European Mathematical Society - imperial college press
https://euro-math-soc.eu/publisher/imperial-college-press
enIntroduction to the Fractional Calculus of Variations
https://euro-math-soc.eu/review/introduction-fractional-calculus-variations
<div class="field field-name-field-review-review field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><div class="tex2jax"><p>
The book provides a comprehensive account of a wide selection of variational problems that include a fractional operator (a derivative or an integral in some cases). Both main formulations (Riemann-Liouville and Caputo) are treated in length and for them the authors derive the corresponding Euler-Lagrange equations and the fractional version of Noether's theorem. They also provide a thorough treatment of many details and extensions. Besides, they also consider other approaches and address the Hamiltonian formulation. The book has the great advantage of presenting an in-depth panoramic view of the field.</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"> Salvador Jiménez</div></div></div><div class="field field-name-field-review-legacy-affiliation field-type-text field-label-inline clearfix"><div class="field-label">Affiliation: </div><div class="field-items"><div class="field-item even">Universidad Politécnica de Madrid</div></div></div><div class="field field-name-field-review-desc field-type-text-long field-label-hidden"><div class="field-items"><div class="field-item even"><div class="tex2jax"><p>
A book on the calculus of variations for systems with some fractional operator.</p>
</div></div></div></div><span class="vocabulary field field-name-field-review-author field-type-taxonomy-term-reference field-label-inline clearfix"><h2 class="field-label">Author: </h2><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/author/agnieszka-b-malinowska" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">Agnieszka B. Malinowska</a></li><li class="vocabulary-links field-item odd"><a href="/author/delfim-f-m-torres" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">Delfim F. M. Torres</a></li></ul></span><span class="vocabulary field field-name-field-review-publisher field-type-taxonomy-term-reference field-label-inline clearfix"><h2 class="field-label">Publisher: </h2><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/publisher/imperial-college-press" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">imperial college 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">2012</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">978-1-84816-966-1</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">275</div></div></div><span class="vocabulary field field-name-field-review-class field-type-taxonomy-term-reference field-label-hidden"><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/imu/analysis-and-its-applications" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">Analysis and its Applications</a></li></ul></span>Tue, 01 Dec 2015 12:22:21 +0000Salvador Jimenez46579 at https://euro-math-soc.euhttps://euro-math-soc.eu/review/introduction-fractional-calculus-variations#commentsBlack Holes. A Student text (3rd ed.)
https://euro-math-soc.eu/review/black-holes-student-text-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 is a student text that revises the previous edition from 2009. The main change is the addition of chapter 6 on black holes in more than four spacetime dimensions and a nonzero cosmological constant.</p>
<p>
The previous editions had the subtitle "An introduction" and the new one is called "A Student text", which perhaps is a better description. It is written for a public of last year undergraduate, first year graduate students. Some training in physics, tensor calculus, and preferably also in relativity theory is strongly advised. The text is peppered with problems for the reader to solve, but solutions are provided at the end. These problems are often shortcuts not to disrupt the flow of the exposition. The chapters mainly restrict to the study of the metric and how this defines motion in the presence of black holes. Long derivations are avoided and it is not shown how these metrics solve Einstein's field equations.</p>
<p>
The book starts by recalling the essential elements from relativity theory (Minowski metric, gravitational field, geodesics, transformations, etc.) and of course the definition of a black hole. Its mass is collapsed into a physical singularity and its boundary is the event horizon, a kind of mathematical one-way membrane represented by a coordinate singularity separating different physics inside and outside. An ousider cannot observe what is happening inside the event horizon.</p>
<p>
