Mathematical Analysis and Proof

This fundamental and straightforward text addresses a weakness observed among present-day students, namely a lack of familiarity with formal proof. Beginning with the idea of mathematical proof and the need for it, associated technical and logical skills are developed with care and then brought to bear on the core material of analysis in such a lucid presentation that the development reads naturally and in a straightforward progression. Retaining the core text, the second edition has additional worked examples which users have indicated a need for, in addition to more emphasis on how analysis can be used to tell the accuracy of the approximations to the quantities of interest which arise in analytical limits.

Addresses a lack of familiarity with formal proof, a weakness observed among present-day mathematics studentsExamines the idea of mathematical proof, the need for it and the technical and logical skills required

1. Setting the Scene 2. Logic and Deduction 3. Mathematical Induction 4. Sets and Numbers 5. Order and Inequalities 6. Decimals 7. Limits 8. Infinite Series 9. The Structure of the Real Number System 10. Continuity 11. Differentiation 12. Functions Defined by Power Series 13. Integration 14. Functions of Several Variables