Mathematics Analysis and Proof
David S. G. Stirling(Author)
Horwood Publishing Ltd
Published on 1. March 1997
Book
Paperback/Softback
250 pages
978-1-898563-36-5 (ISBN)
Description
This text addresses a weakness observed among students, namely a lack of familiarity with formal proof. Dr. Stirling begins with the idea of mathematical proof and the need for it, devoting care to develop associated technical and logical skills. This is then brought to bear on the core material of analysis and a presentation that the development reads naturally and in straight-forward progression, not only by giving proofs, but also indicating how they are constructed. This approach offers intellectual challenge and stimulus to readers by emphasizing two important points: the need for familiarity with long mathematical arguments and manipulation; and the importance of the ability to construct proofs in analysis. The author devotes attention, not only to the results, but to the way in which they are deduced. There are examples linking analysis with other mathematical areas in order to eliminate the risk of its detachment from the "body corpus" of mathematics; and also instances as to why proofs are attempted in a particular way. The text contains over 100 worked examples and more than 200 problem exercises and their solutions and hints.
This text addresses a weakness observed among students, namely a lack of familiarity with formal proof. Dr. Stirling begins with the idea of mathematical proof and the need for it, devoting care to develop associated technical and logical skills. This is then brought to bear on the core material of analysis and a presentation that the development reads naturally and in straight-forward progression, not only by giving proofs, but also indicating how they are constructed. This approach offers intellectual challenge and stimulus to readers by emphasizing two important points: the need for familiarity with long mathematical arguments and manipulation; and the importance of the ability to construct proofs in analysis. The author devotes attention, not only to the results, but to the way in which they are deduced. There are examples linking analysis with other mathematical areas in order to eliminate the risk of its detachment from the "body corpus" of mathematics; and also instances as to why proofs are attempted in a particular way. The text contains over 100 worked examples and more than 200 problem exercises and their solutions and hints.
This text addresses a weakness observed among students, namely a lack of familiarity with formal proof. Dr. Stirling begins with the idea of mathematical proof and the need for it, devoting care to develop associated technical and logical skills. This is then brought to bear on the core material of analysis and a presentation that the development reads naturally and in straight-forward progression, not only by giving proofs, but also indicating how they are constructed. This approach offers intellectual challenge and stimulus to readers by emphasizing two important points: the need for familiarity with long mathematical arguments and manipulation; and the importance of the ability to construct proofs in analysis. The author devotes attention, not only to the results, but to the way in which they are deduced. There are examples linking analysis with other mathematical areas in order to eliminate the risk of its detachment from the "body corpus" of mathematics; and also instances as to why proofs are attempted in a particular way. The text contains over 100 worked examples and more than 200 problem exercises and their solutions and hints.
More details
Series
Language
English
Place of publication
United Kingdom
Publishing group
Elsevier Science & Technology
Target group
College/higher education
Adult education
Illustrations
references, index
Dimensions
Height: 240 mm
Weight
500 gr
ISBN-13
978-1-898563-36-5 (9781898563365)
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Schweitzer Classification
Content
Setting the scene; logic and deduction; mathematical induction; sets and numbers; order and inequalities; decimals; limits; infinite series; structure of real number system; continuity; differentiation; functions defined by power series; integration; functions of several variables. Appendix: decimal expansion of integers.