Book reviews
https://euro-math-soc.eu/book-reviews
Book reviews published on the European Mathematical Society websiteenThe Cosmic Web
https://euro-math-soc.eu/review/cosmic-web
<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 original text is from 2016, but this review is written on the occasion of the unaltered paperback version in 2018. Gott sketches the successive cosmological models that were designed to understand why the universe is behaving the way it does. The description is intended to be understood by anyone interested but what is so nice about reading this ongoing evolution of our insights is that he has known as a young researcher the people who were working on earlier models, and he has contributed himself in his later career. This makes his account very personal. His main interest involves the structure of the universe at very large scale. The galaxies are not uniformly distributed, but they cluster on filaments and form a sponge-like web, The term "web" was first introduced in 1983 in a paper by Klypin and Shandarin. This is the story of the universe told at the mind-blowing scale of billions and trillions of light-years.</p>
<p>
The story starts with the models of the 20th century. Using red-shifts, Hubble showed that the universe is currently expanding. Another debate was about the cosmological constant and its value which defined the shape (flat, hyperbolic or elliptic) of our universe. Only near the end of the century it was observed that the universe is not only expanding, but that the expansion was accelerating.</p>
<p>
Fritz Zwicky contributed to the larger structure studying clusters of galaxies, using gravitational lensing. In the course of this research, some effects could only be explained using a smooth massive presence which is now called dark matter.</p>
<p>
Gott himself enters the scene with his research about the possible ways that galaxies are formed and to what they evolve. Two competing possible structures are considered: either the galaxies cluster together and float like isolated meatballs in a mostly empty cosmic soup or they fill up the universe, but leaving large, almost vacuum holes like a Swiss cheese. The clustering depends on perturbations in the initial conditions of the universe and which of both models will result (the soup or the cheese) depends on whether the density is considered low or high. Zeldovich in the USSR considered a Swiss cheese model where galaxies cluster on relatively thin boundaries of some vacuum 3D Voronoi cells</p>
<p>
The observed uniformity in the microwave background (how we observe the early universe) remained an enigma for some time. Uniformity can only be explained if the whole cosmos had been in a contact close enough to exchange photons, but what we observe is that they are too far apart to have ever met. This can only be solved by accepting an inflationary phase right after the Big Bang when space expanded faster than light, doubling in size every 10−38</p>
<p>
seconds. Thus parts escaped outside our causality horizon and only now, because the expansion has slowed down to below light-speed, they re-enter our causality horizon. So they look like being too far apart, but they were actually very close and in causal contact before the inflation. This explanation for the horizon problem can be understood by realizing that one second after the Big Bang we can only see what is less than one light-second away, but as time continues, we can see farther and also see objects that are much farther apart.</p>
<p>
The expansion during the high energy inflation period gave rise to bubbles of lower energy. Such a bubble creates a universe on its own, and since there are more bubbles, this assumption becomes a possible multiverse model, our universe being in one of these bubbles. The formation of galaxies could be explained by assuming cold dark matter that can clump together spontaneously by gravitation. The next question is how these galaxies are distributed and how they will evolve. What follows is a remarkable story of Gott's high school project on regular space filling polyhedral structures. He detected that by removing some faces to connect all the polyhedral interiors but at the same time leaving all the remaining faces connected too, he got some sponge-like space filling surface. For example a truncated octahedron consists of 8 hexagonal faces and 6 square faces (where the vertices of the octahedron are truncated). These polyhedra can fill 3-space. Now remove all the square faces from the structure, and one gets a sponge-like surface that is neither a soup-with-meatballs models (where the meatballs are disconnected) or the cheese-with-holes model (where the holes are disconnected). All the remaining faces and all the empty space of the octahedral tessellation are connected. Thus 3D space is partitioned in two disjunct yet fully connected subsets like in a sponge. Gott defined the genus of such a surface as the number of holes minus the number of isolated regions of matter. It is equal to the integral of the curvature and equals minus half the Euler characteristic (<em>g=-(V-E+F)/2</em>). The genus is negative for the Swiss cheese model and positive for the meatball model and anything in between is sponge-like.</p>
<p>
But the sponge-like distribution of galaxies is only temporally. Galaxies may be attracted to each other too. One may in fact construct fluid flow lines showing how galaxies and clusters of galaxies are attracted to so called super clusters. We are with our solar system in the Milky Way, part of a Local Group, belonging to the Virgo Supercluster, which is a branch of the Laniakea Supercluster. Like the water in the watershed of a river we are attracted to the center of the Laniakea. Laniakea means immeasurable heaven in Hawaiian.</p>
<p>
Simulations were run and observations were made detecting clusters of galaxies arranged in filaments. So the sponge became a web. The term "cosmic web" was used first in the title of a paper by Bond, Kofman, and Pogosyan "How filaments are woven into the cosmic web" that they posted in 1995 on arXiv.</p>
<p>
The iconic elliptic map of the cosmic background radiation (CBR) is a projection of the celestial sphere showing the radio spectrum observed by the WMAP satellite. Investigation of the curvature of the isothermal contour lines can be used to define the genus of the topology. It showed that this matched the sponge-like structure that was also predicted in the simulations when starting from random quantum fluctuations during the inflation.</p>
<p>
Still one element is missing to explain the acceleration of the expansion of the universe detected in 1995. This is explained by the repulsive effect of a negative pressure from some energy density. However since the gravitational effect of matter density is much higher than the effect of energy density, one needs an enormous amount of energy to explain the acceleration. To match all the observations, one came to a consensus in 2015 that it is required that about 70% of the universe should consist of dark energy and only 30% of matter, most of which is dark matter. As the universe increases, the density of matter will decrease, and the energy density will increase. Current estimates are that the size is currently doubling every 12.2 billion years. Depending on the ratio of the pressures caused by dark energy and dark matter, different scenarios for the ultimate future of the universe in a googol or a googolplex years are proposed.</p>
<p>
The particularly nice thing about the way Gott tells this story is that he can tell it because he personally contributed to it and met or collaborated with many of the other people who have shaped our current knowledge of the cosmos. Moreover he not only describes the models but he also explains why new observations made it necessary to modify a previous model. So he explains not not only the "what" but also the "why". Of course he is not showing the field equations, that would be too technical beyond the understanding of a general reader, but he explains what the different interpretation is of a constant placed on the left-hand side or the right-hand side of the equations. He also gives physical and mathematical information about the phenomena discussed. His topological science project is explained in some detail with classic polyhedra, and we can follow his derivation of the genus of a sponge-like structure and we learn the meaning of curvature. He mentions the use of the Mollweide equal area projection to picture the CBR. There are Gaussian and other curves (like many other graphics) throughout the book. Sixteen colour plates are bundled at the end, like some extra notes to the different chapters and references to the literature. Also the subject and name index is quite effective. This is a very readable account of how our understanding about the cosmos has evolved with some interesting mathematical excursions. In particular the web-like structure at an incredible large scale is very well explained, which fully justifies the title of 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">Adhemar Bultheel</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 book describes how our understanding of the cosmos has evolved since the early 20th century. In particular the study of the cosmos at a very large scale with billions of galaxies organized in clusters and superclusters that form a cosmic web is a key topic of this account since the author was an essential contributor to this concept.</p>
</div></div></div></div>
<span class="field field-name-field-review-author field-type-taxonomy-term-reference field-label-inline clearfix">
<span class="field-label">Author: </span>
<ul class="field-items">
<li class="field-item even"><a href="/author/j-richard-gott" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">J. Richard Gott</a></li>
</ul>
</span>
<span class="field field-name-field-review-publisher field-type-taxonomy-term-reference field-label-inline clearfix">
<span class="field-label">Publisher: </span>
<ul class="field-items">
<li class="field-item even"><a href="/publisher/princeton-university-press" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">princeton university press</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">2016</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">978-0-691-15726-9 (hbk), 978-0-691-18117-2 (pbk)</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">29.95 USD (hbk), 19.95 USD (pbk)</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">272</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="https://press.princeton.edu/titles/10539.html" title="Link to web page">https://press.princeton.edu/titles/10539.html</a></div></div></div>
<span class="field field-name-field-review-class field-type-taxonomy-term-reference field-label-hidden">
<ul class="field-items">
<li class="field-item even"><a href="/imu/mathematical-physics" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">Mathematical Physics</a></li>
</ul>
</span>
<span class="field field-name-field-review-msc field-type-taxonomy-term-reference field-label-hidden">
<ul class="field-items">
<li class="field-item even"><a href="/msc/83-relativity-and-gravitational-theory" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">83 Relativity and gravitational theory</a></li>
