Elementary Applied Topology 1st Edition by Robert Ghrist | (PDF) Free Download

Description

This text gives a brisk and engaging introduction to the mathematics behind the recently established field of Applied Topology. Over a century of development of principles and techniques in algebraic topology has of late crossed over to a variety of application domains. This text gives a completely novel introduction to these methods in the context of the applications. “Elementary Applied Topology” is short (250 pp. plus bibliography and index) and richly illustrated, with 268 figures. It is perfect for both self-study, and as the basis for a course in applied topology. This book is also well-suited for use as a supplementary text in a more traditional algebraic topology course, providing both context and motivation for the tools to be learned. The progression of mathematical techniques is a fresh approach. The book begins with a quick trip through manifolds and cell complexes. The segue to algebraic topology comes in the form of the Euler characteristic and the Euler calculus born from it. Passing from this to homology, exact sequences, and cohomology sets the stage for the innovative content to come. This is comprised of modern Morse theory (including discrete Morse theory, Conley index, and stratified Morse theory), sheaf theory (with an emphasis on cellular sheaves and cosheaves), and, finally, category theory and categorification. Every tool and topic is paired with an application. These range in scope across the biological, economic, engineering, material, physical, and statistical sciences. Of particular note are the applications to topological data analysis, including persistent homology and barcodes. “Elementary Applied Topology” is the first comprehensive text on applied algebraic topology for students of all mathematical sciences.

User’s Reviews

Editorial Reviews: About the Author Robert Ghrist is the Andrea Mitchell PIK Professor of Mathematics and Electrical & Systems Engineering at the University of Pennsylvania. He is a celebrated researcher in Applied Mathematics whose achievements were recognized by President Bush in 2004 [PECASE award] and by Scientific American magazine in 2007 [Top50 for research]. Among his honors is the 2013 Chauvenet Prize, the highest award given for expository writing in mathematics. As a teacher, he is renowned for illustrating difficult mathematics cleanly and clearly, as evidenced by the popularity of his animated on-line “Calculus: Single Variable” video course.

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐I struggle to understand the target audience for this book. Take section 5.1, discussing the basic concept of homotopy invariance. The concept of a chain homotopy is introduced. a boundary operator is introduced as part of the definition — but the word ‘boundary’ is never used until (a sketch of) the proof is provided. In short, one needs to have studied the subject beforehand to understand the passage – which is fine. But then having sketched (that is the best word I can think of) exact sequences, Mayer-vitoris sequences etc, the text covers (5.6) sensors and the problem of sensor coverage. The text describes a theorem (5.10) stating ‘if’ conditions under which coverage is complete and proves it (full page proof – p93). The proof uses winding numbers which wee sketched in a different chapter. There is then a sketch of an if-only-if condition, and there the topic (sensor coverage) stops.The whole text is like this : some fairly specialist knowledge is sketched, a theorem or 2 are stated and proved (sometimes through another sketch), a sketch of an application is provided. Next topic.So I ask: who is the text for ? you cannot learn the elementary material from the book. the proof are not detailed enough to be more than intuitive (and in mathematics, we know that intuition is essential — but it is no proof), and the real-world applications are only outlined.There is a class of books talking about mathematics but not teaching mathematics. Such books are read ‘for culture’, perhaps during a plane flight. It is unclear what one retains from reading these, but they are certainly entertaining. In my opinion this is one of these books, with the caveat that the target audience needs to have studied the material beforehand, making for – in my opinion – a very small audience.

⭐This is an odd and wonderful book. It does NOT fit the mold of either a textbook (exercises are online and it does not use traditional problem/ example/ exercise/ proof/ you try it logic) or a popular account (WAY too advanced, this is grad or post grad level, as the writing is compact and terse and the diagrams, though awesome, are far from explained or intuitive, they are more like puzzles, both in figuring out what they mean, and even how they relate to the surrounding text!Part of this is that “Applied” topology is a very new field. The applications aren’t, but the math behind them are. Engineers have known for a long time how a circle rocker works to change rotational motor motion into the back and forth of windshield wipers, but it is recent that complete topological math now shows how and why at a much deeper level of abstraction. How this will make for better wipers, I’m not sure, but our great grandkids will probably laugh at wipers anyway given either weather control or force fields around windshields!Be very careful of the word “elementary” — unless you already know topology inside and out and the word pertains to applications. The author writes in extremely compact fashion, overloading each paragraph with information and witty cartoons, which is a great value for your buck, but will take deep study of each sentence, including trips back to a more traditional topo text or the web to get even half of it.The cool thing about just reading this for pleasure, and the author’s wit and writing ability makes that possible, is that you’ll get an overview of how one of the most theoretical and abstract topics in math actually has a LOT of impact on the “real” world. In many schools in the US at least it is now possible to get a PhD in math without even covering set theory, for example. Linear algebra is also being dropped from a lot of High School programs. So other reviews around the web that say this is a great companion undergrad text– well, yeah, for a Senior in math at MIT with set and category theory and two topo courses done, maybe. I’m a mathematician from the computational side, and frankly had to study a page a day to understand over half of the material. That said, just reading this almost subliminally cranks your brain with new insights, because the missing proofs and exercises are replaced with three things that are much more intuitive: great cartoons, great writing, and numerous practical examples. After reading thousands of tech books, this is a real unicorn. Stick it with a Springer imprint, and you’ve got an instant $300 classic. Thanks to the author for making such painstakingly written and researched material (the bib is awesome) accessible to those of us on a budget.

⭐I bought this while working at Ayasdi for a nice review of what other folks were doing in the line of applied topology. I have never read a science book like this before. It’s sort of a review article, colliding with comic book written by an avid student of Tufte, M.C. Escher and Martin Gardner.Despite the “elementary” in the title, it’s not particularly elementary. You have to have at least a passing acquaintance with some significant chunk of topology to get anything out of it. I’m not even sure it is very applied, though a mathematician might disagree. In my world, “applied” means “can be applied to something which isn’t in the name.” Distributed homology computations based on the Hodge theory of the Laplacian may sound “applied” to some people, and yeah yeah, math nerds, they’re making convergence statements about the Heat equation, but the “applied” part can get pretty tenuous. There’s also the matter of stuff like like persistent homology and barcodes, which as far as I know is mostly an applied concept; it is covered in a subchapter, sandwiched between stuff on the game of hex, and the topology of natural images. It’s a nice little section on the concept which I can recommend to anyone who cares about this sort of thing, but you’d be hard pressed to understand where barcodes would actually be used (as in, say, an industrial problem: they are useful for industrial problems). Lots of interesting material in the book; curious people and amateur topologists should all have a copy on their shelf.

⭐Well this IS NOT Elementary Topololgy as the title might sugest. Yes it is Applied Topology, no doubt. It is a marvelous journey through the many possible applications of (algebraic and . . .) topology that Prof. Robert Ghrist has travelled through in the last years. It is a kinf of Index List of the many papers he wrote on the subject. So, it is not at all elementary. You are expected to work hard in the examples and for the exercises (that are not there) you have the papers themselves … It is a unique book. Any one who likes Topology and see it “at work” shouldn’t miss it. I just love it !!

⭐Good coverage of all aspects of the subject

⭐Quite original and refreshing in its approach but there are a few misleading statements in it.

⭐Das Buch vermittelt einen unterhaltsamen Zugang zur Topologie. Nötige Definitionen werden anschaulich und mit Beispielen vermittelt.Muy buen libro que mezcla divulgación, contenido y aplicaciones. Fácil de leer y entender, de un nivel medio, asequible para estudiantes de matemáticas con aspiraciones de aprender más.

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