Introduction to Analysis (Dover Books on Mathematics)
by Maxwell Rosenlicht
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Book Summary Information
Author: Maxwell RosenlichtEdition: Paperback
Audio: English (Unknown); English (Original Language); English (Published)
Published: 1985-02-01
ISBN: 0486650383
Number of pages: 272
Publisher: Dover Publications
Product features:
- ISBN13: 9780486650388
- Condition: New
- Notes: BRAND NEW FROM PUBLISHER! BUY WITH CONFIDENCE, Over one million books sold! 98% Positive feedback. Compare our books, prices and service to the competition. 100% Satisfaction Guaranteed
Book Reviews of Introduction to Analysis (Dover Books on Mathematics)
Book Review: a bargain
Summary: 5 Stars
Buying this book is a no-brainer. It's only [price]. Unlike many dover books, it's not a reprint of a hundred year old text or dominated by 19th century style formal manipulations with indices running everywhere and no actual analysis or rigorous proofs. It covers the key topics of elementary real analysis (ie advanced calculus, or calculus with real proofs), which is basic to almost all fields of mathematics. In order to focus on the main ideas and definitions, it leaves out many topics and definitions (like functions of bounded variation, absolute continuity, lebesgue integration, differential forms, lebesgue covering lemma, f.i.c. etc.), so you should definitely have a more complete and comprehensive text like Apostol or Rudin (I prefer Apostol, although Rudin has complementary strengths). But for those omissions, Rosenlicht is quite a bit more readable than Apostol, which is best worked through methodically (since it contains a lot of results explicitly presented, its primary strength). Because it's both short and readable and focused, you can get through it reasonably quickly. Modern secondary school education teaches students to skip over the cursory material on elementary set theory, number systems, and strangely named but apparently obvious concepts like associativity and other field axioms, and to jump straight to the various sections with formulas in outlined boxes and procedure recipes for performing calculations. These rote recipes typically lack any conceptual unity and students are not often worse for wear forgetting or only superficially grasping previous ideas. This is a good way to never actually learn any legimate mathematics. Real math works on the principle of A->B->C->.... A proof (or your understanding of a mathematical concept) is only as strong as the weakest link in a chain. Learn and forget is not an adequate way to study math, and that's why introductory analysis is usually the course which weeds out those who will be able to explore the wider ocean of mathematical knowledge, and those for whom mathematics will be forever a giant forbidding question mark. The reality is, any above average person with the will, patience and time can learn this material and find themselves looking back thinking "Why was that so hard?" Blame it on the shabby state of secondary education. Do not skip over or gloss over the material on the real numbers if you aren't already fully conversant with the notion of l.u.b. and facile with its application (in which case why are you reading this book?). The l.u.b. property of the reals is your first real weapon to actually prove elementary theorem's of Calculus. Anyway this book isn't perfect, it's only good as an intro. and not a reference, but it serves the purpose of being accessible while still covering the key ideas and packing enough wallop to the requisite math whupping required by students numbed by years of inadequate secondary school education and the typical mechanical treatment of calculus and differential equations at the lower division level. And it's dirt cheap.
Summary of Introduction to Analysis (Dover Books on Mathematics)
Written for junior and senior undergraduates, this remarkably clear and accessible treatment covers set theory, the real number system, metric spaces, continuous functions, Riemann integration, multiple integrals, and more. Rigorous and carefully presented, the text assumes a year of calculus and features problems at the end of each chapter. 1968 edition.
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