</ul>
</span>
<span class="field field-name-field-review-msc-full field-type-taxonomy-term-reference field-label-hidden">
<ul class="field-items">
<li class="field-item even"><a href="/msc-full/83f05" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">83f05</a></li>
</ul>
</span>
<span class="field field-name-field-review-msc-other field-type-taxonomy-term-reference field-label-hidden">
<ul class="field-items">
<li class="field-item even"><a href="/msc-full/85a40" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">85A40</a></li>
</ul>
</span>
Tue, 26 Feb 2019 10:36:34 +0000adhemar49152 at https://euro-math-soc.euTotally Random
https://euro-math-soc.eu/review/totally-random
<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 popular science book explaining quantum mechanics (QM), in particular the key element called entanglement, which is surprisingly conceived as a graphical comic. The graphics are in greyscale (but mostly black) and almost all are either collages of drawings and real pictures, or just plain text.</p>
<p>
The book has three parts. The first one brings the essential concept of entanglement to the reader, but without any mathematics. The main instrument is a kind of toaster (the Super Quantum Entangler PR01) that is used throughout the book. Two coins can be inserted in parallel slits and the toaster ejects the two coins landing head or tails as if they were entangled like the spins of entangled photons are. This is actually Bell's theorem stating the dependence of the quantum states of entangled particles. This 'curious correlation' of 3/4 is an upper bound for a kind of instantaneous non-local communication that cannot be explained by classical mechanics, and which Einstein called 'spooky action at a distance'. This is expressed here as an operating scheme of the toaster that will result in the landing of the two tossed (or toasted) coins to end up with a different face (tails-heads or heads-tails) if both are tossed starting heads up. For all other initial conditions, the two coins will land with equal face up (heads-heads or tails-tails). Thus the tossed coins land with different faces up in three quarters of the cases. This correlation can not be explained by randomness if the two coins are uncorrelated, and neither can it be explained by rigging the coins. These entangled coins are called <em>quoins</em> in the book. The authors take their time and quite a number of pages to imprint the concept of quoins on the reader. The off-line characters here are the authors Jeffrey Bub (a physicist at the University of Maryland) explaining this to his daughter Tanya (who attended Art School and develops websites). They initiate the discussion, but the narrator does the explanation, and the reader (we see only the hands) does the tossing.</p>
<p>
The `spooky action at a distance' brings us to Einstein and part 2 in which the main characters of last century's QM debaters are explaining their vision on how it should be interpreted. Einstein is the first and next comes Schrödinger and his cat in the box with a theory that the state describes the whole past and future (the wave function, a term not used here). The wave function collapsing by our observation means that what we measure is different from what the real state actually is if not observed: a mixture of all possible states. Enters Hugh Everett with a universal splitter: All outcomes of a measurement do exist, but in different universes. Since we cannot probe another universe, this is impossible to verify. The Pauli effect (critical equipment tends to fail when someone is present) kills Everett. So Pauli and a private eye (von Neumann) appear to investigating what went wrong. The culprit is the witness who consciously observed the outcome of the coin toss that made the state collapse. The whole bunch ends up in the consultation room of doctor (Niels) Bohr where they investigate the causality involved (which quoin defines the outcome of the other?), but since time is relative, causality becomes difficult to define. There is a pun here because (David) Bohm (who defended the hidden variables theory) is mentioned among the characters, but he seems not to appear in the story. He has hidden himself, disguised in the form of the Einstein character who plays a double-role.</p>
<p>
The third part takes on a more comic kind of style with invented characters and situations. It is about what applications one could think of if we had these quoins, in other words, what are the (practical) applications of QM? The first application is about quantum cryptography. It is presented as if the classical characters Alice and Bob want to escape from some room where the outcome of a toss from one side of the room must be passed to another side. However, every information crossing can be observer by E.V.E., an eavesdropper in the form of a sphinx that sends an all intercepting beam dividing the two parts of the room.<br />
Quantum computing is illustrated by animals (chickens and foxes dressed as humans) who are gambling in a casino.<br />
The last application is about teleportation, at least teleporting Spock's soul, leading to the dissociation of everything in a whirling cloud of particles, referring the reader to page 1.</p>
<p>
If we make abstraction of the QM content, it is also interesting as a comic book. The scenario is witty and has some nice findings like involving the reader as one of the characters. At some point, the reader is sucked inside the story. The scientists sitting in a van with the unconscious Everett, directly address the reader asking to come inside and close the door of the van so that they can bring Everett to doctor Bohr. Another fun element are the dog-eared graphics showing comments of the Bubs with grumpy critique on how the story develops. Most of the graphics combine a collage of pictures with minimal drawing interventions. Sometimes what is being discussed is illustrated with pictures of (the first page of) the actual historic publications in a scientific journal. I guess that to obfuscate the unwanted artefacts from the collage, the graphics are a bit fuzzy and dark-ish. Since there is a lot of explanation to do, there are also frames that are just white text in a black window. Some of the better graphics are in the third part and in the apotheosis.</p>
<p>
This is an interesting experiment. Quantum mechanics is not easy to grasp. What the book somehow makes clear is what entanglement really means, or in this case how quoins (entangled coins) actually behave. The historical discussions by the physicists are reflecting the different opinions that they represent but it has to remain necessarily superficial. I guess that a complete layman can fully understand the discussions they have here in this book, but if not everything is clear, it could of course be an incentive to read more about this. For example with the guidance of a teacher who is using this book as a guideline. There is an appendix with notes, some of which refer to the literature, and there is also a website for the book <a href="http://totallyrandom.info" target="_blank">totallyrandom.info</a> which has some extra material but (at the time of writing this review) it is more a brief summary, serving as teasers to buy the book, rather than adding extra new material. In my opinion, the third part is the most interesting one since it illustrates the power of what could be done with QM. That should be easy to understand once the result of part 1 is accepted.</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">Adhemar Bultheel</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 graphical version of a popular science book, which has a lot of humour, but its serious purpose is to explain what makes quantum mechanics (QM) so unearthly and how it relates (or not) to reality. In particular the focus is on entanglement, which makes QM so difficult to understand, but, if entanglement is accepted, it also allows to illustrate the miracles QM is capable of.</p>
</div></div></div></div>
<span class="field field-name-field-review-author field-type-taxonomy-term-reference field-label-inline clearfix">
<span class="field-label">Author: </span>
<ul class="field-items">
<li class="field-item even"><a href="/author/tanya-bub" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">Tanya Bub</a></li>
<li class="field-item odd"><a href="/author/jeffrey-bub" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">Jeffrey Bub</a></li>
</ul>
</span>
<span class="field field-name-field-review-publisher field-type-taxonomy-term-reference field-label-inline clearfix">
<span class="field-label">Publisher: </span>
<ul class="field-items">
<li class="field-item even"><a href="/publisher/princeton-university-press" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">princeton university press</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">2018</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">978-0-691-17695-6 (pbk)</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">22.95 USD (pbk)</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">280</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="https://press.princeton.edu/titles/11232.html" title="Link to web page">https://press.princeton.edu/titles/11232.html</a></div></div></div>
<span class="field field-name-field-review-class field-type-taxonomy-term-reference field-label-hidden">
<ul class="field-items">
<li class="field-item even"><a href="/imu/mathematical-physics" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">Mathematical Physics</a></li>
<li class="field-item odd"><a href="/imu/mathematics-education-and-popularization-mathematics" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">Mathematics Education and Popularization of Mathematics</a></li>
</ul>
</span>
<span class="field field-name-field-review-msc field-type-taxonomy-term-reference field-label-hidden">
<ul class="field-items">
<li class="field-item even"><a href="/msc/81-quantum-theory" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">81 Quantum theory</a></li>
</ul>
</span>
<span class="field field-name-field-review-msc-full field-type-taxonomy-term-reference field-label-hidden">
<ul class="field-items">
<li class="field-item even"><a href="/msc-full/81p40" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">81P40</a></li>
</ul>
</span>
<span class="field field-name-field-review-msc-other field-type-taxonomy-term-reference field-label-hidden">
<ul class="field-items">
<li class="field-item even"><a href="/msc-full/81-01" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">81-01</a></li>
<li class="field-item odd"><a href="/msc-full/81p05" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">81P05</a></li>
<li class="field-item even"><a href="/msc-full/00a79" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">00a79</a></li>
</ul>
</span>
Tue, 26 Feb 2019 10:31:52 +0000adhemar49151 at https://euro-math-soc.euIntroduction to Geometry and Topology
https://euro-math-soc.eu/review/introduction-geometry-and-topology