The simplest case is a spherical black hole with the Schwarzschild metric (which is diagonal) in a 4-dimensional spacetime. Several orbits are described (radial infall and circular orbits for particles and for light). How does a distant observer sees something falling into a black hole? How does it 'feel' to fall into a black hole? How to describe the physics near the event horizon? What happens inside the black hole? Answers to such questions may appear in popular science books or even in science fiction books, but here the answers are read off from the formulas which is something quite different. What happens inside the event horizon can not be observed but the mathematics can be done and the strange physics can be derived. The coordinate systems are important and some phenomena are better understood in different coordinate systems. An observer at infinity and a particle falling into a black hole have quite different experiences.</p>
<p>
The next complication is when the black hole rotates, i.e., has an angular momentum which defines an axial symmetry. This momentum can range from zero (spherical Schwarzschild case) to some finite upper bound (an extreme Kerr hole). Kerr refers to the Kerr metric that is used in this case (diagonal plus nonzero elements in the NE and SW corners). The same kind of exploring the orbits can be done as in the previous chapter. A new element is the ergo sphere (actually an ellipsoid bulging near the equator) that encloses the sphere defined by the event horizon. Rotational energy can be extracted in this bulging area.</p>
<p>
Black holes do not radiate, so they do not seem to have a temperature. A Kerr hole has several thermodynamic-like properties such as the area of the event horizon cannot decrease, its mass can decrease, but there is a lower bound (the Schwarzschild hole), and hence there is an upper bound for the energy that can be extracted from the ergosphere, but this does not reduce to a physical temperature.<br />
It is shown though that quantum theory does need temperature and there are thermodynamic laws. For example entropy cannot decrease and there is Hawking radiation. It creates some problems that need solution, a solution that could be provided by string theory.</p>
<p>
Chapter 5 is about wormholes and time travel, very popular topics in science fiction. Energy requirements are derived for a macroscopic wormhole to exist. If ever this amount of energy would be available, then wormholes would create shortcuts between two points in spacetime and time travel would be possible. Since this would create the well known paradoxes, there is a chance that such wormholes are highly unstable and collapse immediately or some yet unknown physical laws may just forbid them to exist.</p>
<p>
The new chapter 6 discusses the existence of more than the classical 3 space dimensions. Allowing a negative cosmological constant relaxes the condition of an asymptotically flat spacetime, which allows the introduction of a new parameter. Einstein's field equations are now solved by an anti-de Sitter (AdS) metric and black holes need not be topologically spherical anymore, but they may have a positive genus. Quantum theory of gravity seems to match nicely with a conforming field theory (CFT) on the boundary of an AdS of higher dimension. Strings are alternative 1-dimensional building blocks whose excitations at low energy correspond to point-like particles, one of which could be a graviton. Strings can be connected to higher dimensional objects: the branes. Supersymmetric string theory requires 10-11 dimensions. The extra dimensions can not be observer because they are curled up so tightly, but we experience their existence in the form of fields. Black strings and membranes are discussed and linked to black hole entropy. This chapter is even more a survey than are the other chapters. It certainly is an invitation for further reading.</p>
<p>
The last chapter is about astrophysical black holes. In reality the perfect symmetry studied so far does not exist. So what observations do confirm the existence of black holes? There are the collapsed very massive stars, usually appearing as a dark twin to another star, there might be a massive black hole at the center of the galaxy. However, in principle intermediate or even smaller black holes can exist. The former will still be the result of star evolution, but mini black holes should result from physical conditions in the early universe. Their existence is still hypothetical but of course of great interest to cosmology.</p>
<p>
So it will be clear that with this limited number of papers, one should not start reading the book unprepared. Knowledge of relativity theory is indeed something the reader should be somewhat familiar with, and some cosmology does not harm. The mathematics are relatively elementary, but formulas are often dropped saying that you need to take this and that into account and then such equations will result in this formula, or just a reference is given. Thus, if as a mathematician, you want to learn about black holes, you will get a general idea by reading this book, but it will only be a starting point for further exploration.</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 previous editions from 2005 and 2009 had the subtitle "An Introduction". This new edition is called "A Student Text" and it has a new chapter outlining new research on black holes in more than 4 spacetime dimensions. Its main purpose is to describe the physics in and around black holes.</p>
