Principles of Mathematical Analysis (Int'l Ed) (TMHE IE OVERRUNS)

one of the best books I've read

This book is popularly called the Little Rudin, compared to the Big Rudin which deals with more advanced topics in mathematical analysis. Thought as a textbook for an undergraduate course, it likely spans two years in a student's career, introducing to all the basic topics of univariate and multivariate calculus, together with complex analysis and formal power series, and even more specialized topics such as Euler's gamma function. The text is always clear and the proof are well constructed; some topics are put in the exercises sections, which forces the reader to actually go through them, a choice which I cannot object to. This book should have a place on the bookshelf of everyone who holds mathematics as a strong interest.

If not an introductory text, it is certainly a great review text.1st year mathematics is heavily focused on grounding the student in mathematical analysis. Sequences, series, limits, sums, continuity and differentiability are the bread & butter concepts every maths student needs to know inside out. They call this task, 'the leap from school maths into university maths'.Sets, functions, proofs, linear algebra, groups and permutations are the foundations of the 1st year but they are quite readily taken on board by most new students because they are in a sense more familiar and intuitive.If anything is going to seem unfamiliar to a fresher it will be analysis but by the end of your degree, you will come to regard this stuff to be as fundamental to your maths degree as counting.I found myself using this book quite a lot both in my 1st and 2nd year. By the 2nd year, it tends to replace all your first year analysis notes because it is all concisely laid out in this book for your review.ps: I really like the section about differential forms personally near the end of the book.

This is good as a reference, but rather intimidating as a textbook. There is little in the way of motivation or explanation and the proofs are very concise, which is good if you already get the ideas, but not so good if you're trying to understand them for the first time.

I am a fan of Rudin's books. This one "Principles of Matheamtical Analysis" has served as a standard textbook in the first serious undergraduate course in analysis at lots of universities in the US, and around the world.The book is divided in the three main parts, foundations, convergence, and integration. But in addition, it contains a good amount of Fourier series, approximation theory, and a little harmonic analysis.I loved it when I was a student, and since then I have taught from it many times. It has stood the test of time over almost three decades, and it is still my favorite. I have to admit that it is not the favorite of everyone I know.What I like is that it is concise, and that the material is systematically built up in a way that is both effective and exciting.The exercises and just at the right level. They can be assigned in class, or students can work on them alone. I think that is good, and the exercises serve well as little work-projects. This approach to the subject is probably is more pedagogical as well.I think students will learn things that stay with them for life.Review by Palle Jorgensen.

I can only concur with the reviewers who point out how bad this is to actually sit down and read. I had it recommended as a second text on real analysis, primarily for the extension into higher dimensions. Coming from the impossibly good Spivak ("Calculus") as my introductory text, Rudin was a shock to the system, for a number of reasons:Firstly, the overall feel is of a cheaply made book. The spine on my copy cracked within a few months and pages became unlodged. Maybe the quality is better nowadays, but bear this in mind. This is the same edition (mine was the 15th printing, dated 1989). In comparison, my Spivak still looks as good as new, and it's been read a heck of a lot more!Second, the print is faint and and the fonts appear thin, which is a constant irritation that drains mental energy unnecessarily. Also, the notation is difficult because the italicized letters used to represent some objects are so illegible as to make a mental note impossible ('must remember such-and-such is represented by squiggle'). This again distracts you from the mathematics itself.Lastly, the whole approach is cold and distant. I know this is what most professional mathematicians seem to approve of (can't think why!!) , but I personally don't get it. Mathematics has a hard enough time recruiting and maintaining the interest of students (a high proportion of students on my course - all with 3 A's at A-level when such a feat required intelligence - virtually gave up in the second year, largely through having to refer to books like this), without turning them away with bad teaching. Yes, rigour is absolutely essential, but without providing motivation or at the very least some kind of geometric intuition (a picture is worth...), a text like this seems to lose half its impact. I remember reading Spivak with pleasure, almost without realizing I was studying pure gold that distilled the genius of the some of the finest mathematicians in history.Lastly, the price. Almost twenty years on, my copy still has its price sticker: £10.95 including a very durable removable plastic jacket. Book inflation for the intervening period is not 300%. For such a commonly cited text, this is a disgraceful ask of present students.In summary, BUY WITH EXTREME CAUTION. Sadly, I don't know which text to recommend instead, but MOST undergraduates will regret spending valuable beer money on this book. I'd do a search on Amazon for some newer original books (the Springer series seem to be generally more readable that most of the texts I had to suffer). I hope this review helps you in your search.