<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 excellent companion to everyone involved in a somehow advanced course on Differential Topology and/or Differential Geometry. Either students or professors will find it profitable, although students should have some previous acquaintance with the topics covered. In general, the author gets quite efficiently without diversions to several deep results, with a most friendly style. In some cases he does not try the impossible, and stops where mathematics get too tough, and there he proposes suitable references. Also, we find a selection of problems enough to make the book a valuable reference. </p>
<p>The first chapter on Topology is a kind of (good) speedy introduction to the matter, that one should better classify as a recall. But then there is a beautiful presentation of the Jordan Curve theorem. This is worth by itself, and furthermore provides motivation for the posterior proof of the higher dimension version using de Rham cohomology.</p>
<p>The second chapter is a terse presentation of the notions of differentiable manifolds. However terse, it yet succeeds in doing everything not embedded and very readable. Even vector bundles are defined in general form. True that this chapter does not get much beyond definitions (this reviewer for instance misses some words on flows), but anyway it offers a good introductory view of many things. Lie groups for instance.</p>
<p>The third chapter would alone justify any previous omisions. This is a neat, motivating and accomplished little first course on de Rham Cohomology. A beauty. A lot is motivated, a lot is explained and a lot is distilled: Poincaré Lemma, Mayer-Vietoris, cohomology of spheres, Brouwer fixed point theorem, Jordan-Brouwer separation theorem… </p>
<p>The last chapter on Differential Geometry is truly nice. It gives an account on curves form a higher viewpoint that is a bonus in form and content even for those who already know the matter. Then the author turns to curves in immersed manifolds: first fundamental form and internal geometry. Next, exterior geometry and the second fundamental form. Here the subject are hypersurfaces, enlarging the usual restriction to surfaces in 3-space. In the end, we get to Gauss Egregium theorem, nothing better in closing.</p>
<p>It is clear that the book comes from the experience in the class room, and a good one it seems. We must thank the author for sharing it with us.</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">Jesus 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 is an excellent companion to everyone involved in courses on Differential Topology and/or Differential Geometry. Quite efficiently it gets to several deep results avoiding diversions, still giving a sense of pace friendly to the reader. Otherwise it takes matters till the accesible point and proposes literature for further progress. Strongly recommendable.</p>
</div></div></div></div>
<span class="field field-name-field-review-author field-type-taxonomy-term-reference field-label-inline clearfix">
<span class="field-label">Author: </span>
<ul class="field-items">
<li class="field-item even"><a href="/author/werner-ballmann" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">Werner Ballmann</a></li>
</ul>
</span>
<span class="field field-name-field-review-publisher field-type-taxonomy-term-reference field-label-inline clearfix">
<span class="field-label">Publisher: </span>
<ul class="field-items">
<li class="field-item even"><a href="/publisher/birkh%C3%A4user" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">birkhäuser</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">2018</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">9783034809825</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">40 EUR</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">196</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="https://www.springer.com/us/book/9783034809825" title="Link to web page">https://www.springer.com/us/book/9783034809825</a></div></div></div>
<span class="field field-name-field-review-class field-type-taxonomy-term-reference field-label-hidden">
<ul class="field-items">
<li class="field-item even"><a href="/imu/geometry" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">Geometry</a></li>
<li class="field-item odd"><a href="/imu/topology" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">Topology</a></li>
</ul>
</span>
Tue, 05 Feb 2019 15:55:46 +0000JMRz49085 at https://euro-math-soc.euGraph Theory and Its Applications (3rd ed.)
https://euro-math-soc.eu/review/graph-theory-and-its-applications-3rd-ed
<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 a comprehensive textbook on graph theory is intended as an advanced undergraduate or introductory graduate course. The previous editions of this book had only the first two authors. This edition is a reorganization and makeover of the previous edition with new material added. The style of the previous edition is maintained, meaning that it is a succession of definitions, examples, applications, theorems, proofs, remarks, with little text in between. The many graph drawings and the numerous examples make it easy to understand what the theory is referring to. Many algorithms are presented as high-level pseudo code, but for those students interested in the programming aspects there are extra notes about implementation and several computer programming projects are formulated as exercises. Each chapter is introduced with a brief summary of its objective and contents, and it ends with a glossary giving one-liner descriptions of the new terms that were introduced in that chapter. The preface explains the concept of the book, gives a brief outline of the contents, and some suggestions for the instructor on how to select material from the book for composing a shorter course.</p>
<p>
New to this edition are many "supplementary exercises" (some with hints or solutions at the end) added after each chapter. They complete the many exercises that were included already after the sections of the chapters. Also the algorithmic aspects are more elaborated. The applications of the chapter on colouring and factoring are extended with examples of scheduling problems, map colouring, and problems in computer science, chemistry, circuit theory, etc.</p>
<p>
The compact enumerating style of writing makes it also an excellent reference work. The extensive index, the list of applications, and the glossary of algorithms added at the end are a welcome help for that. The appendices summarizing necessary elements from mathematics (logic and proof techniques, functions, combinatorics, algebraic structures, complexity), and the additional references: books (organized by subject) and papers (organized by chapter), besides the really impressive list of exercises, are of course useful elements helping the students that have to assimilate the material.</p>
<p>
The main contents is organized in 11 chapters. The first two give the basic definitions about concepts, structures, and representations of graphs. Chapter three and four discuss trees and spanning trees. A tree is one of the most important graph structures. They are for example a key-tool in useful applications such as designing different search and coding algorithms. The fifth and sixth chapters introduce connectivity and (optimal) graph traversals. Applications include reliable networks, and routing problems like the Chinese postman and the travelling salesman problem. The Kuratowski theorem is discussed in chapter seven. It characterizes when a graph is planar (no edge crossings). With chapter eight different kinds of graph colouring and graph factorizations are introduced with the applications mentioned above. Students needing operations research or network theory will be most interested in chapters nine and ten, where directed graphs and network flows are discussed. The last chapter is somewhat shorter. It connects the symmetry of the graph with the number of different colourings for that graph.</p>
<p>
Graph theory is applicable in many scientific disciplines, and the book can serve as a basis for any of these. The text is pretty complete in what is discussed but it remains at a basic level. This implies that the math is not so difficult. Of course sets, partitions, and combinatorics are needed but on an algebraic level, permutation groups and morphisms are about the most advanced concepts that are used (for example in the last chapter). The authors chose not to go into problems of spectral graph theory or other more advanced issues.</p>
<p>
The fact that this is the third edition means that the previous editions were already much appreciated, otherwise there would be no need for a third one. With the evolution in the field and extra experience built up by the authors since the last edition (2006), and new ideas brought in by a third author, it is clear that the new edition is an improvement of a textbook that was already a bestseller. In this case it is not only removing typos or clarifying confusing formulations from the previous edition, but it is extended and reorganized. So this is an excellent basic (but more than an introductory) course on graph theory, based on many years of teaching experience. With a volume this size, it is unavoidable that new unintended typos will sneak in. I found some, but there is a website <a href="https://www.graphtheory.com" target="_lank">www.graphtheory.com</a> where more info is available and where suggestions are welcome. The corrections will also be published there. At least that is what is announced in the book, but at the moment of writing this review (January 2019), not many of the links of the website seem to work (e.g. I could not access the errata list for the previous edition) and I doubt that the website is maintained. The last entry dates back to a conference in 2011.</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">Adhemar Bultheel</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 comprehensive textbook on graph theory. It is edition three which is a reorganization and partial rewrite of the previous edition and new material is added. Many new exercises are added after each chapter. It includes not only the definitions and properties of graphs, but also discusses some of the applications and the computational algorithms.</p>
</div></div></div></div>
<span class="field field-name-field-review-author field-type-taxonomy-term-reference field-label-inline clearfix">
<span class="field-label">Author: </span>
<ul class="field-items">
<li class="field-item even"><a href="/author/onathan-l-gross" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">onathan L. Gross</a></li>
<li class="field-item odd"><a href="/author/jay-yellen" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">Jay Yellen</a></li>
<li class="field-item even"><a href="/author/mark-anderson" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">Mark Anderson</a></li>
</ul>
</span>
<span class="field field-name-field-review-publisher field-type-taxonomy-term-reference field-label-inline clearfix">
<span class="field-label">Publisher: </span>
<ul class="field-items">
