Primer of Modern Analysis (Undergraduate Texts in Mathematics) 2nd Edition by K.T. Smith (PDF)

Description

This book discusses some of the first principles of modern analysis. I t can be used for courses at several levels, depending upon the background and ability of the students. It was written on the premise that today’s good students have unexpected enthusiasm and nerve. When hard work is put to them, they work harder and ask for more. The honors course (at the University of Wisconsin) which inspired this book was, I think, more fun than the book itself. And better. But then there is acting in teaching, and a typewriter is a poor substitute for an audience. The spontaneous, creative disorder that characterizes an exciting course becomes silly in a book. To write, one must cut and dry. Yet, I hope enough of the spontaneity, enough of the spirit of that course, is left to enable those using the book to create exciting courses of their own. Exercises in this book are not designed for drill. They are designed to clarify the meanings of the theorems, to force an understanding of the proofs, and to call attention to points in a proof that might otherwise be overlooked. The exercises, therefore, are a real part of the theory, not a collection of side issues, and as such nearly all of them are to be done. Some drill is, of course, necessary, particularly in the calculation of integrals.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐In my introductory course in graduate analysis, I felt that I didn’t get an acceptable return on the amount of time I put into the course; when it finished I was not confident I really understood all the techniques, nor did I feel that I understood why abstract analysis is perhaps preferrable to the Classical variant. For the course, we used E. Stein’s text (mainly, but also bits of Tao and Folland). Stein is attractive to some instructors because he is such a renown analyst. I won’t contribute my lack of understanding entirely to the instructor or the text, but while reading the “Primer” the feeling was that the barriers were just peeling away without much fuss – a much different experience than previously. The weaknesses of the Reimann integral are spelled out clearly and then the modern foundations of analysis are set beautifully. Metric spaces and Lebesque integration are covered in the last half, but the text builds up to the modern notion of derivative as well.One drawback to the text for a graduate course is that the beginning third is really a review (with some additional depth) of undergraduate analysis, but also with a little abstract linear algebra and a discussion of geometry of R^n. Also, there isn’t the rigor or excessive use of notation that is present in many recent texts. However, I will add that often writers feel rigor and notation is an acceptable substitute for clarity. With Smith, I feel the limitations are easily managed because of his skill as a writer. Incidentally, this text is a perfect model of formatting and font — it enhances the reading experience tremendously.If I might use an analogy, often graduate courses are tall buildings with narrow foundations. A course with this text might be a less tall building, but with a broader, sturdier foundation. I prefer this latter style, since going further in the subject is far more seamless when the underlying motives and all the pieces are firmly in place.

⭐I bought two copies of this supposedly Hardcover textbook from the Amazon Marketplace. Both sellers sent me cheap foreign bootleg paperback copies of this textbook, NOT the hardcover edition described in the main Amazon listing. So if you are buying one of the used copies (the cheap $10 copies, especially if they say it is coming from India) be aware that you are getting a cheap inferior imitation version of the book that, technically, is against Amazon rules to sell here.

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