Designed for students preparing to engage in their first struggles to understand mathematics independently, this book teaches in detail how to construct examples and non-examples to help understand a new theorem or definition, and how to discover the outline of a proof in the form of the theorem. It is intended to be used interactively, frequently asking the reader to pause and work on an example or a problem before continuing, and encouraging the student to learn from failed attempts at solving problems.
Reprint of a best-selling title The text is meant to be used interactively, frequently asking the reader to pause and work on an example or a problem before continuing Designed for students preparing to engage in their first struggles to understand and write proofs and to read mathematics independently Bridges the gap between calculus and higher mathematics
George R. Exner
calculus proof set set theory topology