<li class="field-item even"><a href="/publisher/crc-press" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">crc press</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">2018</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">978-1-4822-4948-4 (hbk); 978-0-4294-2513-4 (ebk)</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">GBP 63,99 (hbk); GBP 35.99 (ebk)</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">577</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="https://www.crcpress.com/Graph-Theory-and-Its-Applications/Gross-Yellen-Anderson/p/book/9781482249484" title="Link to web page">https://www.crcpress.com/Graph-Theory-and-Its-Applications/Gross-Yellen-Anderson/p/book/9781482249484</a></div></div></div>
<span class="field field-name-field-review-class field-type-taxonomy-term-reference field-label-hidden">
<ul class="field-items">
<li class="field-item even"><a href="/imu/combinatorics" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">Combinatorics</a></li>
</ul>
</span>
<span class="field field-name-field-review-msc field-type-taxonomy-term-reference field-label-hidden">
<ul class="field-items">
<li class="field-item even"><a href="/msc/97-mathematics-education" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">97 Mathematics education</a></li>
</ul>
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<span class="field field-name-field-review-msc-full field-type-taxonomy-term-reference field-label-hidden">
<ul class="field-items">
<li class="field-item even"><a href="/msc-full/97k10" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">97K10</a></li>
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<span class="field field-name-field-review-msc-other field-type-taxonomy-term-reference field-label-hidden">
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<li class="field-item even"><a href="/msc-full/97k30" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">97K30</a></li>
<li class="field-item odd"><a href="/msc-full/05-01" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">05-01</a></li>
<li class="field-item even"><a href="/msc-full/05cxx" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">05Cxx</a></li>
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Tue, 05 Feb 2019 08:31:27 +0000adhemar49082 at https://euro-math-soc.euLost in Math: How Beauty Leads Physics Astray
https://euro-math-soc.eu/review/lost-math-how-beauty-leads-physics-astray
<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 title of the book says it all, but it may need some explanation. Physicists have learned by experience that mathematics is very effective in describing the physical laws. It has also turned out to be effective when a simpler explanation is preferred over a more complicated one. Simpler means fewer equations, fewer assumptions, and fewer parameters. These simplifications are often the result of symmetry. So physicists came to accept symmetry as a synonym for beauty. This was a success when in astronomy the paradigm shifted from a geocentric to a heliocentric system, and it was useful in particle physics to unify the theory of different forces as in the standard model. But physicists should be warned by the disaster of the models designed and loved by economists for their mathematical beauty but that dramatically crashed in the 1980s with many years of global recession as a consequence.</p>
<p>
To arrive at a Grand Unified Theory (GUT) and design the mathematics for quantum gravity, physicists, intoxicated by this concept of symmetry, could only think of going one rung further up the ladder, and blindly proposed supersymmetry (susy for the intimi) as the logical next step. And mathematically, it is indeed a beautiful theory: a supergroup that incorporates all the symmetries of the underlying laws as subgroups. However mathematics is not physics, and physics requires experimental confirmation. Unfortunately the physicists are now erring in the dark since the Large Hadron Collator (LHC) did not reveal all the expected particles predicted by susy. The Higgs boson observed in 2012 was the last success. But the Higgs is at a scale that is so far off the scale of the other particles that it conflicts with another paradigm of physics: <em>naturalness</em>. This means that a dimensionless constant should at approximately the same scale as the other parameters. If it is not, then it might be a statistically irrelevant outlier. However if statistics shows that it is an important parameter of the theory, then it needs to be shifted or renormalized, which is called <em>fine tuning</em>. The cosmological constant is an example of fine tuning and it is ugly and still a source of much debate. Einstein was the first to introduce the cosmological constant Λ but he did not like it. It was reintroduced to explain the expansion of the universe and dark energy in the ΛCDM (Cold Dark Matter) model, but dark energy is poorly understood.</p>
<p>
So the question that Hossenfelder as a theoretical physicist asks herself is whether physicists are blinded by this mathematical symmetry principle of beauty and naturalness and do not realize that they are barking up a dead end. Mathematics should not lead the way for physics. It should be the other way around: the appropriate mathematics should be derived from the physics. In the past this ideal of symmetry and naturalness were not the lead. Symmetry was observed a posteriori when the paradigm shift was made. Also naturalness has not always been avoided. The parallax of the stars that could explain the heliocentric system, was way off the scale of distances in our solar system, and so are the distances between stars and between galaxies as compared to our solar system.</p>
<p>
She sets on a mission to ask many of the specialists in the field about their opinion. Skyping and travelling all over the world to interview the leading scientists and everyone who might have an opinion on this matter, trying to convince them (and herself) that physicists have driven research into a cul de sac. This book is a report of her crusade searching for answers. It is clearly her conviction that there is something rotten in the state of physics.</p>
<p>
To explain the problem and to understand the arguments given, she also has to discuss the terms and claims of particle physics, cosmology, etc. So at the same time, this book is a very readable popular science book on the subject. Of course there are no technical details, but for the layman, just enough insight into the concepts and problems are given to know what the discussion is about. All this information is nicely interwoven with her travelling experiences, and the interviews. These interviews are related in a very lively and personal way, often in the form of dialogues that she reconstructed from her recordings. So the reader is painlessly introduced to a broad spectrum of concepts. Of course supersymmetry, but also the standard model in particle physics and the concordance model in cosmology, multiverses, strings and branes, dark matter and WIMP, vortex theory, QBism, symmetry and Lie groups, cosmic background radiation, a simplified particle zoo, and many more. But only just enough info to understand the context.</p>
<p>
The interviews are also very personal. These "big shots", sometimes very busy running a research group, sometimes old retired emeriti, they are only humans, yet convinced of their opinion, defending the foundations on which they built their career. The place and circumstances in which the interview takes place, the hesitation or silence in the discussion, that sometimes drifts off to a philosophical discourse, it all contributes to an entertaining story. And there are many she has interviewed. From Nobel Prize winners Frank Wilczek, Murray Gell-Mann, and Steven Weinberg, to a wind-surfing non-academic Garrett Lisi, enjoying life and research on Maui, Hawaii, who proposed a so far not very successful Theory of Everything based on the exceptional E8 Lie group, and there are about a dozen more people that are staged.</p>
<p>
The frustration of Hossenfelder is that theoretical physicists just go on chasing after mathematical results following these assumptions of beauty and naturalness, and they do not even care about experimental verification, which technically means that they leave science behind. Moreover, they live in a closed, isolated environment, publishing in journals refereed by peers that have the same opinions. The pressure of publishing, getting finances, being accepted by peers, all means that young researchers have to conform themselves to these mainstream ideas. In 2016 the LHC detected something that could not be explained by the standard model. A few months later hundreds of papers had appeared in refereed journals about this so-called diphoton anomaly, when it was announced that the observed bump should be disregarded since it could be explained as noise. This illustrates that theoretical physics can invent explanations for whatever data are presented but so far, no experimental data occurred to confirm susy. Susy is called beautiful, but the concept of beauty can change. Perhaps there are physical laws that are beautiful in an unfamiliar way. Clearly Hossenfelder is throwing a bat in the henhouse. Her message is not very welcome in the community. Will she remain a voice calling in the desert? As a mathematician, (not involved in theoretical physics), I would like the math to triumph, but I think Hossenfelder has some good arguments, and in the past paradigm shifts away from what was considered to be perfect and beautiful have been rewarding. For example it was difficult to abandon the perfectly beautiful circular motion of the planets on epicircles in a geocentric system. However, even though the circles had to be replaced by ellipses in a heliocentric system, it only resulted in an even more general and beautiful mathematical theory. Thus there is no doubt that mathematics will prevail, but nature should be the guide and not the other way around.</p>
<p>
I loved reading this bird's-eye vision of the state of confusion and hope against all odds that theoretical physics is in today. It is written in an entertaining and convincing, yet very human way, showing that science is only produced by people. Perhaps it is worthwhile that scientists take a step back from the rat race of producing papers and that they reflect on what they are doing and recall what the ultimate goal of their science is. Reading this book, can be a good start.</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">Adhemar Bultheel</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>
In this book Hossenfelder complains about the current state of theoretical physics. She shows that currently the mathematical beauty of supersymmetry is the guideline for researchers while so far none of it has been experimentally verified. Her plea is to invert the engine and let nature drive theoretical research instead of unverifiable mathematical assumptions. She tells her story by reporting on interviews that she had with peers all over the world.</p>
</div></div></div></div>
<span class="field field-name-field-review-author field-type-taxonomy-term-reference field-label-inline clearfix">
<span class="field-label">Author: </span>
<ul class="field-items">
<li class="field-item even"><a href="/author/sabine-hossenfelder" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">Sabine Hossenfelder</a></li>
</ul>
</span>
