European Mathematical Society - springer-verlag
https://euro-math-soc.eu/publisher/springer-verlag
enA Guide to the Classification Theorem of Compact Surfaces
https://euro-math-soc.eu/review/guide-classification-theorem-compact-surfaces
<div class="field field-name-field-review-review field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><div class="tex2jax"><p>Undoubtedly, one of the most beautiful pieces of the mathematical achievements is the classification of compact surfaces. Among other reasons, the result comprises a splendid combinatin of intuition and rigour as well as the extensive use of many geometric and (mainly) topological tools. In addition, this milestone has been the starting point of many essential contemporary mathematical works.</p>
<p>The book under review tackles this central topic. The classification theorem can be found in many excellent classical monographs, mainly as a part of a course on Algebraic Topology, with different approaches and depth. Under this panorama, the motivation of this book is the presentation of the classification theorem as an only topic, giving the required importance to all its view points: intuition, visualization, topological tools, history,… amenable to a wide audience with certain amount of mathematical maturity.</p>
<p>The book is structured in six chapters, guiding the reader from the presentation and intuition of the problema to the complete proof of it. Each chapter provides a good list of references connnecting its topic to the literature. At the end, some appendices complete the work, the history of the classification problem being specially interesting.</p>
</div></div></div></div><div class="field field-name-field-review-reviewer field-type-text field-label-inline clearfix"><div class="field-label">Reviewer: </div><div class="field-items"><div class="field-item even">Marco Castrillon Lopez</div></div></div><div class="field field-name-field-review-desc field-type-text-long field-label-hidden"><div class="field-items"><div class="field-item even"><div class="tex2jax"><p>This book tackles the classical result of the Theorem of Classification of compact surfaces, starting from the intuition and ending with a rigorous and complete proof.</p>
</div></div></div></div><span class="vocabulary field field-name-field-review-author field-type-taxonomy-term-reference field-label-inline clearfix"><h2 class="field-label">Author: </h2><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/author/jean-gallier" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">Jean Gallier</a></li><li class="vocabulary-links field-item odd"><a href="/author/dianna-xu" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">Dianna Xu</a></li></ul></span><span class="vocabulary field field-name-field-review-publisher field-type-taxonomy-term-reference field-label-inline clearfix"><h2 class="field-label">Publisher: </h2><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/publisher/springer-verlag" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">springer-verlag</a></li></ul></span><div class="field field-name-field-review-pub field-type-number-integer field-label-inline clearfix"><div class="field-label">Published: </div><div class="field-items"><div class="field-item even">2013</div></div></div><div class="field field-name-field-review-isbn field-type-text field-label-inline clearfix"><div class="field-label">ISBN: </div><div class="field-items"><div class="field-item even">978-3-642-34363-6</div></div></div><div class="field field-name-field-review-pages field-type-number-integer field-label-inline clearfix"><div class="field-label">Pages: </div><div class="field-items"><div class="field-item even">178</div></div></div><span class="vocabulary field field-name-field-review-class field-type-taxonomy-term-reference field-label-hidden"><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/imu/geometry" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">Geometry</a></li><li class="vocabulary-links field-item odd"><a href="/imu/topology" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">Topology</a></li></ul></span><div class="field field-name-field-review-website field-type-text field-label-hidden"><div class="field-items"><div class="field-item even"><a href="http://www.springer.com/la/book/9783642343636" title="Link to web page">http://www.springer.com/la/book/9783642343636</a></div></div></div><span class="vocabulary field field-name-field-review-msc field-type-taxonomy-term-reference field-label-hidden"><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/msc/57-manifolds-and-cell-complexes" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">57 Manifolds and cell complexes</a></li></ul></span><span class="vocabulary field field-name-field-review-msc-full field-type-taxonomy-term-reference field-label-hidden"><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/msc-full/57-01" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">57-01</a></li></ul></span><span class="vocabulary field field-name-field-review-msc-other field-type-taxonomy-term-reference field-label-hidden"><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/msc-full/57n05" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">57N05</a></li><li class="vocabulary-links field-item odd"><a href="/msc-full/57m20" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">57M20</a></li><li class="vocabulary-links field-item even"><a href="/msc-full/55-01" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">55-01</a></li></ul></span>Sat, 27 Jan 2018 16:17:28 +0000Marco Castrillon Lopez48208 at https://euro-math-soc.euhttps://euro-math-soc.eu/review/guide-classification-theorem-compact-surfaces#commentsAffine Maps, Euclidean Motions and Quadrics
https://euro-math-soc.eu/review/affine-maps-euclidean-motions-and-quadrics
