I do like is how the exercises are weaved in the sections per chapter. It makes it obvious to the student that this set of problems is heavily related the material that was just read. Nonetheless, after I went through the first four chapters of this book, I gave up on trying to follow it. It’s a good thing I had also been reading Rudin. Through the rest of the course, I just ended up using Rudin’s book, which I think is much more clear. I also like that Rudin goes through more proofs and examples, instead of just listing them off. It’s no wonder why Rudin’s book has been used for so long and at so many universities.I wish I was able to appreciate this book as much as the other viewers had. It’s not as if I have a personal gripe with Carothers, but this was not a happy experience.

⭐I highly recommend this text, especially for self-study.This book is like taking a course from one who loves the subject and knows it very well.And what is more, she wants to communicate her knowledge to you.She has anticipated your difficulties and is prepared to guide you.The material is well motivated; the historical asides help you understand and appreciate the material even more.There are a lot good exercises.One caveat is that analysis is on R not R^n.I particularly liked the discussion on the Cantor set.The material is pitched at the senior level.I wish I had this book when I was studying this subject.

⭐I buy this item for my study of real analysis. The book is soft cover, about A4 size, and the printer is very clear.

⭐I like this book because it is my textbook, and it is much easier to read than those written by Russian mathematicians. It covers most topics in basic analysis, but might be too lengthy to start with.

⭐Great book. Hard to read, but it explained the subject really well. The authors went to great lengths to explain everything clearly. I would suggest this to anyone.

⭐Joy to read and good solved example. Used it for self study.

⭐A good book for a beginning graduate student. I like his conversational writing style and additional historical information. A good book.

⭐One of my favourite treatments of the material typically found in a second course on real analysis, the author does a good job of feeding your intuition while being completely rigorous. The book also provides historical notes of the major problems mathematicians faced that inspired the development of the material.

⭐Writing style is very good. Best book till now I have read.

⭐The book is good for graduate level students.

⭐Good

⭐A wonderful book. A deep insight.

Keywords

Free Download Real Analysis 1st Edition in PDF format
Real Analysis 1st Edition PDF Free Download
Download Real Analysis 1st Edition 2000 PDF Free
Real Analysis 1st Edition 2000 PDF Free Download
Download Real Analysis 1st Edition PDF
Free Download Ebook Real Analysis 1st Edition