<span class="field field-name-field-review-publisher field-type-taxonomy-term-reference field-label-inline clearfix">
<span class="field-label">Publisher: </span>
<ul class="field-items">
<li class="field-item even"><a href="/publisher/basic-books" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">basic books</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">2018</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">978-0-4650-9425-7 (hbk), 978-0-4650-9426-4 (ebk)</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">USD 30.00 (hbk); USD 17.99 (ebk)</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">304</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="https://www.basicbooks.com/titles/sabine-hossenfelder/lost-in-math/9780465094257/" title="Link to web page">https://www.basicbooks.com/titles/sabine-hossenfelder/lost-in-math/9780465094257/</a></div></div></div>
<span class="field field-name-field-review-class field-type-taxonomy-term-reference field-label-hidden">
<ul class="field-items">
<li class="field-item even"><a href="/imu/mathematical-physics" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">Mathematical Physics</a></li>
</ul>
</span>
<span class="field field-name-field-review-msc field-type-taxonomy-term-reference field-label-hidden">
<ul class="field-items">
<li class="field-item even"><a href="/msc/81-quantum-theory" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">81 Quantum theory</a></li>
</ul>
</span>
<span class="field field-name-field-review-msc-full field-type-taxonomy-term-reference field-label-hidden">
<ul class="field-items">
<li class="field-item even"><a href="/msc-full/81-01" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">81-01</a></li>
</ul>
</span>
Tue, 05 Feb 2019 08:26:43 +0000adhemar49081 at https://euro-math-soc.euWeird maths. At the edge of infinity and beyond
https://euro-math-soc.eu/review/weird-maths-edge-infinity-and-beyond
<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 joint venture of an experienced science writer (Darling) and an exceptionally bright young math student (Banerjee). The result is this book popularising mathematics by presenting a set of curious/interesting/surprising (I would not call them weird) mathematical facts in such a way that they are easily accessible for the layman. The topics they cover are close to the topics that are also discussed in other books written with the same objective. There is of course always a new approach and there is always something to learn from a surprising fact or an unexpected link that is made. The authors have adopted the rule that also Hawking used: avoiding mathematical formulas in a popular science book. Each formula would presumably halve the number of readers. Besides symbols like ℵ and ω (when discussing infinities) and notations like 3↑↑3↑↑3 (when discussing large numbers) there are only very few equations or formulas. The authors state in the preface: If we can not explain it in plain language, then we don't properly understand it. This does not mean that hard topics are avoided since there is quantum theory, cosmology, and physics, as well as the foundations of mathematics with for example Gödel's theorems. According to the preface, Darling is responsible for the philosophical and anecdotal aspects, the relation to music, and he polished everything into the final text. Banerjee was more involved with the technical aspects including large numbers, computation, and prime numbers. The result is a pleasant read that anyone with only a remote interested in mathematics will enjoy.</p>
<p>
The breadth of the topics covered is too wide to enumerate them all, but to give a rough idea, what follows is a fistful of topics that are discussed.</p>
<p>
Historically mathematics is of course inspired by the necessity to count and by our surrounding physical world and the stars up above. But how would a four-dimensional being see our three-dimensional world? For us hard to imagine, but mathematics has no problem to function in higher dimensions.</p>
<p>
With probability one can simply explain the birthday paradox, but it is also essential in quantum theory which is hard to understand, certainly when it eventually leads to vibrating strings in an attempt to construct a theory of everything. In chaotic systems such as the weather, the smallest perturbations, in spite of all the laws of probability, may prevent any valid prediction. On the other hand probabilistic systems can obey simple rules like in Brownian motion, or it may generate complex structures such as fractals. Think of automata like the Turing machine or Conway's Game of Life. If we can model a system, this does not mean that it is practically computable because one can hit the boundaries of complexity like problems of class NP.</p>
<p>
Music and prime numbers are classical topics for books like this one. With the title "music of the spheres", there is a reference to Kepler of course but the story of that chapter also meanders by mentioning the music disk sent into space in the SEFI project as well as singing whales. Obviously there is an obligatory extensive discussion of the mathematics of music. The next chapter is discussing the unavoidable prime numbers. We meet for example the 17 year cycle of cicadas, the Ulam spiral, the Riemann hypothesis, and the twin prime gap.</p>
<p>
Two more classical recreational topics are game theory and logical paradoxes. Game theory is discussed in connection with computers playing chess against humans and later also the more complex game go, but game theory can of course be applied to other games as well. One may for example investigate whether winning strategies exist when the human player can start? Game theory may have been developed to help people win an entertaining game, but when it was applied to very real economics, politics and other modelling and optimization problems it became a serious mathematical subject and John Nash won even the Nobel Prize in economics and the Abel Prize with his results. Paradoxes, the foundations of mathematics, and logic get their separate chapter. They may be applied to entertaining logical puzzles, but when digging a bit deeper, one bumps into much harder problems and the chapter ends by mentioning surprising mathematical results such as for example the Banach-Tarski theorem (a solid ball can be cut up into 5 pieces such that these can be reassembled into two solid balls of the same size as the original).</p>
<p>
With large numbers and transfinite numbers we are back in the realm of numbers and mathematics. Infinity and the orders of infinity are discussed including the continuity hypothesis and the existence or not of the absolute infinity Ω. Big numbers (the really really big ones) like googol, googolplex, power towers (as introduced by Knuth), Graham's number, TREE(3), and several other numbers are featuring in a chapter that is less common in popular math books. Yet there is a subculture of googologists challenging each other in competitions to define ever larger (finite) numbers.</p>
<p>
The last two chapters dive somewhat deeper into the less elementary mathematical topics. Of a more geometric nature is a chapter on topology with objects like the Moebius band, the Klein bottle, and different kinds of geometry and how this is applied to our universe. Finally we arrive at fundamentals discussing the completeness of the mathematical system, Gödel's theorems, proof theory, the axiom of choice, the Peano calculus, ZFC axioms, etc. These are clearly among the more advanced topics discussed in this last chapter.</p>
<p>
As can be seen from this (largely incomplete) enumeration of topics, the discussion is rather broad and sometimes also touching upon deeper theoretical problems. The text remains however very readable, even when more advanced problems are carefully dissected. This is a very nice addition to the popular math literature deserving a warm recommendation.</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">Adhemar Bultheel</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 book to popularize mathematics written by a science writer (Darling) and a bright young math student (Banerjee). The authors cover many of the topics that are traditionally covered by this kind of books, but some surprising connections are made. For example the topic of transfinite numbers is a classic but the googology chapter on large (but finite) numbers is not so common.</p>
</div></div></div></div>
<span class="field field-name-field-review-author field-type-taxonomy-term-reference field-label-inline clearfix">
<span class="field-label">Author: </span>
<ul class="field-items">
<li class="field-item even"><a href="/author/david-darling" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">David Darling</a></li>
<li class="field-item odd"><a href="/author/agnijo-banerjee" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">Agnijo Banerjee</a></li>
</ul>
</span>
<span class="field field-name-field-review-publisher field-type-taxonomy-term-reference field-label-inline clearfix">
<span class="field-label">Publisher: </span>
<ul class="field-items">
<li class="field-item even"><a href="/publisher/basic-books" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">basic books</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">2018</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">9781541644786 (hbk), 9781541644793 (ebk)</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">USD 27.00 (hbk), USD 16.99 (ebk)</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">320</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="https://www.basicbooks.com/titles/david-darling/weird-math/9781541644786/" title="Link to web page">https://www.basicbooks.com/titles/david-darling/weird-math/9781541644786/</a></div></div></div>
<span class="field field-name-field-review-class field-type-taxonomy-term-reference field-label-hidden">
<ul class="field-items">
<li class="field-item even"><a href="/imu/mathematics-education-and-popularization-mathematics" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">Mathematics Education and Popularization of Mathematics</a></li>
</ul>
</span>
<span class="field field-name-field-review-msc field-type-taxonomy-term-reference field-label-hidden">
<ul class="field-items">
<li class="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="field field-name-field-review-msc-full field-type-taxonomy-term-reference field-label-hidden">
<ul class="field-items">
<li class="field-item even"><a href="/msc-full/00a09" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">00a09</a></li>
</ul>
</span>
<span class="field field-name-field-review-msc-other field-type-taxonomy-term-reference field-label-hidden">
<ul class="field-items">
<li class="field-item even"><a href="/msc-full/00a06" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">00a06</a></li>
</ul>
</span>
Tue, 05 Feb 2019 08:21:18 +0000adhemar49080 at https://euro-math-soc.euIntroduction to Chemical Graph Theory
https://euro-math-soc.eu/review/introduction-chemical-graph-theory