<div class="field field-name-field-review-review field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><div class="tex2jax"><p>The assertion that this is a <em>textbook</em> may need some nuance, the book being xi+411 pages long. Since quite often readers loose impetus after 150 pages, such a thick book could discourage many. However those 400 pages can be estimated as 200 of real course. Indeed, the last 100 pages include appendices that are themselves mini-courses in <em>Linear Algebra and Quadratic Forms,</em> and maybe almost that many pages could be counted for the lists of exercises suggested at the end of every chapter, and the many examples fully worked out along the lessons either as illustrations of previous results or as motivation for proofs that follow. For instance, there is a 7 page section titled <em>Clarifying Examples</em> prior to the classification of affinities in arbitrary dimension. In addition, there are some sections that could be marked as optional, either because they include material better understood with some extra knowledge (as <em>Projective Geometry</em>), or because they deal with the recovering of classical results. Here one cannot help praising the succinct 5 page introduction where the author summarizes <em>Euclid’s axiomatic of Affine Geometry</em> and explains how it motivates the text. All these are of course added bonuses, but it is good to separate them from the main content of the text. Thus we are left with say 180 pages of <em>Affine and Euclidean Geometry,</em> which cover the usual: <em>Affine spaces, subspaces and their operations; frames; affine maps and invariants, classification; Euclidean affine spaces and Euclidean motions, classification; real affine and Euclidean quadrics, classifications</em>. Very little need to explain further this list, but even running the usual path, several qualities distinguish this text from others. </p>
<p>First, concerning the global view, there is a neat scheme of action: to give the definitions of the objects to study and discuss their classification problems. Here, although the approach is algebraic, the geometric meaning of the corresponding classification results (canonical forms, canonical equations, tables and lists) is always stressed, with careful choices of terminology. Second, the job is done thoroughly without fault. It is not that common to find: (1) a <em>full classification of affinities</em> as given here, (2) the clear distinction between <em>a quadric and its equations</em> and the exact description of their relationship. Third, there are separate sections for every classification question in the low dimensional cases, sometimes preceding as preparation the general result. Fourth, it is quite clear that this is a <em>real life course,</em> that is, a text written for and from true teaching. Thus any professor will easily find the way to adapt the text to particular whims, discarding technicalities or lightening some lessons. Also, students will find a self-contained book containing all they need to catch the matter: full details and many solved and proposed examples.</p>
<p>All in all the text is a highly recommendable choice for a course on <em>Affine Geometry,</em> and fills some gaps in the existing literature.</p>
</div></div></div></div><div class="field field-name-field-review-reviewer field-type-text field-label-inline clearfix"><div class="field-label">Reviewer: </div><div class="field-items"><div class="field-item even">Jesús M. Ruiz</div></div></div><div class="field field-name-field-review-desc field-type-text-long field-label-hidden"><div class="field-items"><div class="field-item even"><div class="tex2jax"><p>This is a textbook on <em>Affine and Euclidean Geometry,</em> with emphasis on <em>classification</em> problems: classification of affinities, of Euclidean motions, of affine quadrics, of Euclidean quadrics. It can be used in a basic course and still to present full results on the topic at a reasonable cost.</p>
</div></div></div></div><span class="vocabulary field field-name-field-review-author field-type-taxonomy-term-reference field-label-inline clearfix"><h2 class="field-label">Author: </h2><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/author/agust%C3%AD-revent%C3%B3s-tarrida" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">agustí reventós tarrida</a></li></ul></span><span class="vocabulary field field-name-field-review-publisher field-type-taxonomy-term-reference field-label-inline clearfix"><h2 class="field-label">Publisher: </h2><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/publisher/springer-verlag" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">springer-verlag</a></li></ul></span><div class="field field-name-field-review-pub field-type-number-integer field-label-inline clearfix"><div class="field-label">Published: </div><div class="field-items"><div class="field-item even">2011</div></div></div><div class="field field-name-field-review-isbn field-type-text field-label-inline clearfix"><div class="field-label">ISBN: </div><div class="field-items"><div class="field-item even">978-0-85729-709-9</div></div></div><span class="vocabulary field field-name-field-review-msc field-type-taxonomy-term-reference field-label-hidden"><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/msc/51-geometry" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">51 Geometry</a></li></ul></span><span class="vocabulary field field-name-field-review-msc-full field-type-taxonomy-term-reference field-label-hidden"><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/msc-full/51n10-51n20" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">51n10, 51n20</a></li></ul></span>Tue, 14 Feb 2012 19:02:04 +0000Jesus M. Ruiz45441 at https://euro-math-soc.euhttps://euro-math-soc.eu/review/affine-maps-euclidean-motions-and-quadrics#commentsMathematical lives. Protagonists of the Twentieth Century
https://euro-math-soc.eu/review/mathematical-lives-protagonists-twentieth-century
<div class="field field-name-field-review-review field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><div class="tex2jax"><p>This is a highly recommendable reading for mathematicians, of course, but also, with some cautions, for non-mathematicians. The sheer description of the book as a set of papers on the lives and scientific results of several important mathematicians does not express well the nature of the book. Let us try to do better. </p>
