European Mathematical Society - american mathematical society
https://euro-math-soc.eu/publisher/american-mathematical-society
enWhat's Happening in the Mathematical Sciences - Volume 8
https://euro-math-soc.eu/review/whats-happening-mathematical-sciences-volume-8
<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 the eighth volume of the series "What's Happening in the Mathematical Sciences". The series, published by the American Mathematical Society, started in 1993 and its goal is to shed light on some of the outstanding recent progress in both pure and applied mathematics.</p>
<p>The book is divided into nine chapters which present some remarkable mathematical achievements.</p>
<p>The first chapter "Accounting for Taste" describes how Netflix, a movie rental company, offered a million-dollar prize for a computer algorithm to recommend videos to customers. The first year of competition identified matrix factorization as the best single approach. However to factor matrices with unknown elements the winner team had to devise their own strategy combining matrix factorization with regularization and gradient descent. After three years of competition the award was given to the team called BellKor’s Pragmatic Chaos. This is an example of the use of mathematics behind the scenes in everyday life.</p>
<p>The second chapter "A Brave New Symplectic World" is devoted to the conjecture of Weinstein saying that certain kinds of dynamical systems with two degrees of freedom always have periodic solutions. The conjecture was proposed in the late 1970s as a problem in symplectic topology and solved thirty years later by Cliff Taubes. The remarkable thing is that Taube's solution does not stay within the original discipline and borrows some ideas from string theory, developed by physicist Edward Witten.</p>
<p>"Mathematics and the Financial Crisis" described the collapse of the world's financial markets in 2008. The Black-Scholes formula to estimate the value of call options is explained in detail. For some time this formula was almost perfect but a mathematical model is only as good as its assumptions.</p>
<p>"The Ultimate Billiard Shot" deals with the game of outer billiards proposed in 1959 by Bernhard Neumann. The outer billiard table is infinitely large and it has a hole in the center. The question is: Does the table need to be infinitely large? In other words, is there any way a ball that starts near the central region can spiral out to infinity? The answer depends on the shape of the hole. In 2007, Schwartz proved that for certain shapes, an outer billiards shot cannot be contained in any bounded region. The game of outer billiards may seem a bit restricted but is of interest to mathematicians as a toy model of planetary motion.</p>
<p>The fifth chapter, "Simpatient", deals with the controversial recommendation in 2009 by the U.S. Preventive Services Task Force that women aged 40-49 should no longer be advised to have an annual mammogram. A public health panel used six breast cancer model to take this decision. This is an example of the growing acceptance of mathematical models for medical decision-making, at least behind the scenes.</p>
<p>"Instant Randomness" addresses questions of the following type: How long does it take to mix milk in a coffee cup, neutrons in an atomic reactor, atoms in a gas, or electron spins in a magnet? In many systems the onset of randomness is quite sudden. This abrupt mixing behavior is the "cutoff phenomenon", and the time when it occurs is called the mixing time.</p>
<p>Quantum chaos is the topic of the seventh chapter "In Search of Quantum Chaos". In the 1970s and 1980s chaos theory revolutionized the study of classical dynamical systems. In the atomic and subatomic realm chaos seems to be absent. However, there is a gray zone, the semiclassical limit, between he quantum world and the macroscopic world. Mathematicians have recently confirmed the occurrence of quantum chaos in this zone.</p>
<p>Even in the twenty-first century mathematics reveal new phenomena in the ordinary three-dimensional space. This is the topic of the chapter "3-D Surprises". In 2008 and 2009, some new ways to pack tetrahedra extremely densely were discovered. In 2005, two engineers in Hungary discovered a new three-dimensional object similar to a tetrahedron but with curvy sides. It is the first homogeneous, self-righting (and self-wronging!) object.</p>
<p>Last chapter is "As One Heroic Age Ends, a New One Begins". In the 1950s John Milnor constructed 7-dimensional "exotic spheres" which are identical to normal spheres from the viewpoint of continuous topology, but different from the viewpoint of smooth topology. This was the starting point of a new era of high-dimensional topology. But one question, the Kervaire Invariant One problem was open for more than forty years. In 2009 three mathematicians, Mike Hill, Michael Hopkins and Doug Ravenel, answered this question. But this may be just the beginning of what topologists will learn from the new machinery used to solved this problem.</p>
