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  • Topology: A Very Short Introduction
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Topology: A Very Short Introduction Paperback – Jan. 11 2020

by Richard Earl (Author)
4.6 out of 5 stars 56 ratings
3.5 on Goodreads
67 ratings

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Topology, the mathematical study of the properties that are preserved through the deformations, twistings, and stretchings of objects, is an important area of modern mathematics. As broad and fundamental as algebra and geometry, its study has important implications for science more generally, especially physics. Most people will have encountered topology, even if they're not aware of it, through Möbius strips, and knot problems such as the trefoil knot. In this Very Short Introduction Richard Earl gives a sense of the more visual elements of topology (looking at surfaces) as well as covering the formal definition of continuity. Considering some of the eye-opening examples that led mathematicians to recognize a need for studying topology, he pays homage to the historical people, problems, and surprises that have propelled the growth of this field. ABOUT THE SERIES: The Very Short Introductions series from Oxford University Press contains hundreds of titles in almost every subject area. These pocket-sized books are the perfect way to get ahead in a new subject quickly. Our expert authors combine facts, analysis, perspective, new ideas, and enthusiasm to make interesting and challenging topics highly readable.
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  1. ISBN-10
    0198832680
  2. ISBN-13
    978-0198832683
  3. Publisher
    Oxford University Press
  4. Publication date
    Jan. 11 2020
  5. Part of series
    Very Short Introductions
  6. Language
    English
  7. Dimensions
    17.27 x 1.02 x 10.41 cm
  8. Print length
    152 pages
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very short introducations, introductions, comprehensive
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Review

"The book is written in an intuitive, informal and motivating style, with emphasis on concepts, ideas, examples and historical comments, and can be recommended as parallel reading for students of a basic course in topology." -- Bruno Zimmermann, zbMATH

Book Description

A sharp, concise introduction to Topology considering some of the eye-opening examples that led mathematicians to recognize a need for studying topology.

Product details

  • Publisher ‏ : ‎ Oxford University Press
  • Publication date ‏ : ‎ Jan. 11 2020
  • Language ‏ : ‎ English
  • Print length ‏ : ‎ 152 pages
  • ISBN-10 ‏ : ‎ 0198832680
  • ISBN-13 ‏ : ‎ 978-0198832683
  • Item weight ‏ : ‎ 1.05 kg
  • Dimensions ‏ : ‎ 17.27 x 1.02 x 10.41 cm
  • Part of series ‏ : ‎ Very Short Introductions
  • 鶹 Rank: #379,185 in Books (See Top 100 in Books)
  • Customer Reviews:
    4.6 out of 5 stars 56 ratings

About the author

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Richard Earl

Richard Earl

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Richard Earl is a departmental lecturer in the Mathematical Institute, University of Oxford, and a Tutor in Mathematics at Worcester College. From 2013-2022 he was Director of Undergraduate Studies in the Institute. From 2003–13, he was Admissions Coordinator and Schools Liaison Officer in the department and has over a decade's experience setting the MAT (Oxford's Mathematics Admissions Test). He has won several teaching awards within the University for his teaching and lecturing. This book grew out of a residential week he ran for several years in Oxford for new students who had not had the chance to study Further Mathematics at A-Level. He is currently the academic lead on the Mathematics and Computer Science Opportunity Oxford programme which includes a fortnight-long residential prior to the academic year and which supports students in their transition to university.

Customer reviews

4.6 out of 5 stars
56 global ratings

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Top reviews from Canada

  • 鶹 Customer
    5.0 out of 5 stars Interesting
    Reviewed in Canada on August 9, 2020
    Verified Purchase
    An interesting book on topology. But you do need certain level of math knowledge to stay engaged.
    Helpful
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Top reviews from other countries

  • Richard Earl
    5.0 out of 5 stars A review sent to the author from a student
    Reviewed in the United Kingdom on December 31, 2019
    Verified Purchase
    Below follows a review sent to the author, from a student, and reproduced with permission.

    "This book is a great introduction to topology. It starts with a discussion of graphs and how they arise in every day circumstances like tube maps, moving on to classifying surfaces, continuity and distance in increasingly general settings. The author explains why certain abstractions are made, and makes them seem natural decisions. The final chapters are devoted to more specialised versions of topology and knot theory, and continues with the theme of looking at invariants, in this case to see when two knots are equivalent.

    The author’s discourse prevents it from being hard to follow. It delivered exactly what I thought it would do, I thoroughly enjoyed it and wouldn’t hesitate to recommend this book."
    Report
  • In dubio veritas
    1.0 out of 5 stars ...too short
    Reviewed in Italy on January 17, 2022
    Verified Purchase
    It may provide more insight in the subject though limits of text lenghth. Good read when borrowed by a library but not worth buying
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  • Martin Vesely
    5.0 out of 5 stars Nice brief introduction to topological and metric spaces
    Reviewed in Germany on May 25, 2022
    Verified Purchase
    Although the book is short (of course, it is part of "Very short introduction to..." series), it covers basics of topological and metric spaces. It starts with very beginning of topology, i.e. Euler formula for edges, faces and vertices of polyhedra and then makes it more abstract and general. The book also containts lot of information on concept of continuity, open sets, convergence and links among these terms. Also, a very very brief introduction to knots theory is comprised in the book and a chapter dedicated to links between topology and other parts of mathematics, like algebra and calculus is not omitted.

    The book is intended for readers already familiar with basics of calculus (i.e. last year of high school students in Czechia), therefore I would not suggest it to a layman. The book would be useful for university students and anybody who wants to refresh his or her understanding of metric spaces and other terms I named above.
    Report
  • Ramkumar R
    5.0 out of 5 stars Good introduction
    Reviewed in India on October 25, 2020
    Verified Purchase
    It introduces the motivation and key results in a simple manner without 2:much mathematical sophistication. I read it aloud on kindle
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  • Surbiton
    2.0 out of 5 stars Another VSI disappointment
    Reviewed in the United Kingdom on December 27, 2019
    Verified Purchase
    Makes you wonder if the publisher actually took the trouble to read this before publishing it. OUP v short intros are a bit hit and miss. Some are gems, other disappointments and others (like this) which should never have seen the light of day.

    These books are pitched as laypersons intros to a subject, so should really make an effort to enthuse and sell the subject with some ‘real world’ wonders and general ‘big ideas’. This text is clearly written by a mathematician who has no understanding of how to covey the wonders or significance of the subject to the outside world (i.e. someone who isn’t a mathematician)

    within the space of the first few pages, after a dazzling opening with the ubiquitous ppt like presentation of an underground map we are catapulted into looking at a problem, we’ve all no doubt spent many a sleepless night pondering over - namely, which characters of the alphabet are topologically equivalent? Then we’re straight into Euler’s formula and of course a discussion of proofs. By this stage anyone who isn’t already a mathematician and a topologist will probably be asking - so what?

    What the author is discussing (like Euler’s formula etc..) are of course fascinating and quite profound when posed in relation to things like popular physics, space-time, the nature / geometry of physical space-time, big questions like ‘what would various space-time geometries with different topologies be like? could time go round in a circle? what would happen to the past and future if it had a möbius structure etc..?’ How about string theory, etc..? The topology of the Internet anyone? AI, data analysis and topology? Computational biology & knots maybe?

    This shouldn’t be an a level students intro to topology. But If you like maths for the sake of maths, and not particularly interested in big question, philosophy or how math relates (in exciting ways) to the real world - then this is a book you may well like. Although I think “understanding topology: a practical introduction” would be a much better bet. If you're looking for a general popular Introduction to the subject, I doubt this will turn you on to the subject
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