How to Think About Analysis

Description

Analysis 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.

• Research-based advice on understanding concepts in Analysis
• Research-based advice on studying definitions, theorems and proofs
• Detailed introductions to the key definitions in the subject
• Information on how to recognize and overcome common errors and misconceptions
• Guidance on linking definitions, theorems and proofs to examples and diagrams

About the Author(s)

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

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. She has been awarded National Teaching Fellows of 2015 by The Higher Education Academy.

Table of Contents

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

Reviews

"What is immediately obvious to the reader (which embraces those about to start a course on undergraduate analysis) is its friendly and accessible style. The text flows in a highly readable manner and ideas are explained with great clarity. ... How to Think about Analysis [is] a very effective and helpful book, a book which should be on every undergraduate reading list and should be available to potential mathematics undergraduates in schools." - John Sykes, Mathematics in School

"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

"How to Think about Analysis offers several insights into the best practices to use when studying upper level mathematics. Not only are these insights helpful to students, but they could also prove helpful to teachers of earlier courses; modifying and incorporating some of these practices into earlier courses may better prepare their students for future mathematics coursework." - Kate Raymond, National Council of Teachers of Mathematics