<p>The book is well written and can be of interest to both mathematicians and general public with some background in mathematics. Many pictures and illustrative diagrams are included in the book.</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">Antonio Díaz-Cano Ocaña</div></div></div><div class="field field-name-field-review-legacy-affiliation field-type-text field-label-inline clearfix"><div class="field-label">Affiliation: </div><div class="field-items"><div class="field-item even">Universidad Complutense de Madrid, Spain</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 the eighth volume of the series "What's Happening in the Mathematical Sciences". The goal of this book, and of the whole series, is to give account for some recent progress in mathematics. The topics covered in the nine chapters of this book range from the high-dimensional topology to quantum chaos and include applications in computer science, medicine, financial markets, ...</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/dana-mackenzie" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">dana mackenzie</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/american-mathematical-society" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">american mathematical society</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-10: 0-8218-4999-9, ISBN-13: 978-0-8218-4999-6</div></div></div><div class="field field-name-field-review-price field-type-text field-label-inline clearfix"><div class="field-label">Price: </div><div class="field-items"><div class="field-item even">US$ 23</div></div></div><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="/www.ams.org/bookpages/happening-8" title="Link to web page">www.ams.org/bookpages/happening-8</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/00-general" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">00 General</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/00a06" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">00a06</a></li></ul></span>Mon, 29 Jul 2013 11:29:44 +0000Anonymous45517 at https://euro-math-soc.euhttps://euro-math-soc.eu/review/whats-happening-mathematical-sciences-volume-8#commentsAn epsilon of room, II: pages from year three of a mathematical blog
https://euro-math-soc.eu/review/epsilon-room-ii-pages-year-three-mathematical-blog
<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 book is a continuation of the series of books by Terence Tao which derive from his mathematical blog. The preceding books were Structure and Randomness and Poincaré’s legacies, both published under the American Mathematical Society. The current review corresponds to An Epsilon of Room, volume 2. The content of this volume has been divided into two large chapters: the first one is devoted to expository articles covering a wide variety of topics, while the second one deals with more technical articles closer to the research interests of the author.<br />
The reader will appreciate from the very first page the exquisite expository style of the author and the beauty of the proofs and ideas that are presented in the text. Though elaborated at certain steps, the technicalities in the arguments are kept to a minimum, while the important ideas are clearly highlighted, in an attempt to make them available in different contexts. The genuine insight of the author provides a perfect approach to each of the topics that are considered in the book.<br />
The articles deal with different aspects of analysis, probability theory, mathematical physics, logic, complexity, combinatorics, number theory… The subjects covered in this volume include, for instance, Talagrand’s concentration inequality and its connection with random matrices, the Agrawal-Kayal-Saxena primality test, Grothendieck’s definition of a group, or the prime number theorem in arithmetic progressions and dueling conspiracies. This is just to mention a few of the subjects corresponding to the first part of the book. Besides, among the topics included in the second half, we find articles devoted to Szemerédi’s regularity lemma via random partitions and the correspondence principle, the Kakeya maximal function conjecture, the prevalence of determinantal point processes, and approximate bases, sunflowers, and nonstandard analysis in additive combinatorics.<br />
Each of the topics is introduced in a very elegant way, including the appropriate motivation, but immediately, the author gets to the point of each problem, revealing where the difficulties lie. He recalls the main contributions to every issue and frequently provides examples and toy versions of the theorems that are considered. Informal overviews of some of the important arguments and/or heuristic proofs are often given in order to clarify the ideas without getting extremely technical.<br />
All these ingredients make the book a wonderful reading to anyone with an interest in current approaches to both classical problems and emerging areas of mathematics. The author really succeeds in transmitting his passion for mathematics, and I am pretty sure that every reader will feel the necessity of broadening his/her area of interest after reading this excellent compilation of mathematical ideas.</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">Pedro Tradacete</div></div></div><div class="field field-name-field-review-legacy-affiliation field-type-text field-label-inline clearfix"><div class="field-label">Affiliation: </div><div class="field-items"><div class="field-item even">Universidad Carlos III de Madrid</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 is a collection of articles originating from Terence Tao’s mathematical blog (terrytao.wordpress.com) which were posted during the year 2009. The material has been updated and improved by the author to reach a publishable form. It contains introductory articles on topics of broad interest, as well as more technical articles mostly related to the research interests of the author.