文件名称:
An Illustrated Introduction to Topology and Homotopy, Kalajdzievski, 2015.pdf
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上传时间: 2017-10-23
详细说明： Chronology. In the year 2000 I was given two courses to teach: analysis and topology. The Analysis course was assigned to me due to an emergency redistribution; Topology was thrown in as an award for accepting to teach Analysis on such short notice. Algebraic to pology, which covered only homotopy theory in its curriculum, was (re)introduced into the undergraduate-graduate program of the Mathematics Department (University of Manitoba) in 2004. I have taught these two courses almost continuously ever since. This book is primarily an upshot of my teaching lifestyle over these years. The level of the book, and the target audience. The book has two clearly differentiated parts: Part 1 is topology and Part 2 is homotopy. As indicated by the title of the book, we do not have any pretense to go very deeply into these subjects. On the other hand, neither could the content be described as too breezy, for we include most of the important theorems of the basic theory. The material covered in this book is on the fuzzy boundary between the undergraduate and the graduate level. One may tentatively state that Part 1 is mostly at the advanced undergraduate level, Part 2 is mostly at the early graduate level. Indeed, the Algebraic topology (Homotopy theory) course that I have been teaching has always been cross-listed, and has almost always been taken by both graduate and advanced undergraduate students. It is my hope that this book will bring this beautiful theory closer to the undergraduate curriculum. ...展开收缩
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