Since you're planning to actually take analysis courses in a few months, rather getting one of the standard real analysis texts that others have suggested, I recommend looking at Andrew M. Apart from a good introduction of the Metric Space Theory (to learn what is open, closed, compact, perfect and connected set), there is a number of results on convergence of sequences of functions, multivariate calculus, introduction of $k-$forms and introduction to Lebesgue measure.Īs a sequel, one should consider the great little classic, Spivak's Calculus on Manifolds, which provides an elegant and concise introduction of $k-$forms and proof of Stokes Theorem in Euclidean spaces and manifolds. Second reading, right after Spivak: Principles of Mathematical Analysis, by W. However, Spivak's book treats only one-dimensional Calculus. a construction of $\mathbbf(y),\quad x\in\mathbb R.I want the book to contain the following topics: I already took proof based courses like linear algebra and group theory, so I think I am ready to start to learn rigorous real analysis, so I'm looking for a book that suits me. The theory I saw contained proofs but the main goal of the course was to succesfully learn to solve integrals (line integrals, surface integrals, double integrals, volume integrals. I did learn about stuff like epsilon and delta proofs but we never made exercises on those things. I got courses of calculus, but these weren't very rigorous. The new edition reads better than the previous editions' already-good presentations." - Javier Trigos, California State University, Bakersfield -This text refers to the paperback edition.I'm a mathematics undergrad student who finished his first university year succesfully. "A classic introduction to a difficult subject. "Buck's book is a classic and is appropriate for our advanced calculus course. "The excellent examples help students get to the heart of mathematical concepts for better understanding of real analysis." - Rahim G. I've used earlier editions several times for a full-year course, much to the beneficial development of the students." - Daniel D. Excellent explanations, good examples, and the problem sets are at the correct level of challenge. "First and foremost, I commend you for providing a classic book at a reasonable student price!" - Paul Loya, Binghamton University Students find it to be readable, which is not the case with many mathematics texts." - Thomas J. "Like the earlier editions, the book is well written and nicely organized. "A classic." - Li Guo, Rutgers University
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