</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/terence-tao" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">terence tao</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/american-mathematical-society" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">american mathematical society</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">2010</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">978-0-8218-5280-4</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/00-general" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">00 General</a></li></ul></span>Sun, 19 May 2013 15:16:24 +0000Anonymous45509 at https://euro-math-soc.euhttps://euro-math-soc.eu/review/epsilon-room-ii-pages-year-three-mathematical-blog#commentsFamous Puzzles of Great Mathematicians
https://euro-math-soc.eu/review/famous-puzzles-great-mathematicians
<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 book is an interesting work on recreational problems on mathematics in the history. This entertaining book presents a collection of 180 famous mathematical puzzles and intriguing elementary problems that great mathematicians have posed, discussed, and/or solved. About 65 intriguing problems, marked by *, are given as exercises, to the readers. The selected problems do not require advanced mathematics, making this excellent book accessible to a variety of readers.<br />
The book is intended principally to amuse and entertain, incidentally to introduce the general reader to other intriguing mathematical topics and ideas. Important relations and connections exist between those problems originally meant to amuse and entertain and mathematical concepts critical to combinatorial and chess, geometrical, and arithmetical puzzles, geometry, graph theory, optimization theory, probability, number theory, and related areas.<br />
The book contains eleven chapters and four appendices.<br />
The first six chapters are on: recreational mathematics (a brief and concise history of mathematics); arithmetics; number theory; geometry; tiling and packing and physics.</p>
<p>The chapter one is on Recreational Mathematics contains, before taking up the noteworthy mathematical thinkers and their memorable problems, a brief overview of the history of mathematical recreations. Perhaps the oldest known example is the magic square. Known as lo-shu to Chinese mathematicians around 2200 B.C., the magic square was supposedly constructed during the reign of the Emperor Yii. Chinese myth holds that Emperor Yii saw a tortoise of divine creation swimming in the Yellow River with the lo-shu, or magic square figure, adorning its shell. The Rhind (or Ahmes) papyrus dating to around 1650 B.C., suggests that the early Egyptians based their mathematics problems in puzzle form. Perhaps their main purpose was to provide intellectual pleasure. The ancient Greeks also delighted in the creation of problems strictly for amusement. The cattle problem is one of the most famous problems in number theory, whose complete solution was not found until 1965 by a digital computer. The Dido´s problem, cited by Virgil, and the elegant solution, established by Jacob Steiner, regarded as first problem in a new mathematical discipline, established 17 centuries later, as calculus of variations. Others interesting problems are included in this book, as Josephus problem; Alcuin of York´s problems and variants; Fibonacci´s amusing problems; IbnKallikan´s problem about the number of wheat grains on a standard 8x8 chessboard; and many instances interesting.<br />
In chapter two, named Arithmetics, are related many instances of famous puzzles: Diophantus´ age; Mahavira: number of arrows; Fibonacci´s: square numbers problem, money in a pile, sequence, how many rabbits?; triangle with integral sides (Bachet); sides of two cubes (Viète), and others puzzles.<br />
Chapter three on Number Theory deal with the following famous: cattle problem; dividing the square; wine problem; amicable numbers, Qorra formula; how many soldiers?; horses and bulls; the sailors, the coconuts and the monkey; stamp combinations, with a generalized problem of Frobenius and Sylvester.<br />
In chapter four, on Geometry, are related some instances: Arbelos problem of Arquimedes, archimedean circles, perpendicular distance and two touching circles; minimal distance of Heron, a fly and a drop of honey, peninsula problem; dissection of three squares; dissection of four triangles; the minimal sum of distances in a triangle; volumes of cylinders and spheres of Kepler; Dido´s problem; the shortest bisecting arc of area de Polya, and other interesting problems.<br />
Chapter five on Tiling and Packing deal interesting and amusing problems in the history of mathematics as: mosaics; non-periodic tiling; maximum area by pentaminoes; kissing spheres; the densest sphere packing, and the cube-packing puzzles.<br />
The chapter six is related to famous problems on Physics as the gold crown of King Hiero; the length of traveled trip; meeting of ships; a girl and the bird, and the lion and the man.</p>
