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Mar 13, 2016 Richard rated information technology really liked it

This is a fantastic introduction to real analysis. All the concepts are explained and motivated very well. It is great for self study, and requires merely as much as the calculus sequence and a previous exposure to proofs. This is a relatively easy book, though some of the exercises are really good. Do them all if you can. My merely gripes with this volume is that information technology could at least attempt to be more ambitious in its complexity. For example, it describes the backdrop of the real numbers in the beginning This is a fantastic introduction to real assay. All the concepts are explained and motivated very well. It is nifty for self written report, and requires only as much as the calculus sequence and a previous exposure to proofs. This is a relatively easy book, though some of the exercises are really good. Do them all if y'all can. My only gripes with this book is that it could at to the lowest degree endeavor to be more ambitious in its complexity. For example, it describes the properties of the real numbers in the first few chapters really only implicitly, and doesn't mention fields. I was confused past this, equally fields aren't all that hard to empathise as a general construction at this level (peculiarly if one has, say, seen vector spaces in a linear algebra course). Ultimately, I would recommend this volume to someone who is struggling with analysis, though you could certainly argue that this book isn't really necessary if you are studying from a more avant-garde book, with a stronger mathematical background. That is really my ultimate recommendation, as I think that students coming into real analysis should already take a off-white amount of mathematical maturity. If that isn't you, then become for this one. ...more

Easily the best math textbook I've ever used. One major frustration I take with university math texts that challenge their readers to think deeper is that the student'southward piece of work can often feel useless or misguided. The writing tin be unfocused or too presumptuous of what the the student can do. Yet, a balance must be struck against the other extreme: and so uncomplicated and repetitive that a student begins to think of the concepts every bit a collection of algorithms to complete.

This volume achieves a perfect residual

Easily the best math textbook I've ever used. One major frustration I have with university math texts that challenge their readers to think deeper is that the student'due south work can ofttimes feel useless or misguided. The writing can be unfocused or too presumptuous of what the the student tin practise. All the same, a balance must exist struck against the other extreme: so uncomplicated and repetitive that a student begins to recall of the concepts as a drove of algorithms to complete.

This book achieves a perfect residue of asking the reader to think deeper and persistently, gradually guiding them along. This book should be a aureate standard of how to begin each topic (and the unabridged book) with unproblematic concepts and issues, and grow each with complexity and difficulty until the student reaches such great heights of mathematical thinking and capability. Yet all of this happens without the reader dreading its difficulty. Material is presented so clearly, intuitively, and lightly. I highly recommend this book to anyone who wants the clearest pic of introductory analysis or an understanding of why calculus works and then well.

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January 11, 2021 Rafał Grochala rated it really liked it

Quite clear, approachable, prissy to follow. Filled in a lot of gaps afterwards Tao's Analysis. Quite articulate, approachable, overnice to follow. Filled in a lot of gaps after Tao'southward Analysis. ...more

Jun 30, 2019 Davi Barreira rated it information technology was amazing

This is the best book I found for learning assay the first fourth dimension, specially for self-study! The exercises evolve in difficulty, which gives y'all confidence that you are actually learning the discipline (considering yous are able to do the easy exercises as you read the chapter). As well, the examples and the writing are just swell! It felt like a novel! I merely wish I could discover other textbooks with the same "spirit".

This is the best presentation on Analysis I've read.

He does a really not bad job of motivating the ideas, and gives actually interesting and unusual examples, not just the normal basic examples.

Lot's of exercises for each chapter ranging from unproblematic to pretty involved proofs (no solutions).

Above all that information technology's just well written and a pleasure to read.

This is the best presentation on Analysis I've read.

He does a really nifty job of motivating the ideas, and gives really interesting and unusual examples, not just the normal basic examples.

Lot's of exercises for each chapter ranging from simple to pretty involved proofs (no solutions).

Above all that information technology's just well written and a pleasance to read.

...more

February 22, 2016 Kiên Trần rated information technology it was astonishing

concise, crystal clear, complete cadre of calculus/real analysis.

I wish nosotros had more maths textbooks like this. An outgoing and uncomplicated introduction to Existent Analysis, written in an engaging style and always focusing on the big picture and keeping track of where a sure theorem or fact fits in the scheme of things. The book is suitable for cocky-study, and is comprehensive equally far as a beginning-grade in analysis is concerned. Some exercises are usually part of the analysis which forces one to work on them. I accept done almost half of the exercises but I recomme I wish we had more than maths textbooks like this. An approachable and simple introduction to Existent Analysis, written in an engaging way and e'er focusing on the big moving-picture show and keeping track of where a certain theorem or fact fits in the scheme of things. The book is suitable for self-study, and is comprehensive equally far as a first-form in assay is concerned. Some exercises are usually part of the analysis which forces one to piece of work on them. I have done almost half of the exercises but I recommend doing all of them if you can.
To go the best results out of your self-study, you may supplement it with "counterexamples in assay" by Gelbaum and Olmsted. At that place is also a nifty playlist on youtube past Prof Christopher Staecker that follows this volume. ...more

