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(This book) does a masterful job of introducing the study of surfaces to advanced undergraduates. ... The authors succeed in pulling in many topics while keeping their story coherent and compelling. This book would work well as the text for a capstone course or independent reading. ----- MAA Reviews
This book will be a welcome addition to college and university libraries and an excellent source for supplementary reading. ---- Mathematical Reviews
This book would be helpful if you want to put in order surface theory in your mind. But there is some ambiguity about the audience of this book. If you are interested in surface theory as an undergraduate student, this book would be hard. If you are a post-doc, many parts of this book would be already familiar to you. But it was good for me though I am a post-doc.
The whole title of this book is Lectures on Surfaces: (Almost) Everything You Wanted To Know About Them. But it seems to be that the subtitle is a little bit exaggerated. For example, only a little attention is given to surface with boundary or with puncture, and there is no argument about surface automorphisms and surfaces embedded or immersed in higher dimensional manifolds. And there are only basics about Teichmuller space. But still, I believe that this is an appropriate title.
The best thing for me in this book was an understanding of the meaning of the following theorem: given a triangulation of a surface, there exists a smooth atlas on the surface, and vice versa (page 112). If you are a math-graduate student, then you may have heard of the theorem and take it as a fact. But do you exactly understand what the theorem means? Have you ever seen proofs of it? I do not say a proof is important (of course, it is important), but the precise-understanding of its content is important. If you are going to read this book, please follow carefully how the authors dealt with it. They don't give a full proof of it. But it suffices to understand the meaning of the theorem.
I'd like to give you, a future reader, a piece of advice about how to read this book efficiently. First, you would better read this book within two or three weeks. In my opinion, this is not the kind of the textbooks in math curriculum.Read more ›
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This book is mainly established on the lecture notes of the course "Surfaces" in the MASS program 2007 at Penn State. As a participant in the course, I hereby give my strongest rate to memorise that unforgettable semester. I can not think, any other course, can be comparable to this one which gives an innovative, comprehensive introduction to the mathematical theory of surfaces in such a genius way. Thanks for the lecturer Professor Katok and also our best TA Vaughn.