<p>There follows chapters on combinatorics; probability; graphs; chess and miscellany which contains problems from Alcuin de York, Abu´lWafa, Fibonacci, Bachet, Huygens, Newton and Euler.</p>
<p>The chapter seven on Combinatorics, deal the Josephus problem; rings puzzle; the problem of the misaddressed letters; eulerian squares, and the famous Kirkman´s schoolgirls problem. Others interesting problems as counting problem, the tower of Hanoi, the tree planting problem, etc., are included in this chapter.<br />
In the chapter 8 on Probability are considered, the famous problem of the points, gambling game with dice, gambler´s ruin, Petersburg paradox, the probability problem with the misaddressed letters, and the match problem are all treated of elegant form.<br />
The chapter nine deal on Graphs. Contains the famous problem of Königsberg´ bridges, Hamilton´game on a dodecahedron, some problems of Alcuin of York, Erdös, Poinsot, Poisson, Listing, and others problems of interest.<br />
In the chapter ten on chess, many instances and problems are considered: classical knight, queen, rooks and the longest uncrossed knight´s tour.<br />
The chapter eleven, titled Miscellany, contains problems from Alcuin de York, Abu´lWafa, Fibonacci, Bachet, Huygens, Newton and Euler.<br />
Finally, the four appendices, for to help readers, on refer: method of continued fractions for solving Pell´s equation; geometrical inversion; some basic facts from graph theory; linear differences equations with constant coefficients.<br />
The author includes bibliographical references and index, and sometimes amusing anecdotal material, with the objective that to underscore the informal and recreational character of the book.<br />
The book is also high recommended also for individual study. In my opinion, it is a stimulating and excellent text will be for amuse and entertaining, and the teaching in recreational mathematics.</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">Francisco José Cano Sevilla</div></div></div><div class="field field-name-field-review-legacy-affiliation field-type-text field-label-inline clearfix"><div class="field-label">Affiliation: </div><div class="field-items"><div class="field-item even">Universidad Complutense de Madrid</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 is an interesting work on recreational problems on mathematics in the history. These problems have survived, not because they were fostered, by the textbook writers, but because of their inherent appeal to our love of mystery. This entertaining book presents a collection of 180 famous mathematical puzzles and intriguing elementary problems that great mathematicians have posed, discussed, and/or solved. About 65 intriguing problems, marked by * in the book, are given as exercises, to the readers. The selected problems do not require advanced mathematics, making this excellent book accessible to a variety of readers.<br />
The history of mathematics is replete with examples of puzzles, games and entertaining problems that have fostered the development of new and emergent disciplines and sparked further research. The book is intended principally to amuse and entertain, incidentally to introduce the general reader to other intriguing mathematical topics and ideas. With this book, many stories and famous puzzles can be very useful to prepare teaching or lecture notes, to inspire and amuse students, and to instill affection for mathematics. In my opinion, it is a stimulating and excellent text will be for amuse and entertaining, and the teaching in recreational mathematics.</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/miodrag-s-petkovi%C3%A7" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">miodrag s. petkoviç</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/american-mathematical-society" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">american mathematical society</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">2009</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-10: 0-8218-4814-2; ISBN-13: 978-0-8218-4814-2</div></div></div><div class="field field-name-field-review-price field-type-text field-label-inline clearfix"><div class="field-label">Price: </div><div class="field-items"><div class="field-item even">US36$ (List Price); US28.80$ (Member Price)</div></div></div><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://w.w.w.ams.org; http://w.w.w.ams.org/bookpages/mbk-63; order code: MBK/63." title="Link to web page">http://w.w.w.ams.org; http://w.w.w.ams.org/bookpages/mbk-63; order code: MBK/63.</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/00-general" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">00 General</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/2000-msc-00a08-97a20-01a05-01a70-05a05-05c45-05c90" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">2000 msc: 00a08, 97a20, 01a05, 01a70, 05a05, 05c45, 05c90</a></li></ul></span>Fri, 01 Mar 2013 07:53:06 +0000Anonymous45496 at https://euro-math-soc.euhttps://euro-math-soc.eu/review/famous-puzzles-great-mathematicians#commentsThe intrinsic nature of things. The Life and Science of Cornelius Lanczos
https://euro-math-soc.eu/review/intrinsic-nature-things-life-and-science-cornelius-lanczos
