An Accompaniment to Higher Mathematics (Undergraduate Texts in Mathematics) by George R. Exner
An Accompaniment to Higher Mathematics (Undergraduate Texts in Mathematics)
Author: George R. Exner
Title: An Accompaniment to Higher Mathematics (Undergraduate Texts in Mathematics)
ISBN10: 0387946179
ISBN13: 978-0387946177
Format: .PDF .EPUB .FB2
Pages:
Publisher: Springer (1997)
Language: English
Size pdf: 1808 kb
Size epub: 1638 kb
Rating: 4.5 ✪
Votes: 282
Category: Science & Math
Subcategory: Mathematics
Designed for students preparing to engage in their first struggles to understand and write proofs and to read mathematics independently, this is well suited as a supplementary text in courses on introductory real analysis, advanced calculus, abstract algebra, or topology. The book teaches in detail how to construct examples and non-examples to help understand a new theorem or definition; it shows how to discover the outline of a proof in the form of the theorem and how logical structures determine the forms that proofs may take. Throughout, the text asks the reader to pause and work on an example or a problem before continuing, and encourages the student to engage the topic at hand and to learn from failed attempts at solving problems. The book may also be used as the main text for a "transitions" course bridging the gap between calculus and higher mathematics. The whole concludes with a set of "Laboratories" in which students can practice the skills learned in the earlier chapters on set theory and function theory.