<p>Being a collection of independent chapters, the reader can proceed by browsing through the sections guided by the contents table. The table sure contains so famous names that this will give immediate spontaneous choices according to the reader particular interests. Not surprisingly, our reader could discuss the list of mathematicians present: some are missing, some are not that important (or are they?, there is something to learn, then). Also, our reader can find the papers a little unbalanced: some very short, some too technical, some too well known information (how to tell new on John Nash?). But we can be sure that this appreciation goes with him, and another reader will find enough the very short paper, quite interesting those technical details, and a pleasure to find once again the same information with a somehow different twist. Furthermore this double impression will most likely be felt by all readers. In fact, this quality shows the book is right in its tone and scope, and guarantees some good pieces to anyone. </p>
<p>Now, the reader can pick the book as a novel and read it from first page to last. This is relevant, because the organization and ordering of the chapters contribute to the overall effect, by combining in different doses mathematics and life, research and civil or political activism, detail and overall view. Not to be forgotten the great mathematicians appearing in this book are men who have lived through the Second World War and the posterior Cold War, and at one time or another many have taken definite positions. Often great man take very strong positions, which their prominence can amplify, and this is also explained in the corresponding place.<br />
It is clear that a mathematician is best prepared to extract the most from this kind of book. So what for non-mathematicians? Clearly, lives and miracles, true (or imaginary) stories, will interest them. And there is a lot of this stuff for them in the book (beaches of Rio de Janeiro included). But this does not mean they must limit their reading to that. Clearly they should discard many technicalities. Despite the efforts made in many parts, Mathematics are for specialists, for professional mathematicians. However, a sensible diagonal reading of those parts should help anyone to understand the high quality and deep difficulty of the achievements that matter, and the ways they were reached. Those ways may take many years and involve many people, but most often an outstanding scientist can be singled out as leading the track. As a mathematician myself, I find difficult to transmit my own amazed view of the really great mathematics made by really great mathematicians. This book is another try at this, and very welcome.</p>
<p>This review is deliberately imprecise, to avoid spoiling the pleasure of the surprise. However one cannot help listing some unusual names to be found in the book: Verlaine, Musil, Queneau, Borges. (These mentioned in the hope of promising further surprises.) This is a book to read and enjoy, not to study, which for a book classified as Mathematics is not common.</p>
</div></div></div></div><div class="field field-name-field-review-reviewer field-type-text field-label-inline clearfix"><div class="field-label">Reviewer: </div><div class="field-items"><div class="field-item even">Jesús M. Ruiz</div></div></div><div class="field field-name-field-review-desc field-type-text-long field-label-hidden"><div class="field-items"><div class="field-item even"><div class="tex2jax"><p>This book consists of a collection of essays on the lives of an ample choice of important mathematicians of the twentieth century. The essays attempt to convey a global idea of Mathematics through what those mathematicians achieved from a scientific, but also from a social or political viewpoint.</p>
</div></div></div></div><span class="vocabulary field field-name-field-review-author field-type-taxonomy-term-reference field-label-inline clearfix"><h2 class="field-label">Author: </h2><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/author/claudio-bartocci" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">claudio bartocci</a></li><li class="vocabulary-links field-item odd"><a href="/author/renato-betti" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">renato betti</a></li><li class="vocabulary-links field-item even"><a href="/author/angelo-guerraggio" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">angelo guerraggio</a></li><li class="vocabulary-links field-item odd"><a href="/author/roberto-lucchetti" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">roberto lucchetti</a></li></ul></span><span class="vocabulary field field-name-field-review-publisher field-type-taxonomy-term-reference field-label-inline clearfix"><h2 class="field-label">Publisher: </h2><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/publisher/springer-verlag" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">springer-verlag</a></li></ul></span><div class="field field-name-field-review-pub field-type-number-integer field-label-inline clearfix"><div class="field-label">Published: </div><div class="field-items"><div class="field-item even">2011</div></div></div><div class="field field-name-field-review-isbn field-type-text field-label-inline clearfix"><div class="field-label">ISBN: </div><div class="field-items"><div class="field-item even">ISBN 978-3-642-13605-4</div></div></div><span class="vocabulary field field-name-field-review-msc field-type-taxonomy-term-reference field-label-hidden"><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/msc/01-history-and-biography" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">01 History and biography</a></li></ul></span><span class="vocabulary field field-name-field-review-msc-full field-type-taxonomy-term-reference field-label-hidden"><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/msc-full/01a70" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">01a70</a></li></ul></span>Tue, 09 Aug 2011 18:31:35 +0000Jesus M. Ruiz45419 at https://euro-math-soc.euhttps://euro-math-soc.eu/review/mathematical-lives-protagonists-twentieth-century#comments