<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 author begins with a brief description of Hungary at the end of the XIX century and Lanczos’ family. Then she goes into the early works of Lanczos on Relativity and Quantum Mechanics. Then she writes about the american tour of Lanczos from Purdue University (Indiana) to Boeing in Seattle and the interest Lanczos paid to numerical and Fourier analysis. Finally, we learn about his come back to Europe at the Dublin Institute for Advanced Studies, where he continued his research on Relativity and the Unified Field Theory.</p>
<p>The reader will find many curious things about Lanczos' private life, which are very useful to grasp that Lanczos was a humble person, involved with pedagogical questions on the teaching and learning of science and so we can read on the preface of his book “The variational principles of mechanics” the following:<br />
“Many of the scientific treatises of today are formulated in a half-mystical language, as though to impress the reader with the uncomfortable feeling that he is in the permanent presence of a superman. The present book is conceived in a humble spirit and is written for humble people.”<br />
Also H. Goldstein refers to that book in a manner which reflects the character of Lanczos. He say in his famous book “Classical Mechanics”:<br />
“Lanczos has a different point of view (from the rest of the authors of mechanical treatises); he talks a lot and writes few equations”</p>
<p>On the other side, I miss some chapter dedicated to show and explain a little bit further the mathematical and physical work of Lanczos. Perhaps, it would be nice to have some formulas for trained readers, for instance, his description of the electromagnetic field with quaternions, or a much more deep explanation of his operator of quantum mechanics in contrast to the Schrodinger equation. Also some examples of his use of the Fast Fourier Transformation in numerical examples would be fine.<br />
Nonetheless, she gives detailed references of the cites she uses throughout the book.</p>
<p>Ultimately, it is very pleasant to read as it is written in a very concise manner.</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">José L. Guijarro</div></div></div><div class="field field-name-field-review-legacy-affiliation field-type-text field-label-inline clearfix"><div class="field-label">Affiliation: </div><div class="field-items"><div class="field-item even">Universidad Complutense Madrid</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>The author begins with a brief description of Hungary at the end of the XIX century and Lanczos’ family. Then she goes into the early works of Lanczos on Relativity and Quantum Mechanics. Then she writes about the american tour of Lanczos from Purdue University (Indiana) to Boeing in Seattle and the interest Lanczos paid to numerical and Fourier analysis. Finally, we learn about his come back to Europe at the Dublin Institute for Advanced Studies, where he continued his research on Relativity and the Unified Field Theory.</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/barbara-gellai" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">barbara gellai</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/american-mathematical-society" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">american mathematical society</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">2010</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">9780821851661</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/01a60" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">01a60</a></li></ul></span>Tue, 07 Feb 2012 13:48:17 +0000Anonymous45438 at https://euro-math-soc.euhttps://euro-math-soc.eu/review/intrinsic-nature-things-life-and-science-cornelius-lanczos#commentsComputational Topology
https://euro-math-soc.eu/review/computational-topology
<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">Martin Raussen</div></div></div><div class="field field-name-field-review-legacy-affiliation field-type-text field-label-inline clearfix"><div class="field-label">Affiliation: </div><div class="field-items"><div class="field-item even">Aalborg University, Denmark</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 is an introduction to the field of computational topology. Starting with motivating problems in both mathematics and computer science and building up from classic topics in geometric and algebraic topology, the third part of the text advances to persistent homology. The main approach is the discovery of topology through algorithms.</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/herbert-edelsbrunner" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">herbert edelsbrunner</a></li><li class="vocabulary-links field-item odd"><a href="/author/john-l-harer" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">john l. harer</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/american-mathematical-society" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">american mathematical society</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">2010</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">978-0-8218-4925-5</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/55-algebraic-topology" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">55 Algebraic topology</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="/taxonomy/term/181" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype=""></a></li></ul></span>Tue, 20 Dec 2011 17:41:49 +0000Anonymous45433 at https://euro-math-soc.euhttps://euro-math-soc.eu/review/computational-topology#commentsThirty-three Miniatures
