Mathematics Analysis and Proof

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.