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Cover

Undergraduate Topology

A Working Textbook

Aisling McCluskey and Brian McMaster

July 2014

ISBN: 9780198702344

160 pages
Paperback
234x156mm

In Stock

Price: £19.99

Point-set topology, important in itself as a research discipline, underpins a wide range of mathematical areas and is consequently taught as a component of many university mathematics degree programmes. This textbook offers an accessible, modern introduction, with a particular focus on helping students to build theory for themselves.

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Description

Point-set topology, important in itself as a research discipline, underpins a wide range of mathematical areas and is consequently taught as a component of many university mathematics degree programmes. This textbook offers an accessible, modern introduction, with a particular focus on helping students to build theory for themselves.

  • Accessible, carefully paced presentation informed by the experiences of educationally committed academics and their students.
  • Provides the opportunity to utilise discovery learning, allowing the reader to build some of the theory for themself, with the security of accessing detailed model arguments for study and comparison later in the text.
  • Wide range of exercises and examples, many with specimen solutions.
  • Flexibility that allows for different levels of motivation, preparedness, and tutor support.

About the Author(s)

Aisling McCluskey, Senior Lecturer in Mathematics, National University of Ireland, Galway, and Brian McMaster, Honorary Senior Lecturer, Queen's University Belfast

Aisling McCluskey graduated at Queen's University Belfast with a doctorate in Pure Mathematics (topology) in 1990 and subsequently was awarded a postdoctoral fellowship in Toronto in 1991. She was appointed to a permanent lectureship in Mathematics in the National University of Ireland (NUI), Galway, Ireland in January 1992. Since then, she has established a meaningful and rewarding academic career, maintaining an active research profile in the field whilst holding the teaching and learning of mathematics central to her academic endeavour. In recent years, her research interests have diversified into undergraduate mathematics education. She was awarded an institutional award in 2008 for excellence in teaching and then a national award in 2009 across all higher education institutions in Ireland.

Brian McMaster studied at Queen's University Belfast, graduating with a PhD in 1972, and has served his alma mater department in various capacities including those of Adviser of Studies, Head of Research and Associate Director of Education. His publication profile covers over sixty refereed journal articles, mostly in the area of general topology but incorporating applications in disciplines as diverse as probabilistic metric spaces and decision support theory. He is presently formally retired but continues to deliver a full undergraduate teaching load on a voluntary basis, following his lifelong commitment to and passion for communicating mathematics to students. His teaching interests focus around analysis (real and complex) and set theory and their development into various fields especially that of analytic topology.

Table of Contents

    Preface
    1: Introduction
    2: Topological Spaces
    3: Continuity and Convergence
    4: Invariants
    5: Base and Product
    6: Separation Axioms
    Essential Exercises
    Solutions to Selected Exercises
    Further Reading

Reviews

"The text offers a step-by-step learning with motivation, help and guidance; lucidity takes priority over elegant prose ... in only 144 pages, the excellent book covers most of the topics that a well-read graduate student is expected to know in basic general topology." - Peter Shiu, Mathematical Gazette

"General Topology is a vast fundamental domain of mathematics. Its basic concepts, and central ideas of convergence and continuity, are connected by a multitude of links to practically every domain of mathematics. This makes writing a reasonably balanced undergraduate textbook on General Topology a formidable task. The authors have resoundingly accomplished this task in the creation of a unique textbook, less than 150 pages long, which offers the core basics of General Topology in a manner that allows instructor and student alike to take an active and insightful approach to their teaching and learning. Even more, students can select their own measure of initiative and creativity as they proceed." - A. V. Arhangel'skii, Ohio University

"This approachable and engaging book should help students gain confidence and practice in building mathematical theory by themselves." - Stephen Watson, York University Toronto

"This text marks a timely addition to the literature; it provides a rich resource and opportunity for the contemporary student to learn deeply, to learn as a âworkingâ mathematician, to learn by doing mathematics . . . That learning is cleverly and subtly supported throughout by the text's novel and engaging presentation." - Jan van Mill, University of Amsterdam