Ebook Analysis I: Third Edition (Texts and Readings in Mathematics)

Ebook Analysis I: Third Edition (Texts and Readings in Mathematics)

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Analysis I: Third Edition (Texts and Readings in Mathematics)

Ebook Analysis I: Third Edition (Texts and Readings in Mathematics)

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From the Back Cover

This is part one of a two-volume book on real analysis and is intended for senior undergraduate students of mathematics who have already been exposed to calculus. The emphasis is on rigour and foundations of analysis. Beginning with the construction of the number systems and set theory, the book discusses the basics of analysis (limits, series, continuity, differentiation, Riemann integration), through to power series, several variable calculus and Fourier analysis, and then finally the Lebesgue integral. These are almost entirely set in the concrete setting of the real line and Euclidean spaces, although there is some material on abstract metric and topological spaces. The book also has appendices on mathematical logic and the decimal system. The entire text (omitting some less central topics) can be taught in two quarters of 25–30 lectures each. The course material is deeply intertwined with the exercises, as it is intended that the student actively learn the material (and practice thinking and writing rigorously) by proving several of the key results in the theory.

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About the Author

Terence "Terry" Chi-Shen Tao, FAA FRS, is an Australian mathematician. His areas of interests are in harmonic analysis, partial differential equations, algebraic combinatorics, arithmetic combinatorics, geometric combinatorics, compressed sensing and analytic number theory. As of 2015, he holds the James and Carol Collins chair in mathematics at the University of California, Los Angeles. Professor Tao is a co-recipient of the 2006 Fields Medal and the 2014 Breakthrough Prize in Mathematics. He maintains a personal mathematics blog, which has been described by Timothy Gowers as “the undisputed king of all mathematics blogs”.

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Product details

Series: Texts and Readings in Mathematics (Book 37)

Hardcover: 347 pages

Publisher: Hindustan Book Agency; 1st ed. 2016 edition (June 27, 2016)

Language: English

ISBN-10: 9789380250649

ISBN-13: 978-9380250649

ASIN: 9380250649

Product Dimensions:

6.5 x 1 x 9.5 inches

Shipping Weight: 1.7 pounds (View shipping rates and policies)

Average Customer Review:

4.8 out of 5 stars

14 customer reviews

Amazon Best Sellers Rank:

#202,807 in Books (See Top 100 in Books)

You know, I'm honestly surprised that this book has not been adopted at colleges and universities other than UCLA. I've read all the analysis books on the market at this point, Rudin, Johnsonbaugh, Abbott and Ross, and to be honest, this particular book stands out among the others in that none of the content of this book is a regurgitation of memorized content. So many instructors, graduate students and textbooks simply memorize their material without questioning it, and then regurgitate the "industry standard, or accepted standard" methods in textbooks they write, and this is apparent if you read enough books. But Tao is different. You won't find a single reference to another book, and you won't find a single standard proof. Instead, what you'll see is exactly what and how Terrance Tao himself understands the concepts he writes about, and every proof and explanation is 100% original. The benefits of this is that you will never be questioning why something is the way it is since Tao personally goes out of his way to thoroughly explain every little darn thing inside and out with an obvious complete mastery over the subject. And along the way he challenges students to stop memorizing theorems, and rather, to start understanding them. I love this.

This book may not have the normal flavor of other analysis books. But it is by no means inferior. Especially if you are more of an algebra brain than an analysis brain, this book transfers you safely from your familiar world of algebra to that of analysis. Rudin will be more accessible afterwards.

As described, thanks

Solid text.

This is the best Mathematical Analysis book I know.Wonderful!!!

This isn't a reference text, this is a book meant to be read from beginning to end. If you are the type of person who likes to start from first principles then this is the book for you. There are no answers, but for the most part I didn't need them. A lot of the difficult problems are often broken down hence almost everything is manageable.Note: If you are currently in the middle of a real analysis class then this book likely isn't for you. By the time you get to page 90 you start to cover the same content most analysis books start to cover at around page 20-25. You NEED to start from the beginning to get the most from Tao's brilliant introduction to real analysis.Most real analysis books assume you have an understanding of the basics (sets, number systems, functions, etc). Tao does too, but he also assumes your understanding of the material is unrefined and hand-wavy at best and takes the opportunity to construct everything from the ground up. You start with the notion of an object, using this you define the Peano axioms and construct the natural number, as well as define what addition and multiplication are. After you take a detour and construct what is essentially Zermelo–Fraenkel set theory (axiom of choice comes much later near the end of the book). At around page 79 you define what subtraction is. Finally, at page 94 you begin your construction of the reals.Don't let the definition-proposition/lemma-proof style scare you. As you start by constructing everything from the ground up you are at no point confused as to what you need to do--the first principles approach gives you a sense of clarity you won't get from other books.I highly recommend some learning aids such spaced repetition (I used ANKI) and concept mapping. As you start from the very beginning there is quite a lot to take in hence without a way to organize your thoughts and revise you will easily find yourself forgetting things from the start.

Nothing was left behind on this book!

This book is extremely well written. I'd recommend it for everyone who wants to learn basics of analysis extremely well. I cannot think of such a book that goes to this fundamendal level of material as this one.

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Analysis I: Third Edition (Texts and Readings in Mathematics) PDF

Analysis I: Third Edition (Texts and Readings in Mathematics) PDF

Analysis I: Third Edition (Texts and Readings in Mathematics) PDF

Analysis I: Third Edition (Texts and Readings in Mathematics) PDF