</div></div></div></div><span class="vocabulary field field-name-field-review-author field-type-taxonomy-term-reference field-label-inline clearfix"><h2 class="field-label">Author: </h2><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/author/derek-raine" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">Derek Raine</a></li><li class="vocabulary-links field-item odd"><a href="/author/edwin-thomas" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">Edwin Thomas</a></li></ul></span><span class="vocabulary field field-name-field-review-publisher field-type-taxonomy-term-reference field-label-inline clearfix"><h2 class="field-label">Publisher: </h2><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/publisher/imperial-college-press" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">imperial college 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">2015</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">978-1-78326-481-0 (hbk)</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 54.00 (hbk)</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">300</div></div></div><span class="vocabulary field field-name-field-review-class field-type-taxonomy-term-reference field-label-hidden"><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/imu/mathematical-physics" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">Mathematical Physics</a></li><li class="vocabulary-links 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><li class="vocabulary-links field-item even"><a href="/imu/mathematics-science-and-technology" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">Mathematics in Science and Technology</a></li></ul></span><div class="field field-name-field-review-website field-type-text field-label-hidden"><div class="field-items"><div class="field-item even"><a href="http://www.worldscientific.com/worldscibooks/10.1142/p947" title="Link to web page">http://www.worldscientific.com/worldscibooks/10.1142/p947</a></div></div></div><span class="vocabulary field field-name-field-review-msc field-type-taxonomy-term-reference field-label-hidden"><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/msc/97-mathematics-education" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">97 Mathematics education</a></li></ul></span><span class="vocabulary field field-name-field-review-msc-full field-type-taxonomy-term-reference field-label-hidden"><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/msc-full/97m50" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">97M50</a></li></ul></span><span class="vocabulary field field-name-field-review-msc-other field-type-taxonomy-term-reference field-label-hidden"><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/msc-full/83-01" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">83-01</a></li><li class="vocabulary-links field-item odd"><a href="/msc-full/83c57" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">83C57</a></li></ul></span>Wed, 04 Feb 2015 14:58:11 +0000Adhemar Bultheel46002 at https://euro-math-soc.euhttps://euro-math-soc.eu/review/black-holes-student-text-3rd-ed#commentsGeometric Realizations of Curvature
https://euro-math-soc.eu/review/geometric-realizations-curvature
<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>A central area of study in Differential Geometry<br />
is the examination of the relationship between<br />
purely algebraic properties of the Riemannian<br />
curvature tensor and the underlying geometric<br />
properties of the manifold. The decomposition<br />
of the appropriate space of tensors into irreducible<br />
modules under the action of the appropriate structure<br />
group is crucial. This book is focus on the geometric<br />
realizations of curvature. The authors have organized<br />
some of the results in the literature which fall into<br />
this genre. The findings of numerous investigations<br />
in this field are reviewed and presented<br />
in a clear form, including the latest developments<br />
and proofs.</p>
<p>We recall that, given a family of tensors<br />
$\{T_1,\dots ,T_k\}$ on a vector space $V$,<br />
the structure $\left( V,T_1,\dots ,T_k\right) $ is<br />
said to be \emph{geometrically realizable} if there exist<br />
a manifold $M$, a point $P$ of $M$, and an isomorphism<br />
$\phi \colon V\rightarrow T_PM$ such that<br />
$\phi ^{\ast }L_i(P)=T_i$ where $\{L_1,\dots ,L_k\}$<br />
is a corresponding geometric family of tensor fields on $M$.</p>
<p>The book is organized as follows: In Chapter 1 the authors<br />
introduce some notations and state the main results of the book.<br />
They also discuss the basic curvature decomposition results<br />
leading to various geometric realization results in a number<br />
of geometric contexts. The details and proofs can be found<br />
in the rest of the Chapters. Chapter 2 is devoted to<br />
representation theory and in Chapter 3 some results<br />
