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Anneli Lax New Mathematical Library
First Concepts of Topology
Educational math textbook.
- GenresMathematics
160 pages, Paperback
First published January 1, 1966
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Displaying 1 - 5 of 5 reviews
June 11, 2022
TLDR: Very nice intro to point set topology first and later to combinatorial (algebraic) topological concecepts.
Longer (taken from Amazon's page):
Presents topology as a unifying force for larger areas of mathematics through its application in existence theorems. Our purpose in writing this book is to show how topology arose, develop a few of its elements, and present some of its simpler applications. Topology came to be recognized as a distinct area of mathematics about fifty years ago, and its major growth has taken place within the last thirty years. It is the most vigorous of the newer branches of mathe- matics and has been producing strong repercussions in most of the older branches. It got its start in response to the needs of analysis (the part of mathematics containing calculus and differential equations). However, topology is not a branch of analysis. Instead, it is a kind of geometry. It is not an advanced form of geometry such as projective or differential geometry, but rather a primitive, rudimentary form-one which underlies all geometries. A striking fact about topology is that its ideas have penetrated nearly all areas of mathematics. In most of these applications, topology supplies essential tools and concepts for proving certain basic propositions known as existence theorems.
Longer (taken from Amazon's page):
Presents topology as a unifying force for larger areas of mathematics through its application in existence theorems. Our purpose in writing this book is to show how topology arose, develop a few of its elements, and present some of its simpler applications. Topology came to be recognized as a distinct area of mathematics about fifty years ago, and its major growth has taken place within the last thirty years. It is the most vigorous of the newer branches of mathe- matics and has been producing strong repercussions in most of the older branches. It got its start in response to the needs of analysis (the part of mathematics containing calculus and differential equations). However, topology is not a branch of analysis. Instead, it is a kind of geometry. It is not an advanced form of geometry such as projective or differential geometry, but rather a primitive, rudimentary form-one which underlies all geometries. A striking fact about topology is that its ideas have penetrated nearly all areas of mathematics. In most of these applications, topology supplies essential tools and concepts for proving certain basic propositions known as existence theorems.
February 2, 2022
This book was very illuminating for me.itÌý shows how from elementary analysis the topological concepts came out.the introduction of this book clearly try to explain what Topology is and why we care about it.we care about topology because it helps us solve equations,ok not quite find a method form solving but to ensure what we are trying to find is really is there! this book argues that topological concepts allow us derive many kind of "existence theorems". Theorems like Brouwers fixed point theorem,Borsuk-Ulam theorem,Existence of roots of complex polynomialsÌý are all existence theorems and can be proved by the help some basic theorems. " This is not a metaphysical question becomes clear if we consider the history of famous problems of trisecting an angle and squaring the circle using only straightedge and compass". I remember the two videos about 3blue1brown about Topology and those two are also about existence of something! This book is not the first book one should read about this subject rather one should keep it besides while reading other books.the analysis are hard somewhere but it becomes easier by second reading after a while.Recommended for those who love to learn about topology(atleast read the introduction)."topology is not a branch of analysis. Instead it is a kind of geometry.it is not an advanced form of geometry such as projective or differential geometries,but rather a primitive, rudimentary form - one which underlies all geometries"
December 29, 2016
This book is purportedly aimed at young people with little training, but I suspect parts may give them trouble. I found it a handy way to jump in and prepare myself for bigger things soon to come.
I've seen various treatments and, not withstanding the lack of evenness, I like the approach here. The existence theorems are rather magical.
I've seen various treatments and, not withstanding the lack of evenness, I like the approach here. The existence theorems are rather magical.
February 10, 2023
Topology is one of the first undergraduate course which makes full usage of the second layer of abstraction after first order logic, set theory, and is often the first time where numbers and computation takes the back seat for proof and conceptual thinking. Steenrod, one of the greatest mathematicians within the 20th century, explicate the ideas behind topology using the tools of Calculus and modern analysis as a guiding hand for college students to embark into higher mathematics with proper intuitions. A great place to start, as it short and rather sweet. If you do understand topology or understand things better through abstraction, you might not need this book. A great tool to teach a younger person with a deep interest in the world of mathematics. Could be interesting for a computer scientist as well, although a categorical dressing might be a better framework.
March 1, 2015
I completed only about 30 pages a while back and I thought it was one of the worst introductions possible to formal mathematical texts with proofs and all. It is very dry stuff. I'm writing this review after exposing myself to other more well-known textbooks, written in a far livelier and more conversational style, explaining motivation, concepts and conventions well. this is not what you want. stay away.
Displaying 1 - 5 of 5 reviews
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