<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 representation of an atomic structure by a graph where the vertices represent atoms and the edges the bondings, is an important application of (connected undirected) graphs, studied in a field called chemical graph theory. The overall (topological) structure of such a graph can be caught into just one number called a chemical index and they are often related to chemical properties (like boiling point or energy). Especially the maximum or minimum values of such an index for a given graph topology are particularly important.</p>
<p>
Many of these chemical indices have been proposed. They are often defined in terms of (topological) distances between the vertices, vertex degrees, or on the spectra of matrices describing the graph (like the adjacency matrix or the Laplacian) as in spectral graph theory. This book studies some of the most important of these indices. Although a previous course on graph theory is not really necessary (the main concepts and definitions are recalled in the beginning) it might help if the reader is somewhat familiar with the terminology. So after a brief introduction, the four other chapters are an in-depth discussion of the Wiener index, the Radić index, the dual Merrifield-Simmons and Hosoya indices, and several spectral indices.</p>
<p>
The approach is systematic and theoretical with many definitions and proofs of lemmas, propositions and theorems. The indices are studied for general graphs as well as for particular graph structures such as trees, stars, or caterpillars so that exact values or bounds for maxima and minima can be derived. Trees are the main ingredient and they have a prominent role throughout the book. Each chapter has a list of exercises appended that are usually asking to prove a result in some special case or to prove a property of the chapter whose proof has been skipped. Although it is all about applications in chemistry, the chemical interpretation of all these properties is not worked out and in the best case only briefly mentioned. It is a nice feature though that the chapters start with some overview of what is to follow before one gets lost in the technical details. The practical implementation of how all these indices should be computed or the complexity estimates of the algorithms that should be used are not the main concerns of the authors (at least not in this book). This computational aspect should however not be underestimated because some of these problems are of combinatorial nature and computing can become an issue for large general non-planar graphs representing crystal structures, but this is not an application that the authors have in mind here. Clearly special procedures can be used for special structures that reduce the computing time.</p>
<p>
The Wiener index is the most classic of all these indices. Proposed in 1947 by Harry Wiener (the chemist, not Norbert Wiener the mathematician). It can be defined as the sum of the distances between any couple of vertices of the graph. It is obviously an integer. Its properties are mainly studied here on trees and caterpillars and other special cases. Both the properties of the Wiener index for a certain structure, and the inverse problem of checking the existence of a structure having a given Wiener index are discussed.</p>
<p>
The Radić index (1975) is based on vertex degrees. Classically it is the sum over all edges of the inverses of the geometric means of the degrees of the two endpoints but several variations are possible. More generally the indices are the sum over all edges <em>uv</em> of a function <em>f(u,v)</em> which depends on the degrees of the vertices <em>u</em> and <em>v</em>. Hence several other indices based on vertex degrees with different levels of complexity are also discussed (Zagreb, connectivity, ABC).</p>
<p>
A subset of vertices in which no couple is connected by an edge is an <em>independent set</em>. Its dual is called a <em>matching</em>, that is a subset of edges without a common vertex. The independence and matching number of a graph are defined as the corresponding maxima. The Merrifield-Simmons index (1980) counts the number of independent sets and the Hosoya index (1971) the number of matchings. Clearly both have again integer values. Fibonacci numbers appear naturally as extreme values obtained for a path.</p>
<p>
Finally the classical 0-1 adjacency matrix and its dual, the incidence matrix, are introduced. Even more interesting is the Laplacian (and signless Laplacian), which consist of the diagonal matrix of the vertex degrees minus (respectively plus) the adjacency matrix. Since these matrices are symmetric, their spectra are real. This is a property from linear algebra not proved here. This chapter certainly requires more mathematics outside of combinatorial calculus in the sense that one needs several other properties from linear algebra too and for example trigonometric polynomials are employed to describe the spectra. This expects that the reader has some knowledge about these domains. On the other hand, this spectral analysis gives much more possibilities to analyse the properties of the graph than the indices of the previous chapters. But there are also some surprising relations. For example, for a graph with <em>n</em> vertices, 1/<em>n</em> times the sum of the inverses of the nonzero eigenvalues of the Laplacian is known as the Kirchoff index. For a tree, it is equal to the Wiener index.<br />
The energy of a graph is the sum of the absolute values of the eigenvalues of the adjacency matrix. Explicit expressions are computed for special graphs, but in general nontrivial integral representations are obtained. An energy index can also be defined based on eigenvalues of the Laplacian matrix and several variants are possible. For example the spectral radius can be used as an invariant, or the Estrada index (2000) which is the sum of the exponentials of the eigenvalues.</p>
<p>
Although the main interest of the text is to introduce all these definitions and properties for applications in molecular chemistry, some of these, especially the spectral and energy indices, have also applications in other domains such as networks. The treatment is however focussing on the theory and the mathematics. The applications as well as the numerical or algorithmic computations are not included. The book is introductory in the sense that only the main indices are discussed and is restricted to planar graphs, but what is included is worked out in detail. It can be used for a course in mathematical chemistry, or it can be used for self study.</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">Adhemar Bultheel</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 theoretical introduction to the most important indices for molecular graphs. These indices are distance related like the Wiener index, vertex degree related like the Radić index, independent set or matching related like the Merrifield-Simmons and Hosoya indices, and finally there are the spectral indices. Definitions, properties and proofs for special graphs (mainly trees) and extremality properties of the indices are derived.</p>
</div></div></div></div>
<span class="field field-name-field-review-author field-type-taxonomy-term-reference field-label-inline clearfix">
<span class="field-label">Author: </span>
<ul class="field-items">
<li class="field-item even"><a href="/author/stephan-wagner" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">Stephan Wagner</a></li>
<li class="field-item odd"><a href="/author/hua-wang" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">Hua Wang</a></li>
</ul>
</span>
<span class="field field-name-field-review-publisher field-type-taxonomy-term-reference field-label-inline clearfix">
<span class="field-label">Publisher: </span>
<ul class="field-items">
<li class="field-item even"><a href="/publisher/chapman-and-hallcrc" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">Chapman and Hall/CRC</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">2018</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">9781138325081 (hbk); 9780429450532 (ebk)</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">GBP 79,20 (hbk); GBP 31.99 (ebk)</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">259</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="https://www.crcpress.com/Introduction-to-Chemical-Graph-Theory/Wagner-Wang/p/book/9781138325081" title="Link to web page">https://www.crcpress.com/Introduction-to-Chemical-Graph-Theory/Wagner-Wang/p/book/9781138325081</a></div></div></div>
<span class="field field-name-field-review-class field-type-taxonomy-term-reference field-label-hidden">
<ul class="field-items">
<li class="field-item even"><a href="/imu/combinatorics" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">Combinatorics</a></li>
</ul>
</span>
<span class="field field-name-field-review-msc field-type-taxonomy-term-reference field-label-hidden">
<ul class="field-items">
<li class="field-item even"><a href="/msc/92-biology-and-other-natural-sciences-behavioral-sciences" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">92 Biology and other natural sciences, behavioral sciences</a></li>
</ul>
</span>
<span class="field field-name-field-review-msc-full field-type-taxonomy-term-reference field-label-hidden">
<ul class="field-items">
<li class="field-item even"><a href="/msc-full/92e10" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">92E10</a></li>
</ul>
</span>
<span class="field field-name-field-review-msc-other field-type-taxonomy-term-reference field-label-hidden">
<ul class="field-items">
<li class="field-item even"><a href="/msc-full/92-02" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">92-02</a></li>
<li class="field-item odd"><a href="/msc-full/97k3a" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">97K3a</a></li>
<li class="field-item even"><a href="/msc-full/05c900" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">05C900</a></li>
</ul>
</span>
Tue, 05 Feb 2019 08:10:40 +0000adhemar49079 at https://euro-math-soc.euGiovanni Battista Guccia. Pioneer of International Cooperation in Mathematics
https://euro-math-soc.eu/review/giovanni-battista-guccia-pioneer-international-cooperation-mathematics
<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">Ángeles Prieto</div></div></div><div class="field field-name-field-review-appendix field-type-file field-label-hidden"><div class="field-items"><div class="field-item even"><span class="file"><img class="file-icon" alt="" title="application/pdf" src="/modules/file/icons/application-pdf.png" /> <a href="https://euro-math-soc.eu/sites/default/files/book-review/GucciaBongiornoCurbera_1.pdf" type="application/pdf; length=73197" title="GucciaBongiornoCurbera.pdf">This book examines the life and work of the geometer G.B. Guccia and the first decades of the Circolo Matematico di Palermo.</a></span></div></div></div>
<span class="field field-name-field-review-author field-type-taxonomy-term-reference field-label-inline clearfix">
<span class="field-label">Author: </span>
<ul class="field-items">
<li class="field-item even"><a href="/author/benedetto-bongiorno" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">Benedetto Bongiorno</a></li>
<li class="field-item odd"><a href="/author/guillermo-p-curbera" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">Guillermo P. Curbera</a></li>
</ul>
</span>
<span class="field field-name-field-review-publisher field-type-taxonomy-term-reference field-label-inline clearfix">
