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In addition to everything else you do, I recommend the following book: "Counterexamples in Analysis" by Gelbaum and Olmsted. You will find that many of your i
by trendia 9y ago
In addition to everything else you do, I recommend the following book:
"Counterexamples in Analysis" by Gelbaum and Olmsted.
You will find that many of your intuitions you picked up in calculus are violated in analysis. For instance, in calculus, many examples are both continuous and differentiable everywhere. But is every continuous function also differentiable? Nope! See the Weierstrass function [0].
The book is full of such counterexamples that will help you understand analysis at a deeper level (and avoid many pitfalls)
[0] https://en.wikipedia.org/wiki/Weierstrass_function https://en.wikipedia.org/wiki/Weierstrass_function
- marktangotango 9y agoWhen I took this course, several exam questions where of this form; give an example of a function that is something or satisfies something else. Reading this book would have helped.
- rocqua 9y agoReally, for me most of my analysis knowledge is based on counter-examples. The counter-examples motivate the theorems and definitions, help check intuitions, and sometimes even help me remember the theorems and definitions.