Dec 12, 2019 Owen Jepps rated it really liked it

I like this book very much as an introduction to analysis, considering it motivates the concepts much more than strongly than most books from the traditional canon. I use this book for a reading course in assay: the chapters are well structured with a hook to motivate the content, and a squeamish summary at the terminate. I agree with some other reviewer'south comment that the treatment of the existent numbers is a picayune confusing due to the order, and 1 pupil noted that with so many parts of proofs left every bit exercises I similar this book very much as an introduction to assay, because information technology motivates the concepts much more strongly than about books from the traditional canon. I use this volume for a reading course in analysis: the chapters are well structured with a hook to motivate the content, and a nice summary at the stop. I agree with another reviewer's comment that the treatment of the real numbers is a little confusing due to the gild, and one student noted that with so many parts of proofs left as exercises (a corking idea in principle), readers have to suspend disbelief if they are unable to fill in those blanks. Only overall a great book., motivating some important concepts in mod analysis ...more

Feb 25, 2019 Tim Wetzel rated it it was amazing

Honestly the thing that pisses me off virtually about math books is when they're disorganized and written for the author, rather than for the students. This one has all the definitions, theorems, proofs, and problems arranged in a really digestible fashion. I really struggled with the concepts in this form (fuck serial, am I right) but the volume fabricated it possible to teach myself a lot of the harder concepts, which is a tough feat specially for a proofs course. This is ane of the notoriously hard classes a Honestly the affair that pisses me off well-nigh almost math books is when they're disorganized and written for the writer, rather than for the students. This one has all the definitions, theorems, proofs, and problems bundled in a really digestible way. I actually struggled with the concepts in this class (fuck serial, am I right) only the book made it possible to teach myself a lot of the harder concepts, which is a tough feat specially for a proofs class. This is one of the notoriously hard classes at Cal Poly, merely this book fabricated information technology a lot more than palatable. ...more than

Feb 21, 2021 Kevin Doran rated it it was amazing

Brilliant. Covers the essence of concepts that are easy to miss in other texts.

Update 1: it'south really amazing. I highly recommend reading information technology fifty-fifty if yous have read other analysis texts. I feel like a lot of other books brand you work hard but don't reveal the cardinal insights at play. If you have washed the hard piece of work from other texts, please take an amazing feel of skimming though this book.

Vivid. Covers the essence of concepts that are piece of cake to miss in other texts.

Update 1: it's really amazing. I highly recommend reading it even if you take read other analysis texts. I feel like a lot of other books make you work difficult just don't reveal the key insights at play. If you accept done the hard work from other texts, please have an amazing feel of skimming though this book.

...more

Nov 17, 2020 Thor rated it really liked it

I wish he covered the transition into higher analysis better. If you have a decent point set up topology background this book more often than not covers merely that. Finding a book that transitions, more strongly, into Lp Infinite and Fourier Series would be great. So, for case, yous can't easily read this book and and so jump into Rudin'due south Real and Circuitous Assay.

Otherwise, this is a v star book and very readable.

I wish he covered the transition into higher analysis better. If yous have a decent betoken set topology background this book more often than not covers just that. Finding a volume that transitions, more strongly, into Lp Space and Fourier Series would exist great. So, for case, you can't easily read this book and and so jump into Rudin's Real and Complex Analysis.

Otherwise, this is a v star book and very readable.

...more

Cracking introductory volume in analysis. Presents the material in a straightforward manner accessible to those with introductory calculus, and the many stories, backgrounds, and explorations the author offers help ground understanding. Just an accommodating great introductory math text for building conceptual agreement of analysis as a start await.

May xiv, 2017 Erickson rated it it was amazing

Very prissy introduction to analysis with adept background and motivation of why we are interested in diverse theorems or problems. Even the chapter on Fourier series was splendid. Naturally, this book doesn't go likewise far and then more difficult analysis must search elsewhere. Very nice introduction to analysis with good background and motivation of why nosotros are interested in diverse theorems or problems. Even the chapter on Fourier series was splendid. Naturally, this book doesn't go also far so more difficult analysis must search elsewhere. ...more

Practiced introductory undegrad assay text

Jun 27, 2021 Marcelo Coto rated information technology it was amazing

Great volume. This text, and Calculus ny Michael Spivak, were my main references during my first calculus course.

Sep 14, 2017 Randall rated it it was astonishing

It's a fine book, but the second edition is much better in that it has several additional sections which encompass the Lebesgue integral and some other very fine topics that the beginning edition doesn't embrace at all. Non that in that location isn't plenty for a get-go-semester grade in analysis in the 1st but the 2nd is just much meliorate for that very reason. It'due south a fine book, simply the second edition is much better in that it has several boosted sections which embrace the Lebesgue integral and another very fine topics that the get-go edition doesn't cover at all. Not that there isn't plenty for a first-semester grade in analysis in the 1st but the 2nd is simply much better for that very reason. ...more

Oct 01, 2008 Nina rated it information technology was astonishing

This volume was intense pain and utter pleasure for a class I worked extremely hard on - ultimately my favorite class. A keen reference for me as I learned the proofs backside why Calculus works.

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