Principles of Mathematical Analysis

Principles of Mathematical Analysis The third edition of this well known text continues to provide a solid foundation in mathematical analysis for undergraduate and first year graduate students The text begins with a discussion of the r

  • Title: Principles of Mathematical Analysis
  • Author: Walter Rudin
  • ISBN: 9780070542358
  • Page: 329
  • Format: Hardcover
  • The third edition of this well known text continues to provide a solid foundation in mathematical analysis for undergraduate and first year graduate students The text begins with a discussion of the real number system as a complete ordered field Dedekind s construction is now treated in an appendix to Chapter I The topological background needed for the development ofThe third edition of this well known text continues to provide a solid foundation in mathematical analysis for undergraduate and first year graduate students The text begins with a discussion of the real number system as a complete ordered field Dedekind s construction is now treated in an appendix to Chapter I The topological background needed for the development of convergence, continuity, differentiation and integration is provided in Chapter 2 There is a new section on the gamma function, and many new and interesting exercises are included This text is part of the Walter Rudin Student Series in Advanced Mathematics.

    One thought on “Principles of Mathematical Analysis”

    1. A remarkable text, but on reflection, perhaps not the most helpful read by itself- unless frustration is just your kind of motivator.Here are some supplementary resources-analysisyawp/rudinium.herokuapp/#/help(lectures based on this text)math.ucdavis/~emsilvi.rkeley/~gbergman/ug(companions for the text)mathcs/analysis/reals/ in AnalysisCounterexamples in TopologyA Companion to Analysis: A Second First and First Second Course in AnalysisA Radical Approach T [...]

    2. It's the classic. Terse, direct, clear, and horribly painful.This book forms the basis for the first class in real analysis (in a single variable) for countless thousands of hapless students who decide to concentrate on math. It's chosen by professors who have had decades of experience as university mathematicians, and have achieved a certain Zen-like understanding of the knowledge contained within.It's too bad they forget what it was like to receive that knowledge.As the purchaser and consumer [...]

    3. my god. this is the best mathematics book i've ever had a pleasure of using, even if it totally reduced my brain to oatmeal. don't let the size of the book deceive you (it's much smaller than most math textbooks.) it's incredibly terse, the problem sets are "fucking bullshit" (mind you, this is what me and my classmates would usually say after trying to attack a single problem for about a good couple of hours - but as "fucking bullshit" the problems were, they are pedagogically EXCELLENT problem [...]

    4. 'Baby Rudin' is to learning analysis as artificial insemination is to sexual reproduction. It's not good, it's not bad, and there are more fun ways of going about it, but at least it gets the job done.

    5. This was the text book for my real analysis course. I did not like this text book. I found it dense and hard to gain relevant information from it. Rudin optimized this book for the shortest proofs, and that isn't particularly useful for learning the material. Important results in Mathematics are given as exercises, which is cool, except that they are really hard, and there isn't enough material in the book to cover the problems.

    6. Going to commit to reading this book as a bedtime story each night since what better way to fall asleep than amidst some analysis.

    7. I used this book to learn analysis upon arrival at UW. Rudin is a professor at UW. There is nothing unnecessary in this book! In this way it reminded me of Gallagher's stochastic processes book. Every detail counts. This is the kind of textbook I appreciate, because I have a hard time reading long-winded explanatory text when it comes to math and engineering.

    8. What else would one pick if s/he wanted to understand analysis in a higher level? Anyone who wants to begin studying analysis he could use this book to establish the necessary fundamentals in his head. Then he can go for other books (as I will go) to check their problems and find out about the structure they have used to think about various topics of this field. :)

    9. The standard by which introductory real analysis texts are judged. Rudin's treatment is terse, but beautiful. This book is the one that convinced me that mathematics, and especially analysis, is my true love intellectually.

    10. The title of this calculus bible should have been "So you are a mathematical genius". Rudin introduces everything as if they came from out of nowhere, like a black hole. Counter-intuitive! Too bad!

    11. Baby Rudin is one of the clearest introductory level analysis textbooks out there. The price might not be ideal (over a hundred dollars for a book the size of a DVD), but the directness of the proofs is fantastic. There is no fluff in this book.