from differential geometry are presented. In Chapter 4 and 5<br />
the authors work in the real affine and (para)-complex affine<br />
setting respectively. In Chapter 6 and 7<br />
they perform a similar analysis for real Riemannian geometry<br />
and (para)-complex Riemanian geometry. The results in the<br />
(para)-complex and in the complex settings are presented in<br />
parallel. Finally the authors present a list of the main notational<br />
conventions. Following the list a lengthy bibliography is included.<br />
The book concludes with an index.</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">Mª Eugenia Rosado María</div></div></div><div class="field field-name-field-review-legacy-affiliation field-type-text field-label-inline clearfix"><div class="field-label">Affiliation: </div><div class="field-items"><div class="field-item even">Departamento de Matemática Aplicada, Escuela Técnica Superior de Arquitectura, UPM, Spain</div></div></div><div class="field field-name-field-review-desc field-type-text-long field-label-hidden"><div class="field-items"><div class="field-item even"><div class="tex2jax"><p>This book is focus on the geometric<br />
realizations of curvature. The authors have organized<br />
some of the results in the literature which fall into<br />
this genre. The findings of numerous investigations<br />
in this field are reviewed and presented<br />
in a clear form, including the latest developments<br />
and proofs.</p>
</div></div></div></div><span class="vocabulary field field-name-field-review-author field-type-taxonomy-term-reference field-label-inline clearfix"><h2 class="field-label">Author: </h2><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/author/miguel-brozos-v%C3%A1zquez" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">miguel brozos vázquez</a></li><li class="vocabulary-links field-item odd"><a href="/author/peter-b-gilkey" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">peter b gilkey</a></li><li class="vocabulary-links field-item even"><a href="/author/stana-nikcevic" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">stana nikcevic</a></li></ul></span><span class="vocabulary field field-name-field-review-publisher field-type-taxonomy-term-reference field-label-inline clearfix"><h2 class="field-label">Publisher: </h2><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/publisher/imperial-college-press" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">imperial college 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">2012</div></div></div><div class="field field-name-field-review-isbn field-type-text field-label-inline clearfix"><div class="field-label">ISBN: </div><div class="field-items"><div class="field-item even">ISBN-13 978-1-84816-741-4, ISBN-10 1-84816-741-5</div></div></div><span class="vocabulary field field-name-field-review-msc field-type-taxonomy-term-reference field-label-hidden"><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/msc/53-differential-geometry" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">53 Differential geometry</a></li></ul></span><span class="vocabulary field field-name-field-review-msc-full field-type-taxonomy-term-reference field-label-hidden"><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/msc-full/53b20" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">53b20</a></li></ul></span>Mon, 22 Jul 2013 14:58:44 +0000Anonymous45515 at https://euro-math-soc.euhttps://euro-math-soc.eu/review/geometric-realizations-curvature#commentsGeometry of Mobius Transformations: Elliptic, Parabolic and Hyperbolic Actions of SL_2(R)
https://euro-math-soc.eu/review/geometry-mobius-transformations-elliptic-parabolic-and-hyperbolic-actions-sl2r
<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 deep analysis of Möbius transformations from an unusual point of view. The approach is based on the Erlangen programme of Felix Klein, who defined geometry as a study of invariants under a transitive group action. The book focuses on the group $SL_2({\mathbb R})$ and its action by Möbius transformations: $x \mapsto \frac{ax+b}{cx+d}$. This acts on the complex plane, but it also acts on the plane of dual numbers and on the plane of double numbers. Actually, these are the three possible non-isomorphic commutative associative two-dimensional algebras over the real numbers, which are ${\mathbb R}[\sigma]$, with $\sigma^2=-1,0,+1$. The corresponding actions are called elliptic, parabolic and hyperbolic Möbius transformations. The three geometries correspond to the homogeneous spaces with group $SL_2({\mathbb R})$ for the three possible one-dimensional subgroups. </p>
