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Book details
Author : Lara Alcock
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Pages : 272 pages
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Publisher : Oxford University Press 2014-12-01
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Language : English
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ISBN-10 : 0198723539
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ISBN-13 : 9780198723530
Book Synopsis
Analysis (sometimes called Real Analysis or Advanced Calculus) is a core subject in most undergraduate mathematics degrees. It is elegant,
clever and rewarding to learn, but it is hard. Even the best students find it challenging, and those who are unprepared often find it
incomprehensible at first. This book aims to ensure that no student need be unprepared. It is not like other Analysis books. It is not a
textbook containing standard content. Rather, it is designed to be read before arriving at university and/or before starting an Analysis
course, or as a companion text once a course is begun. It provides a friendly and readable introduction to the subject by building on the
student s existing understanding of six key topics: sequences, series, continuity, differentiability, integrability and the real numbers. It
explains how mathematicians develop and use sophisticated formal versions of these ideas, and provides a detailed introduction to the
central definitions, theorems and proofs, pointing out typical areas of difficulty and confusion and explaining how to overcome these. The
book also provides study advice focused on the skills that students need if they are to build on this introduction and learn successfully in
their own Analysis courses: it explains how to understand definitions, theorems and proofs by relating them to examples and diagrams,
how to think productively about proofs, and how theories are taught in lectures and books on advanced mathematics. It also offers
practical guidance on strategies for effective study planning. The advice throughout is research based and is presented in an engaging style
that will be accessible to students who are new to advanced abstract mathematics.