A Sequential Introduction to Real Analysis

Real analysis provides the fundamental underpinnings for calculus, arguably the most useful and influential mathematical idea ever invented. It is a core subject in any mathematics degree, and also one which many students find challenging. A Sequential Introduction to Real Analysis gives a fresh take on real analysis by formulating all the underlying concepts in terms of convergence of sequences. The result is a coherent, mathematically rigorous, but conceptually simple development of the standard theory of differential and integral calculus ideally suited to undergraduate students learning real analysis for the first time.

This book can be used as the basis of an undergraduate real analysis course, or used as further reading material to give an alternative perspective within a conventional real analysis course.

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Real analysis provides the fundamental underpinnings for calculus, arguably the most useful and influential mathematical idea ever invented. It is a core subject in any mathematics degree, and also one which many students find challenging. A Sequential Introduction to Real Analysis gives a fresh take on real analysis by formulating all the underlying concepts in terms of convergence of sequences. The result is a coherent, mathematically rigorous, but conceptually simple development of the standard theory of differential and integral calculus ideally suited to undergraduate students learning real analysis for the first time.

This book can be used as the basis of an undergraduate real analysis course, or used as further reading material to give an alternative perspective within a conventional real analysis course.

Request Inspection Copy

Contents:Basic Properties of the Set or Real NumbersReal SequencesLimit TheoremsSubsequencesSeriesContinuous FunctionsSome Symbolic LogicLimits of FunctionsDifferentiable FunctionsPower SeriesIntegrationLogarithms and Irrational PowersWhat are the Reals?
Key Features:Unique treatment of real analysis focusing entirely on sequential notions, which students usually learn more easily than with the conventional approachCoherent and consistent mathematical approachConcise development of all the fundamental results in differential and integral calculus