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9780198702337

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R.L. Moore, distinguished mathematician and teacher at the University of Texas, developed a Socratic method of teaching in which students are challenged to construct their own proofs of theorems. While hugely successful in influencing students to pursue advanced studies in mathematics, the Moore method can be intimidating to someone who has only experienced traditional-style mathematics coursesEL With this book instructors can choose what level of discovery learning to incorporate into their course, depending upon the backgrounds and aptitudes of their students. The chapters are nicely organized with definitions, exercises, and propositions preceding the skeleton proofs that followELThis textbook will introduce the Moore method to the wider audience it deserves. Walter Richardson, Jr., The University of Texas at San Antonio This is a well-motivated guided tour through the main areas of modern general topology. Because of this, I highly recommend it both as a textbook for advanced undergraduates and as a main resource for anyone setting out to learn the subject on their own. Paul Bankston, Marquette University

This is a well-motivated guided tour through the main areas of modern general topology. Because of this, I highly recommend it both as a textbook for advanced undergraduates and as a main resource for anyone setting out to learn the subject on their own. * Paul Bankston, Marquette University * R.L. Moore, distinguished mathematician and teacher at the University of Texas, developed a Socratic method of teaching in which students are challenged to construct their own proofs of theorems. While hugely successful in influencing students to pursue advanced studies in mathematics, the Moore method can be intimidating to someone who has only experienced traditional-style mathematics courses... With this book instructors can choose what level of discovery learning to incorporate into their course, depending upon the backgrounds and aptitudes of their students. The chapters are nicely organized with definitions, exercises, and propositions preceding the skeleton proofs that follow...This textbook will introduce the Moore method to the wider audience it deserves. * Walter Richardson, Jr., The University of Texas at San Antonio *

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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.

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