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(More customer reviews)After finishing the first 3 semesters of what is basically applied Calculus, majors in pure mathematics part company with their fellow students and move on to what is called "advanced calculus" or "functional analysis". This jump to the next level of mathematics, in which basically students have to be taught calculus all over again from a rigorous proof-based method, is a rude awakening to many. Most textbooks used in this situation, such as those by Rudin, assume that a talented and enthusiastic instructor will be acting as tour guide for the student, and will fill in the gaps. Unfortunately, this is not always the case. This Schaum's outline works well for such a situation. It not only covers what you would expect to see in undergraduate analysis, it mixes proofs with solved numerical problems and applications so that the student does not get bogged down or bored as can be the case with many of the texts on the subject that have nothing but proofs as exercises. In that way, it is unconventional in its treatment of the subject. Also, it provides more explanation and tutorial than you will find in the average Schaum's outline, and is pretty good at illustrating the correct way to perform a proof. If you can afford it, an excellent companion text to this Schaum's outline is Abbott's "Understanding Analysis", which can be used for self teaching of analysis because it is so detailed and clear.
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