    12. This book is the textbook for my first undergrad math upper div course. It's very challenging. In order to understand it fully, reading it once would not be enough.

    13. Excellent approach from metric spaces at the very beginning. A good book that worth trying. Stuck at differential forms

    14. This is indeed a textbook directed more towards a class of Functional Analysis. The good news about this is that the author left a couple of chapters of "basic" analysis. If you've been out of the field for a while (a year or two), I do suggest looking over these two chapters (1 and 5) and possibly your initial material from your first analysis class. (The material is more directed towards how the teacher/professor teaches the class compared to your first analysis class.)

    15. I have mixed feelings about this book. How to describe it ok, let's talk kung-fu movies. So there's a standard trope in martial arts movies where the young apprentice shows up at the stoop of the Old Master and says, "teach me to fight". And the Old Master decides that instead of doing the obvious thing and having our hapless padawan practice something reasonable like, you know, punching techniques, the Old Master tells the aspirant do a series of incomprehensible and difficult tasks. Carrying t [...]

    16. Challenging, but richly rewarding.Excellent for developing mathematical maturity if you work hard at filling in details and trying to sketch proofs before reading those given. Useful for learning what are typically the most elegant approaches to proving theorems (which may be desirable from a mathematical perspective or simply a cognitive perspective - it can be difficult to remember the details of a messier proof).For first exposures to the field, this should be complemented with a book that ta [...]

    17. It's pretty much great, but the last 2 chapters are not for a beginner. The first chapter on mutlivariable analysis sounded fine, but the others were pretty painful to read. However, for someone with exposition to Manifolds, this seems like a perfect reference to come back too. The measure theory chapter wasn't easy to read, but I guess if one knows some measure theory, this chapter will come off as easy, and it'll be a great reference. Those last chapters are why I'll give Baby Rudin 4/5. But f [...]

    18. Rudin's Principles of Mathematical Analysis provides a pretty decent grounding in Real Analysis. Anyone who does anything with calculus should probably read it.That said, it isn't a perfect primer. The proofs can be difficult to follow, and the language is very high-level. Some chapters suffer from a lack of examples or explanation. To get the most out of this book, it really has to be a classroom companion; you're not going to get too much out of just reading it in your spare time.

    19. My textbook for Real Analysis. I've only read the first five or six chapters (up to differentiation), as those were the only topics we dealt with in Analysis I (Analysis II covers the second half). The textbook is well written, I think. It goes into very detailed proofs of the theorems in the text and the section about the construction of the reals was written in great depth. I thought it was an extremely useful book for the class. Also, the exercises were quite challenging (but that might just [...]

    20. Lives up to its reputation for excellence. If you are a young student of mathematics who wants to one day be deserving of the title of 'mathematician', you must prove yourself on the first seven chapters of this book. It is to the math community what the Bar Mitzvah represents to the Jewish community.

    21. I will take the opportunity to suggest that Lang's Undergraduate Analysis (probably) has a better selection of topics.Chapters 1 - 6 are excellent, 7 is pretty good (but maybe if you're going to only introduce Banach algebras for Stone-Weierstrass, and do nothing else about it, you might as well omit it), and the rest are not bad.

    22. This is an incredible book for budding mathematicians. Be prepared to fill in the gaps in Rudin's propositions. Not an easy read by any means, but worth it! I recommend this book to anyone about to undertake graduate work in Mathematics or to anyone who compulsively thinks about the underpinnings of Calculus on a daily basis.

    23. Pretty much a standard book in analysis. I always get a sense of "safety" when reading Rudin's material. There's the feeling that he's teaching you only the necessities; you know you are going to get where you need to in the most efficient way.

    24. Principles of Mathematical Analysis aka Baby Rudin is a classic introductory book on Real Analysis.Though it might be difficult for a beginner to get into the book.I think Terence Tao's Analysis I&II better serve the purpose.

    25. خلاقيت در اوج! تا به حال اينقدر نديده ام كسي اينقد پايه اي با مسائل تو رياضي برخورد كنه مخصوصن در اثباتبهار ٩١

    26. We used this textbook in our graduate analysis class. A great book, as long as you pay attention. Rudin's writing style is terse: say just what needs to be said, and little more.

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