<span class="field-label">Publisher: </span>
<ul class="field-items">
<li class="field-item even"><a href="/publisher/springer-international-publishing" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">Springer International Publishing</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">2018</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">978-3-319-78666-7</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">34,31€</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">316</div></div></div>
<span class="field field-name-field-review-class field-type-taxonomy-term-reference field-label-hidden">
<ul class="field-items">
<li class="field-item even"><a href="/imu/history-mathematics" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">History of Mathematics</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="https://www.springer.com/gp/book/9783319786667" title="Link to web page">https://www.springer.com/gp/book/9783319786667</a></div></div></div>
<span class="field field-name-field-review-msc field-type-taxonomy-term-reference field-label-hidden">
<ul class="field-items">
<li class="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="field field-name-field-review-msc-full field-type-taxonomy-term-reference field-label-hidden">
<ul class="field-items">
<li class="field-item even"><a href="/msc-full/01a70" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">01a70</a></li>
</ul>
</span>
<span class="field field-name-field-review-msc-other field-type-taxonomy-term-reference field-label-hidden">
<ul class="field-items">
<li class="field-item even"><a href="/msc-full/01a60" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">01a60</a></li>
<li class="field-item odd"><a href="/msc-full/01a55" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">01A55</a></li>
</ul>
</span>
Tue, 29 Jan 2019 16:49:09 +0000Ángeles Prieto49057 at https://euro-math-soc.euThe Art of Logic
https://euro-math-soc.eu/review/art-logic
<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 book about applied logic. Books that popularize mathematics (and logic) often have chapters about paradoxes, or logic puzzles. If you were expecting something in that style, then it will soon become clear that you are mistaken. Eugenia Cheng who combined in her previous book <em>Cakes, Custard + Category Theory</em> her profession as a mathematician specialised in category theory and her hobby of cooking. In <em>Beyond Infinity</em> she discussed the infinitely small and the infinitely large, which is also rather mathematical, but it can also lead to paradoxes such as the Hilbert Hotel.</p>
<p>
In the current books she discusses the roots that govern all mathematics: the rules of logic and axioms that lay at the origin. Close as this may be to the heart of a mathematician, she considers here however how logic also applies to our daily life, although in a much fuzzier way and lacking the mathematical formalism. As a consequence misunderstandings will occur. These will result in endless and unsolvable discussions, because the opponents apply different rules or different axioms and so both claim to be correct in coming to opposing conclusions.</p>
<p>
Cheng applies this to unravel some of the currently hot topics that roam the media like (political) discussions about health care, or racism and sexism. She clearly explains why the different parties can not come to an agreement. People come to their own version of "The Truth" by making logical mistakes. For example a negation is mistaken for a contraposition, or they use a false premise which logically allows to imply anything, or people apply the rules to different classes of subjects, etc.</p>
<p>
To be able to point out where things go wrong in many practical situations, Cheng of course needs to explain some rules and terms form logic that are much more clearly defined in a mathematical situation. Mathematicians will agree on what is true or correct because they are arguing within a much more abstract and unambiguous universe, using generally accepted rules, even though they need not make all the details of their logical deduction steps explicit. As long as their peers will be able to see how the gaps need to be filled, they will accept the result. Only if the gaps are too large, a referee will require more details.</p>
<p>
So the first part of this book is explaining what logic actually is and how it is experienced every day by anyone. Using many examples from social discussions, political disagreement, or just parent-kid discussions, Chen introduces the different terms, using some necessary abstraction, to talk properly about the terms that are used in more formal proposition logic, including quantifiers, Venn diagrams, truth tables, negation of implications, equivalence, but also fuzzy logic (the world has many "grey zones"),... When there is a discussion about who is to blame for some unfortunate event, then one should first see how it is possible that the event came about, and those previous events are caused in turn by some other events, etc. So there can be a very complex network of causal coincidences that have eventually led to the event that is the subject of the dispute (Chen uses all these relations as a pretext to smuggle in some of her beloved category theory).</p>
<p>
In a second part she explains the limits of logic. In practice there is no peer reviewing process of some person's argument like in a mathematical environment of publishing a paper. Which mechanisms (correct or inappropriate) are used to convince people? Perhaps (Internet) memes are assumed correct while they are not. When one comes to paradoxes, some alarm should go off to revise the system applied. In other situations, logic will not be useful like in emergencies, or when we do not have all the information to act logically, in which cases we may perhaps just follow a reflex, a gut feeling, or trust the judgement of others.</p>
<p>
The third and last part is called beyond logic. This is where one should agree on axioms, the things that are accepted without a (logic) proof. Then there are of course the many grey zones where binary logic is not the proper tool to use. What universe is one talking about (all humans, all men, all women, all white women, all rich and white women,...?) Things may be considered equivalent (the same) for somebody, but not for the adversary. And then there are of coarse emotions that are important factors in everything we do or say.</p>
<p>
In this book Chen is strongly engaged in social justice, minority groups, gurus, religion, climate issues, the role of science, etc. So in her last chapter she somehow summarizes how logic can help you to be a reasonable and intelligent person. There should be some framework that one believes in, and one should be sceptical towards charismatic "superstars". You should realize that there are a lot of grey zones and that you are not alone so that reaching a joint objective can be more rewarding than reaching your own. Correct and reasonable logical arguments should be used, even in a world that is not always logical.</p>
<p>
This is an engaging book, that should be read by everyone. It will help solving disagreements, or direct discussions away from and "it is - it isn't" arguments, and help you focus on the underlying cause of the dispute. Of course real life is not mathematics, boundaries are fuzzy, and obviously, it can not prevent that people disagree, and they should if for the proper reasons and when using the correct arguments, and this is the main message of 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">Adhemar Bultheel</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>
In this book, Cheng illustrates how by using logic, one can become a better, reasonable, and intelligent human. She describes the possibilities, the limitations, and the pitfalls of logic when it is applied beyond the abstract context of mathematics. Can it define what is right or wrong or help to resolve a deadlock in political or social discussions about subjects such as solidarity principles, climate issues, racism, or sexism?</p>
</div></div></div></div>
<span class="field field-name-field-review-author field-type-taxonomy-term-reference field-label-inline clearfix">
<span class="field-label">Author: </span>
<ul class="field-items">
<li class="field-item even"><a href="/author/eugenia-cheng" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">Eugenia Cheng</a></li>
</ul>
</span>
<span class="field field-name-field-review-publisher field-type-taxonomy-term-reference field-label-inline clearfix">
<span class="field-label">Publisher: </span>
<ul class="field-items">
<li class="field-item even"><a href="/publisher/profile-books" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">profile books</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">2019</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">978-1-78816038-4 (hbk); 978-1-78283442-7 (ebk)</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">£14.99 (hbk); £12.99 (ebk)</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">320</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="https://profilebooks.com/the-art-of-logic-hb.html" title="Link to web page">https://profilebooks.com/the-art-of-logic-hb.html</a></div></div></div>
<span class="field field-name-field-review-class field-type-taxonomy-term-reference field-label-hidden">
<ul class="field-items">
<li class="field-item even"><a href="/imu/mathematics-education-and-popularization-mathematics" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">Mathematics Education and Popularization of Mathematics</a></li>
</ul>
</span>
<span class="field field-name-field-review-msc field-type-taxonomy-term-reference field-label-hidden">
<ul class="field-items">
<li class="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="field field-name-field-review-msc-full field-type-taxonomy-term-reference field-label-hidden">
<ul class="field-items">
<li class="field-item even"><a href="/msc-full/00a06" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">00a06</a></li>
</ul>
</span>
<span class="field field-name-field-review-msc-other field-type-taxonomy-term-reference field-label-hidden">
<ul class="field-items">
<li class="field-item even"><a href="/msc-full/03-01" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">03-01</a></li>
<li class="field-item odd"><a href="/msc-full/97a40" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">97a40</a></li>
<li class="field-item even"><a href="/msc-full/00a09" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">00a09</a></li>
</ul>
</span>
Thu, 03 Jan 2019 08:09:55 +0000adhemar48975 at https://euro-math-soc.euAlice and Bob Meet the Wall of Fire
https://euro-math-soc.eu/review/alice-and-bob-meet-wall-fire
<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>