<p>The book studies in depth the geometry associated to the "cycles" in these spaces (circles in the first case, parabolas with horizontal directrix in the second, and equilateral hyperbolas in the third). There is a three dimensional real projective space parametrising such cycles, and a corresponding action of $SL_2({\mathbb R})$ on it. Moreover, there is a naturally defined (indefinite) quadratic form on the space of cycles which serves to recover the initial geometric space, and the usual geometric transformations on it. Then the books moves on to analyse many geometric properties of cycles. This is completed with several aside considerations: the relationship with the physics of Minkowski and Galilean space-time, the more classical point of view of (semi)riemannian geometry, questions on conformal geometry, and more far away subjects like optics or tropical algebra.</p>
<p>The book is accompanied by a DVD with a program which runs under linux (also freely available in internet) which serves the reader to perform computations that appear along the book. This is used often in the book to complete some proofs, which are done by brute force calculation. However, the use of the program requires some knowledge of programming, as the interface is not very user-friendly. This is useful to the reader to complete the arguments and get convinced that the results are true. However, I would have preferred at some points to read a concise and theoretic proof, much more appealing than checking a calculation.</p>
<p>The book is addressed to undergraduate and graduate students in the areas of geometry and algebra. The presentation is basically self-contained. There are many exercises scattered along the book for the interested reader. On the one hand, the point of view is not classical, so a student trying to learn basic properties of Möbius transformations and the relation with complex/Kähler geometry may not get totally satisfied. On the other hand, I think that the author has been successful in transmitting the idea (as he confess in the epilogue that this was his intention) that the three geometries: elliptic, parabolic and hyperbolic deserve to be treated on an equal footing, and that all of them are very rich.</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">Vicente Muñoz</div></div></div><div class="field field-name-field-review-legacy-affiliation field-type-text field-label-inline clearfix"><div class="field-label">Affiliation: </div><div class="field-items"><div class="field-item even">UCM</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 exposition of geometries associated with Möbius transformations of the plane, based on properties of the group $SL_2({\mathbb R})$. The presentation is self-contained, starting from elementary facts in group theory, and unveiling surprising new results about the geometry of circles, parabolas and hyperbolas. The treatment of elliptic, parabolic and hyperbolic Möbius transformations is provided in a uniform way. This is possible due to an appropriate usage of complex, dual and double numbers, which represent all non-isomorphic commutative associative two-dimensional algebras over the real numbers.</p>
</div></div></div></div><span class="vocabulary field field-name-field-review-author field-type-taxonomy-term-reference field-label-inline clearfix"><h2 class="field-label">Author: </h2><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/author/vladimir-v-kisil" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">vladimir v. kisil</a></li></ul></span><span class="vocabulary field field-name-field-review-publisher field-type-taxonomy-term-reference field-label-inline clearfix"><h2 class="field-label">Publisher: </h2><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/publisher/imperial-college-press" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">imperial college 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">2012</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">978-1848168589</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">$78</div></div></div><span class="vocabulary field field-name-field-review-msc field-type-taxonomy-term-reference field-label-hidden"><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/msc/51-geometry" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">51 Geometry</a></li></ul></span>Tue, 26 Feb 2013 21:33:39 +0000Anonymous45493 at https://euro-math-soc.euhttps://euro-math-soc.eu/review/geometry-mobius-transformations-elliptic-parabolic-and-hyperbolic-actions-sl2r#commentsCalculating Catastrophe
https://euro-math-soc.eu/review/calculating-catastrophe
<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>
Let me start by a warning. Just as his earlier <em>The Mathematics of Natural Catastrophes</em> (World Scientific, 1999) which was not a book about `mathematics; this one is not about `calculating' either. This one is a timely update of the predecessor, broadening it and including data of the last decade. The reader will not find the precise models, or computational methods to rigorously simulate or predict catastrophes. There are however a lot of data and many underlying principles are explained.</p>
<p>
