How to Think About Analysis

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Lara Alcock (Senior Lecturer, Senior Lecturer, Mathematics Education Centre, Loughborough University)

How to Think About Analysis

Lara Alcock (Senior Lecturer, Senior Lecturer, Mathematics Education Centre, Loughborough University)

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English

Oxford University Press
09 October 2014

Mathematics & Sciences; Real analysis, real variables; Educational: Mathematics & numeracy

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.

By: Lara Alcock (Senior Lecturer Senior Lecturer Mathematics Education Centre Loughborough University)
Imprint: Oxford University Press
Country of Publication: United Kingdom
Dimensions: Height: 195mm, Width: 129mm, Spine: 14mm
Weight: 288g
ISBN: 9780198723530
ISBN 10: 0198723539
Pages: 272
Publication Date: 09 October 2014
Audience: Professional and scholarly , Undergraduate
Format: Paperback
Publisher's Status: Active

Part 1: Studying Analysis 1: What is Analysis like? 2: Axioms, Definitions and Theorems 3: Proofs 4: Learning Analysis Part 2: Concepts in Analysis 5: Sequences 6: Series 7: Continuity 8: Differentiability 9: Integrability 10: The Real Numbers

Lara Alcock is a Senior Lecturer in the Mathematics Education Centre at Loughborough University. She studied Mathematics to Masters level at the University of Warwick before going on to doctoral study in Mathematics Education at the same Institution. She spent four years as an Assistant Professor in Mathematics at the Graduate School of Education at Rutgers University in the USA, and two as a Teaching Fellow in Mathematics at the University of Essex in the UK before taking up her present position. In her current position she teaches undergraduate Mathematics, works with PhD students in Mathematics Education, and conducts research studies on the ways in which people learn, understand and think about abstract mathematics.

Reviews for How to Think About Analysis

There are very few books on pure mathematics which I consider to be page-turners, but this book is definitely one of them. It is written using a friendly and informal tone yet carefully emphasizes and demonstrates the importance of paying attention to the details. It is an excellent read and is highly recommended for anyone interested in Analysis or any area of pure mathematics Stanley R. Huddy, MAA