An Accompaniment To Higher Mathematics - Exner George

Descripción

LIBRERÍA LEA+

This text prepares undergraduate mathematics studens to meet two challenges in the study of mathematics, namely, to read mathematics independently and to understand and write proofs.

The book begins by teaching how to read mathematics acively, constructing examples, xtreme cases, and non-examples to aid in understanding an unfamiliar theorem or definition (a tech-nique familiar to any mathematician, but rarely taught); it provides practica by indicating explicitly where work with pencil and paper must interrupt reading. The book hen urns to proofs, showing in detail how to discover the sructure of a potential proof from the form of the theorem. It shows the logical sructure behind proof form, analyzes, throughly, the often sketcy coding of these forms in proofs as they are ordinarily written. The common introductory material is used for the numerous exercises, and the book concludes with a set of "Laboratories" on these topics in which the student can practive the skills learned in the earlier chapters.

Intended for use as a supplementary text in courses on inroductory real analysis, advanced calculus, abstract algebra, or topology, the book may also be used as the main text for a "transitions" course bridging the gap between calculus and higher mathematics.

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