https://euro-math-soc.eu/review/thirty-three-miniatures
<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 book is a collection of problems in which linear algebra appears as an aid to find a solution. The author calls them "miniatures". </p>
<p> The topics of these problems fall into the fields of combinatorics, geometry, and computer science, the author's main fields of mathematical interest. The linear-algebraic methods used cover most techniques learned in a first Linear Algebra course: linear dependence and linear maps, infinite dimensional vector spaces, eigenvalues, determinants, bilinear forms, inner products and norms. Some more advanced tools as tensor and exterior products are also used after a brief introduction with the basic definitions.</p>
<p>The book is addressed mainly to lectures and also to students interested in nice mathematical ideas even when they require some thinking. Each miniature is presented in a self-contained way and it is short enough so that, in the author's experience, it can be taught to the students in a 90-minute lecture. </p>
<p>Right in the first paragraph (or even before, in the title), each miniature presents a problem in an appealing way. Examples of the problems are: How fast can you find a triangle in a very big graph? How many points can you have in the plane so that the distances between any two of them attain exactly two values? How many spanning trees does a graph have? In how many ways can you fill a chessboard with domino tilings? Can you turn around a ladder inside a small garden? The story of the secret agent sending messages in the most efficient way... At this point I strongly recommend the reader to spend a while playing with the problem and looking for a solution. Not only for amusement, but also because, even if no solution is found -which might be quite possible- he will better appreciate and will be greatly surprised by the beautiful and clever ideas behind the problem. </p>
<p>Applications of linear algebra is the common denominator of the thirty-three miniatures, but the reader can learn much more mathematics. On the one hand, other techniques are also commonly used in the proofs, such as polynomials or finite fields. On the other hand, most of the problems presented constitute a very good introduction to some mathematical fields, like coding theory, complexity of algorithms, geometric topics as Gram matrices, the Kakeya problem or the Knaster problem, as well as many topics in graph theory, as spanning trees, complete matchings, spectral graph theory, or the Shannon capacity. Many of them connect with some research problems and open conjectures. At the end of each miniature there are some references for further reading. </p>
<p>The exposition is clear and didactic, starting with motivating examples before going to the mathematical formulations, and giving hints why some techniques work or do not work. Finally the book is carefully written, in a very agreeable and sometimes humoristic style, which makes its reading a really pleasant one. </p>
<p>All the above makes this book highly recommendable.</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">Raquel Díaz</div></div></div><div class="field field-name-field-review-legacy-affiliation field-type-text field-label-inline clearfix"><div class="field-label">Affiliation: </div><div class="field-items"><div class="field-item even">Universidad Complutense de Madrid</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 is a collection of problems in which linear algebra appears as an aid to find a solution. The topics of these<br />
problems fall into the fields of combinatorics, geometry, and computer science, and the linear-algebraic methods used<br />
cover most techniques learned in a first Linear Algebra course.</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/ji%C5%99%C3%AD-matou%C5%A1ek" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">jiří matoušek</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/american-mathematical-society" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">american mathematical society</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">2010</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">978-0-8218-4977-4</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/00-general" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">00 General</a></li></ul></span>Fri, 02 Dec 2011 20:25:59 +0000Anonymous45431 at https://euro-math-soc.euhttps://euro-math-soc.eu/review/thirty-three-miniatures#commentsHadamard's Plane Geometry: A reader's companion
https://euro-math-soc.eu/review/hadamards-plane-geometry-readers-companion
<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>Many relevant mathematicians have yielded to temptation of exploring the realm of classical and Euclidean Geometry together with his/her research activity. Jacques Hadamard, the famous French Mathematician was not an exception. Besides his profound contributions, mainly in Analysis and Number Theory, Hadamard dedicated part of his bright talent in writing a collection of two volumes, the former about plane Geometry and solid Geometry for the latter. This work made part of a collection of textbooks, resources for the teaching of mathematics at high school, edited by G. Darboux, from whom he received the invitation to write these volumes. Since their first edition, Hadamard completed and improved the exposition and the collection of the problems along his fruitful and long life.<br />
