## 10 thoughts on “Understanding Analysis”

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➶ [Read] ➲ Understanding Analysis By Stephen Abbott ➾ – Centrumpowypadkowe.co.uk This book outlines an elementary, one semester course which exposes students to both the process of rigor, and the rewards inherent in taking an axiomatic approach to the study of functions of a real This book outlines an elementary, one semester course which exposes students to both the process of rigor, and the rewards inherent in taking an axiomatic approach to the study of functions of a real variable The aim of a course in real analysis should be to challenge and improve mathematical intuition rather than to verify it The philosophy of this book is to focus attention on questions which give analysis its inherent fascination.

- Hardcover
- 260 pages
- Understanding Analysis
- Stephen Abbott
- English
- 03 November 2017 Stephen Abbott
- 0387950605

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 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 you can My only gripes with this book is that it could at least attempt to beambitious in its complexity For example, it describes the properties of the real numbers in the first 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 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 you can My only gripes with this book is that it could at least attempt to beambitious 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 by this, as fields aren t all that difficult to understand as a general structure at this level especially if one has, say, seen vector spaces in a linear algebra course Ultimately, I would recommend this book to someone who is struggling with analysis, though you could certainly argue that this book isn t really necessary if you are studying from aadvanced book, with a stronger mathematical background That is really my ultimate recommendation, as I think that students coming into real analysis should already have a fair amount of mathematical maturity If that isn t you, then go for this one

concise, crystal clear, complete core of calculus real analysis.

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 s work can often feel useless or misguided The writing can be unfocused or too presumptuous of what the the student can do Yet, a balance must be struck against the other extreme so simple and repetitive that a student begins to think of the concepts as a collection of algorithms to complete.This book achieves a perfect balance 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 s work can often feel useless or misguided The writing can be unfocused or too presumptuous of what the the student can do Yet, a balance must be struck against the other extreme so simple and repetitive that a student begins to think of the concepts as a collection of algorithms to complete.This book achieves a perfect balance of asking the reader to think deeper and persistently, gradually guiding them along This book should be a gold standard of how to begin each topic and the entire book with simple concepts and problems, 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 picture of introductory analysis or an understanding of why calculus works so well

I like this book very much as an introduction to analysis, because it motivates the concepts muchstrongly than most books from the traditional canon I use this book for a reading course in analysis the chapters are well structured with a hook to motivate the content, and a nice summary at the end I agree with another reviewer s comment that the treatment of the real numbers is a little confusing due to the order, and one student noted that with so many parts of proofs left as exercises I like this book very much as an introduction to analysis, because it motivates the concepts muchstrongly than most books from the traditional canon I use this book for a reading course in analysis the chapters are well structured with a hook to motivate the content, and a nice summary at the end I agree with another reviewer s comment that the treatment of the real numbers is a little confusing due to the order, and one student noted that with so many parts of proofs left as exercises a great idea in principle , readers have to suspend disbelief if they are unable to fill in those blanks But overall a great book., motivating some important concepts in modern analysis

Honestly the thing that pisses me off most 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 way I really struggled with the concepts in this class fuck series, am I right but the book made it possible to teach myself a lot of the harder concepts, which is a tough feat especially for a proofs class This is one of the notoriously hard classes a Honestly the thing that pisses me off most 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 way I really struggled with the concepts in this class fuck series, am I right but the book made it possible to teach myself a lot of the harder concepts, which is a tough feat especially for a proofs class This is one of the notoriously hard classes at Cal Poly, but this book made it a lotpalatable

This is the best book I found for learning analysis the first time, specially for self study The exercises evolve in difficulty, which gives you confidence that you are actually learning the subject because you are able to do the easy exercises as you read the chapter Also, the examples and the writing are just great It felt like a novel I just wish I could find other textbooks with the same spirit.

This is the best presentation on Analysis I ve read.He does a really great 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 it s just well written and a pleasure to read.

Great introductory book 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 all around great introductory math text for building conceptual understanding of analysis as a first look.

Very nice introduction to analysis with good background and motivation of why we are interested in various theorems or problems Even the chapter on Fourier series was excellent Naturally, this book doesn t go too far sodifficult analysis must search elsewhere.

Simple and great book to get started with real analysis.