This is a great book to get started with analysis; it has lots of information about math in general, and would be a good introduction to higher math for a high achieving high school student or undergrads at university. I recommend this book. I read it alongside Spivak An alright math book. I read it alongside Spivak calculus.
Great text. Material is quite well organized but the presentation is entirely too pedantic. I think it is too hard to read for the average undergraduate who approaches the two semesters of "Advanced Calculus" AC with great trepidation. Instructors: look elsewhere for a good text and students, which has continuity for two semesters.
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If this has been adopted for your AC course, READ the first few chapters, just to feel it out then look at the many other books cf. This book was written for Berkeley Math course almost 50 years ago. That it is still occasionally used for it as it was for the fall semester suggests that it does get the job done, so to speak. I spoke to an old-timer member of the math faculty at Berkeley and they described it as "a good book, if a little too dry". There are things to like about this book.
Its treatment of metric spaces so early and so extensively is refreshing. The material is presented clearly and if you're willing to take the time to push through it it's a well-crafted book. The exercises are a good mix of easy practice problems to mind-benders.
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I would not recommend trying to do all of the exercises in the book outside of the context of a course because they can be treacherously difficult. There are also some gaps in the coverage that might be due to its age and approach. For one, I don't think I saw a definition of closure, denseness, and a few other topics and the construction of the reals is very superficial. Still, the core ideas are communicated well. I'd probably recommend Pugh for something more complete and readable for an intro course but for the price I can't really complain about Rosenlicht.
It is also written in much clearer prose, which certainly offsets the panic you get when reading Rudin for the first time. The real numbers and their properties 2. Metric spaces, basic topology, open and closed sets 3. Compactness kind of a big deal, especially later on 4. Sequences and series 5.
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Continuous functions 6. As someone who has taken courses in analysis and topology, this book helped me very much. I somehow managed to make it through with excellent grades without ever truly understanding what was going on. Out of my own curiosity to truly learn and understand I picked up a copy of this book. I now feel as though I really understand the importance of things like compactness, completeness, and so on. This book also helped me understand the connection between analysis and topology. It is an excellent book for someone with passing familiarity of concepts. Join our Signed First Edition Club or give a gift subscription for a signed book of great literary merit, delivered to you monthly.
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