There are several editions of Hadamard’s Leçons de Géométrie. Among them, an English translation has been recently done by M. Saul (Lessons in Geometry I. Plane Geometry, American Mathematical Society, 2008). The basic structure of all the lessons is divided in two parts: a theoretical one (including definitions, explanations, results and remarks) followed by a list of unsolved problems. The goal of the book under review is the exposition of the solution of the exercises and problems of the first volume. Together with the original work of Hadamard, the reader now has a companion (as it is explicitly said in the title) for a complete reading of Lessons in Geometry I. The solutions for the section of Miscellaneous Problems have not been included but can be found in the web site of the AMS at <a href="http://www.ams.org/bookpages/mbk-70">www.ams.org/bookpages/mbk-70</a>.</p>
<p>The philosophy of this book is based upon the following points. First, the solutions (most of them done by the author) are complete and rigorous, enriched with many intuitive ideas. The rigor and the intuition are essential ingredients for a companion of Hadamard’s work. Secondly, the book is full of cross references. This simplifies the exposition of those solutions needing results included in previous problems. These cross references may be uncomfortable in a first reading of some particular solutions. A second and more laborious reading gets more benefit from them. Finally, the author incorporates remarks and software explorations at the end of some solutions to be done with the any of the current dynamic geometry software. These applications are not intended to be part of the solution itself but provide insight for both teachers and students in some particular exercises.</p>
<p>Hadamard’s Lessons together with this companion can be of interest to high school teachers, gifted students, students participating in Mathematical contests and any person interested in Geometry. In particular, the ambitious contents of this books is food for though about the evolution of the teaching of Mathematics since the volumes were written. The contents of school geometry have suffered, in general, successive reductions. Hadamard’s opinion about this could be summarized in a short but clear sentence contained in the Preface of the first edition of his Lessons: “Geometry reveals itself capable of exercising an undeniable influence on the activity of the mind”. This could be a good point to reflect about the evolution of this part of Mathematics in the last decades.</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 contains the solutions of the Lessons in Geometry (Volume I) written by the famous French mathematician Jacques Hadamard.</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/mark-saul" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">mark saul</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/american-mathematical-society" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">american mathematical society</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">2010</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">978-0-8218-4368-0</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/01a73" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">01a73</a></li></ul></span>Tue, 13 Sep 2011 10:04:08 +0000Anonymous45422 at https://euro-math-soc.euhttps://euro-math-soc.eu/review/hadamards-plane-geometry-readers-companion#commentsA Course in Algebra
https://euro-math-soc.eu/review/course-algebra
<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 book covers all topics, which are usually included in basic courses on linear algebra and algebra in the first two years of study. In addition, it also includes a lot of non-standard and interesting material going into several different directions. The book is based on the long time teaching experience of the author. At the beginning, main algebraic structures are introduced (groups, rings, fields, algebras, vector spaces). Polynomial algebra is studied in detail and basic facts of group theory are covered. Linear algebra is covered in Chapter 2, Chapter 5 and Chapter 6, together with bilinear and quadratic functionals. Chapter 8 contains a description of general multilinear algebra. The last four chapters are devoted to commutative algebra (principal ideal domains, Noetherian rings, algebraic extensions, and affine algebraic varieties), groups (Sylow theorems, simple groups Galois extensions and Galois theory), linear representations of associative algebras (complete reducibility, invariants, division algebras) and linear Lie groups (the exponential map, the adjoint representation, basic facts on linear representations). The book is beautifully written, the choice of topics and their order is excellent and the book is very carefully produced. It contains a huge number of exercises and it appeals to geometric intuition whenever possible. It can be highly recommended for independent reading or as material for preparation of courses.