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Real Mathematical Analysis



This is another excellent Springer undergraduate Mathematics textbook. This book is clearly written. The book goes systematically progressively deeper. It covers continuty, differntiability, integration, introduces differential forms and Lebesgue theory. In addition to showing the results, the author shows the “pathological” functions, spaces and points to the wonderful unexpected results, e.g. unmeasurable sets and Banach-Traski paradox. I learned a lot from the Cantor sets.

I should have taken the time to dive into this book but even with my quick read, this book explains the strong foundations of  real analysis and calculus that we use in tame, smooth, well behaved domains and provides insights into the world beyond the tame shores I usually play in…”there be dragons out there”.

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