Thomas Lin was science editor for the online <em>New York Times</em> before he decided in 2012 to become the founder and editor in chief of the online <a href="https://www.quantamagazine.org" target="_blank"><em>Quanta Magazine</em></a>. By now it has become a highly appreciated freely available online source for journalists to find information about (hard) science: physics, biology, computer science, and mathematics. Quanta is sponsored by the <em>Simons Foundation</em>, an organization for the promotion of science created by James Simons, the billionaire mathematician and hedge-fund founder. The editorial policy is to cover in about five to ten pages the cutting edge topics that fall somewhat outside the interest of the mainstream media. The texts are engaging newspaper style stories that are rigorous without being really technical. It should catch the attention of any science minded reader. The authors are mostly reporters that have talked to or interviewed the scientists. Only in very exceptional cases, it is written by the scientists themselves.</p>
<p>
After the first five years of Quanta's existence, Lin has made a "Best of"-selection of the texts in two volumes. One is entitled <em>The prime number conspiracy</em> and collects papers dealing with mathematical subjects. That involves obviously prime numbers, but is not restricted to number theory. The remaining subjects (physics, computer science, and biology) is covered in the present volume. The texts are only slightly edited to add the latest news. Clearly some are older while others are more recent. By reading subsequent texts on the same or a closely related topic it is seen how science advances.</p>
<p>
The present collection consists of 38 texts, grouped in eight parts. Clearly it is not possible to cover each of the subjects here in detail, but the titles of the eight parts can give an idea of what is covered. Note that they are all formulated as questions, which reflects that they relate to some of the "big questions" that humans naturally ask and that scientists have been trying to solve, often replacing them by new, even more challenging ones. What follows is a selective survey.</p>
<ol><li>
<em>Why doesn't our universe make sense?</em><br />
This is all about cosmology, space-time, multiverse collision, etc. It contains the article that delivered the book's title. Alice and Bob are the usual persons used in thought experiments. The wall of fire is how an outside observer would see the event horizon of a black hole, if Hawking radiation is accepted, but there are still paradoxes connected to black holes that could not be solved yet.</li>
<li>
<em>What is quantum reality, really?</em><br />
Although quantum theory was conceived about a century ago, it is still not completely understood. It is very real as confirmed by experiments over and over again. So there are still attempts to provide new explanations or old ones are revived. For example various multiverse concepts have their believers and non-believers based on different arguments. We can read about the amplituhedron, a geometrical object that should simplify the quantum field theoretical computations, a considerable improvement over Feynman diagrams. Noteworthy is also a text by Nobel Prize winner Frank Wilczek about quantum entanglement (he also had a contribution in the previous part about Feynman diagrams). He is one of the three authoring scientists in this collection (Robbert Dijkgraaf, director of the IAS in Princetion is another exception, with a contribution in the last part).</li>
<li>
<em>What is time?</em><br />
Time is in many aspects an "outsider" in physical quantities. Physicists have developed several theories about what it is and what is causing it. It is intimately related to an increase of entropy described by the second law of thermodynamics. Entropy is a measure of information. It quantifies the amount of uncertainty, and hence directly links to quantum theory. The preferred laboratory to investigate time (and other quantum physical effects) in extreme circumstances are black holes. Mathematically, time just stops at the singularity of a black hole like it popped into existence with the Big Bang. Quantum entanglement comes into the picture because entanglement happens in space-time, and hence there can also be this "spooky action" at a distance in time which makes causality questionable, but it may explain the evaporation of black holes that Hawking predicted.</li>
<li>
<em>What is life?</em><br />
A lot of progress has been made in cell biology up to the tiniest scale, and that has sparked some hypotheses about the origin of life. Life seems to counteract the second law of thermodynamics, creating structure from chaos. Again, the intimate relation between entropy and information can bring insight. External energy can make self-replication possible, but is it life? Should a sharp boundary between living and non-living be erased? Artificial life, editing and generating new DNA became reality. Animal life with asexual self-replication was discovered. And there is debate when in the course of evolution neurons where developed. All of these questions are discussed in this part.</li>
<li>
<em>What makes us human?</em><br />
The brain is still one of the most complex and least understood organs. There are speculations of why about 3 million years ago the brain of humans started to quadruple in size although size is not the only thing that counts. Why do we have an evolutionary aversion to loneliness? Why do we sometimes make bad decisions, and neuroscientists investigate how the brain of a child changes into the brain of an adult. This part is connected to the next one where machines simulate how the brain operates.</li>
<li>
<em>How do machines learn?</em><br />
Here it is explained how computers are programmed to win in chess or Go from humans. However, this is a machine programmed by humans who feed the rules of the game. In this setting a machine can beat a human only because it is faster. The proper learning machine is however obtained by neural nets where deep learning and reinforced learning are the driving mechanisms that make the machine learn on its own. It will be clumsy in the beginning, but it never gets tired and hence can learn much faster than humans.</li>
<li>
<em>How will we learn more?</em><br />
Here we are back into cosmology and quantum theory. Since the LIGO has measured gravitational waves, a whole new area has opened to scientists. The waves emerge from colliding black holes, but how did these black holes come about and why did they collide? Also a pair of neutron stars can collapse and how did that happen?</li>
<li>
<em>Where do we go from here?</em><br />
It was hoped or expected that the LHC at CERN would detect new particles, but except for the Higgs boson, which was predicted, none other new particle has been observed. So what about the speculative string theory? Will there ever be evidence for some of the, by now many, versions of string theory? Can we ever arrive at a Theory of Everything, and at explaining quantum gravity, or will a completely new vision emerge? Hawking was very optimistic at first to have a ToE at the beginning of the 21st century, but he eventually had admit that it will take a while longer.</li>
</ol><p>
</p>
<p>
Of course most of the topics covered in this book rely on mathematics, fundamental or applied. However, because of the purpose of these texts is to inform the non-specialist about the latest developments, the mathematics are left out and reference to the underlying mathematics is only rarely made. Nevertheless, I believe that also mathematicians, certainly mathematicians, will and should be interested. These applied topics is where mathematical tools are needed that may not be available yet. Here models and simulations of ever higher complexity are required, and more complex abstract tools should be developed. Anyone can read this to stay informed about recent developments in science, but young mathematicians may find here inspiration on which applied direction they want to build their career.</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">Adhemar Bultheel</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 collection of texts from the first five years (2012-2017) of the highly appreciated <em>Quanta Magazine</em>. The articles deal with cutting edge achievements from physics, biology, and computer science brought in a thorough, yet generally accessible form.</p>
</div></div></div></div>
<span class="field field-name-field-review-author field-type-taxonomy-term-reference field-label-inline clearfix">
<span class="field-label">Author: </span>
<ul class="field-items">
<li class="field-item even"><a href="/author/thomas-lin" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">Thomas Lin</a></li>
<li class="field-item odd"><a href="/author/ed-1" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">(ed.)</a></li>
</ul>
</span>
<span class="field field-name-field-review-publisher field-type-taxonomy-term-reference field-label-inline clearfix">
<span class="field-label">Publisher: </span>
<ul class="field-items">
<li class="field-item even"><a href="/publisher/mit-press" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">MIT Press</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">2018</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">9780262536349 (pbk)</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">GBP 14.99 (pbk)</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">328</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://mitpress.mit.edu/books/alice-and-bob-meet-wall-fire" title="Link to web page">http://mitpress.mit.edu/books/alice-and-bob-meet-wall-fire</a></div></div></div>
<span class="field field-name-field-review-class field-type-taxonomy-term-reference field-label-hidden">
<ul class="field-items">
<li class="field-item even"><a href="/imu/mathematical-physics" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">Mathematical Physics</a></li>
<li class="field-item odd"><a href="/imu/mathematics-education-and-popularization-mathematics" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">Mathematics Education and Popularization of Mathematics</a></li>
</ul>
</span>
<span class="field field-name-field-review-msc field-type-taxonomy-term-reference field-label-hidden">
<ul class="field-items">
<li class="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="field field-name-field-review-msc-full field-type-taxonomy-term-reference field-label-hidden">
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<li class="field-item even"><a href="/msc-full/00-01" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">00-01</a></li>
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<span class="field field-name-field-review-msc-other field-type-taxonomy-term-reference field-label-hidden">
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<li class="field-item even"><a href="/msc-full/81-01" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">81-01</a></li>
<li class="field-item odd"><a href="/msc-full/83-01" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">83-01</a></li>
<li class="field-item even"><a href="/msc-full/85-01" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">85-01</a></li>
<li class="field-item odd"><a href="/msc-full/68-01" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">68-01</a></li>
<li class="field-item even"><a href="/msc-full/98-01" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">98-01</a></li>
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Thu, 03 Jan 2019 08:00:25 +0000adhemar48974 at https://euro-math-soc.eu