</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">vs</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/e-b-vinberg" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">e. b. vinberg</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/american-mathematical-society" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">american mathematical society</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">2003</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">0-8218-3318-9</div></div></div><div class="field field-name-field-review-price field-type-text field-label-inline clearfix"><div class="field-label">Price: </div><div class="field-items"><div class="field-item even">$89</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/13-commutative-rings-and-algebras" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">13 Commutative rings and algebras</a></li></ul></span>Mon, 12 Sep 2011 15:38:48 +0000Anonymous39693 at https://euro-math-soc.euLectures on Coarse Geometry
https://euro-math-soc.eu/review/lectures-coarse-geometry
<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 book is based on lectures given by the author at the Penn State university. The notion of ‘coarse geometry’ was invented to keep track of large scale properties of metric spaces. The first part of the book introduces an abstract notion of a coarse structure, a notion of a bounded geometry coarse space, its growth and a notion of an amenable metric space, and discusses coarse algebraic topology. The main topic in the middle part is the Mostow rigidity theorem saying that if two compact hyperbolic manifolds of dimensions at least 3 are homotopy equivalent, they are isometric. The last part of the book contains a discussion of a notion of asymptotic dimensions and uniform embeddings into Hilbert spaces, together with relations to the Kazhdan property of discrete groups. The book offers a very readable description of a circle of ideas around the notion of coarse geometry.</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">vs</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/j-roe" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">j. roe</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/american-mathematical-society" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">american mathematical society</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">2003</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">0-8218-3332-4</div></div></div><div class="field field-name-field-review-price field-type-text field-label-inline clearfix"><div class="field-label">Price: </div><div class="field-items"><div class="field-item even">$39</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/53-differential-geometry" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">53 Differential geometry</a></li></ul></span>Mon, 12 Sep 2011 15:29:06 +0000Anonymous39690 at https://euro-math-soc.euFoliations II
https://euro-math-soc.eu/review/foliations-ii
<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 the second volume of the two-volume series with the title Foliations. It has three independent parts, describing three special topics in the theory of foliations: Analysis on foliated spaces, Characteristic classes of foliations and Foliated 3-manifolds. Each part contains a description of a topic in foliation theory and its relation to another field of contemporary mathematics. In the first part, the C*- algebras of foliated spaces are studied and some of the classical notions from Riemannian geometry (heat flow and Brownian motion) are generalized to foliated spaces. Necessary analytic background can be found in three appendices. The second part is devoted to characteristic classes and foliations. Here the reader can find constructions of exotic classes based on the Chern-Weil theorem, vanishing theorem for Godbillon-Vey classes and a discussion on obstructions to existence of a foliation transverse to the fibres of circle bundles over surfaces. In the third part, compact 3-manifolds foliated by surfaces are studied. Special methods of 3-manifolds topology yield existence theorems and further results unique for dimension three. There is an appendix with a proof and further discussion of Palmeiras theorem, which says that the only simply connected n-manifold foliated by leaves diffeomorphic to Rn-1 is Rn. The book contains a lot of interesting results and can be recommended to anybody interested in the topic.</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">jbu</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/candel" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">a. candel</a></li><li class="vocabulary-links field-item odd"><a href="/author/l-conlon" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">l. conlon</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/american-mathematical-society" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">american mathematical society</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">2003</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">0-8218-0809-5</div></div></div><div class="field field-name-field-review-price field-type-text field-label-inline clearfix"><div class="field-label">Price: </div><div class="field-items"><div class="field-item even">$79</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>Mon, 12 Sep 2011 13:14:48 +0000Anonymous39665 at https://euro-math-soc.eu