David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
This text prepares undergraduate mathematics students 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 actively, constructing examples, extreme cases, and non-examples to aid in understanding an unfamiliar theorem or definition (a technique famililar to any mathematician, but rarely taught); it provides practice by indicating explicitly where work with pencil and paper must interrupt reading. The book then turns to proofs, showing in detail how to discover the structure of a potential proof from the form of the theorem (especially the conclusion). It shows the logical structure behind proof forms (especially quantifier arguments), and analyzes, thoroughly, the often sketchy coding of these forms in proofs as they are ordinarily written. The common introductroy material (such as sets and functions) is used for the numerous exercises, and the book concludes with a set of "Laboratories" on these topics in which the student can practice the skills learned in the earlier chapters. Intended for use as a supplementary text in courses on introductory real analysis, advanced calculus, abstract algebra, or topology, the book may also be used as the main text for a "transitions" course bridging the gab between calculus and higher mathematics.
|Categories||categorize this paper)|
|Buy the book||$17.95 used (71% off) $36.94 new (39% off) $39.09 direct from Amazon (35% off) Amazon page|
|Call number||QA9.54.E96 1997|
Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
|Through your library|
References found in this work BETA
No references found.
Citations of this work BETA
No citations found.
Similar books and articles
James Franklin (1996). Proof in Mathematics. Quakers Hill Press.
René Cori (2000). Mathematical Logic: A Course with Exercises. Oxford University Press.
M. W. Liebeck (2006). A Concise Introduction to Pure Mathematics. Chapman & Hall/Crc.
R. B. J. T. Allenby (1997). Numbers and Proofs. Copublished in North, South, and Central America by John Wiley & Sons Inc..
Daniel J. Velleman (2006). How to Prove It: A Structured Approach. Cambridge University Press.
James Robert Brown (1999). Philosophy of Mathematics: An Introduction to the World of Proofs and Pictures. Routledge.
Peter J. Eccles (1997). An Introduction to Mathematical Reasoning: Lectures on Numbers, Sets, and Functions. Cambridge University Press.
Added to index2009-01-28
Total downloads6 ( #292,803 of 1,696,808 )
Recent downloads (6 months)1 ( #346,744 of 1,696,808 )
How can I increase my downloads?