Brian McMaster

Aisling McCluskey

This textbook offers an accessible, modern introduction at undergraduate level to an area known variously as general topology, point-set topology or analytic topology with a particular focus on helping students to build theory for themselves. It is the result of several years of the authors' combined university teaching experience stimulated by sustained interest in advanced mathematical thinking and learning, alongside established research careers in analytic topology. Point-set topology is a discipline that needs relatively little background knowledge, but sufficient determination to grasp ideas precisely and to argue with straight and careful logic. Research and long experience in undergraduate mathematics education suggests that an optimal way to learn such a subject is to teach it to yourself, pro-actively, by guided reading of brief skeleton notes and by doing your own spadework to fill in the details and to flesh out the examples. This text will facilitate such an approach for those learners who opt to do it this way and for those instructors who would like to encourage this so-called 'Moore approach', even for a modest segment of the teaching term or for part of the class. In reality, most students simply do not have the combination of time, background and motivation needed to implement such a plan fully. The accessibility, flexibility and completeness of this text enable it to be used equally effectively for more conventional instructor-led courses. Critically, it furnishes a rich variety of exercises and examples, many of which have specimen solutions, through which to gain in confidence and competence.

A Working Textbook

Undergraduate Topology

Simon Wood

Angela Keil

Claire Wood

Eleanor Trevena

Syllabus: CfE (Curriculum for Excellence, from Education Scotland) and SQA Level: BGE S1-3: Second, Third and Fourth Levels Subject: History Discover, debate and work like historians in S1 to S3. From Iron Age Scotland, through the Atlantic slave trade, women's suffrage and the World Wars to 1960s America, this source-rich, research-based narrative explores diverse and dynamic historical contexts. Covering CfE Second, Third and Fourth Level Benchmarks for Social Studies: People, Past Events and Societies, this ready-made and differentiated course puts progression for every pupil at the heart of your curriculum. Pupils' understanding of Scottish, British, European and World History develops as they analyse and evaluate contemporary source material Each lesson begins with a learning intention and thought-provoking starter before progressing to exposition and activities The content and activities are designed to ensure accessibility for those with low prior attainment, while extension tasks will stretch high achieving pupils End-of-lesson questions and research tasks support formative assessment, helping you to monitor progression against the Experiences & Outcomes and Benchmarks The skills, knowledge and understanding established through the course will set up pupils for success at National 5 and beyond Literacy skills are given great prominence throughout the book, with comprehension and extended writing underpinning many activities

Brian McMaster

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