The first two chapters form a phenomenal collection of data about all kinds of hazards both natural (extra terrestrial, meteorological, geomorphic, or hydrological) or man-made (political violence, infectious diseases, industrial accidents, or financial crises) that have happened or could happen in the future. Notable (but essential in chaotic systems) are the almost philosophical reflections about whether some event is a cause or a consequence of another one. The problem being posed, the subsequent chapters will point to some possible answers.</p>
<p>
Chapter 3 discusses the different scales and units in which the strength of all these phenomena are measured. Richter's scale for earthquakes is well known, but how to measure e.g. a volcanic eruption, and how far in time and space will cataclysmic effects propagate? That brings us to uncertainty and evidence. Historical and philosophical issues of probability theory and related notions are contemplated in chapter 4. This in turn forms the basis to explain some statistics and stochastic processes (chap. 5). Although precise prediction of the start of a war or a financial crash is very difficult, it is possible to recognize the conditions for instability and indicators for an imminent outbreak (chap. 6). Threats of terrorist attacks follow different mechanisms (chap. 7). The next chapter on forecasting is somewhat more precise on earthquakes, tsunamis, tornadoes and floods. Once a disaster is predicted, one should decide what precautions to take, what scenarios to follow and when and how to inform the public (chap. 8-9). After the event is over, insurance companies have to deal with the consequences. What should they cover? How to calculate the risk? What and how to reinsure? (chap. 10-12). The final chapter deals with long-term planning (global warming, global war).</p>
<p>
As it is stated in the conclusion: the majority of catastrophes will not be controlled by force or science. The only thing one can do is to try and understand the principles. That is exactly what the author has achieved for a very broad audience. Mathematical knowledge from secondary school suffices. After the reader-mathematician has accepted that this is not a book about the mathematics, but a book for a broad audience about facts and principles, he will definitely enjoy the reading. The erudition and literacy of the author are amazing and an intellectual pleasure to read. Besides the names of scientists, you can find a lot of names of artists and citations from their work: from Henry Longfellow and Graham Green to Fyodor Dostoevsky and from Paul Cézanne to Franz Kafka, Samuel Becket and Hokusai. Even phenomena such as Harry Potter and Star Wars are part of the game. Read and enjoy all of that!</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">A. Bultheel</div></div></div><div class="field field-name-field-review-legacy-affiliation field-type-text field-label-inline clearfix"><div class="field-label">Affiliation: </div><div class="field-items"><div class="field-item even">KU Leuven</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 an update of the author's previous book <em>The Mathematics of Natural Catastrophes</em> (1999). It is an abundant source of data of natural and man-made hazards that can occur or have occurred. Rather than giving detailed mathematics it explains the underlying principles to a broad audience.</p>
</div></div></div></div><span class="vocabulary field field-name-field-review-author field-type-taxonomy-term-reference field-label-inline clearfix"><h2 class="field-label">Author: </h2><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/author/gordon-woo" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">gordon woo</a></li></ul></span><span class="vocabulary field field-name-field-review-publisher field-type-taxonomy-term-reference field-label-inline clearfix"><h2 class="field-label">Publisher: </h2><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/publisher/imperial-college-press" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">imperial college 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">2011</div></div></div><div class="field field-name-field-review-isbn field-type-text field-label-inline clearfix"><div class="field-label">ISBN: </div><div class="field-items"><div class="field-item even">978-1-84816-739-1</div></div></div><div class="field field-name-field-review-price field-type-text field-label-inline clearfix"><div class="field-label">Price: </div><div class="field-items"><div class="field-item even">US$29 / £19 (paperback) </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">368</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://www.worldscientific.com/worldscibooks/10.1142/p786" title="Link to web page">http://www.worldscientific.com/worldscibooks/10.1142/p786</a></div></div></div><span class="vocabulary field field-name-field-review-msc field-type-taxonomy-term-reference field-label-hidden"><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/msc/60-probability-theory-and-stochastic-processes" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">60 Probability theory and stochastic processes</a></li></ul></span><span class="vocabulary field field-name-field-review-msc-full field-type-taxonomy-term-reference field-label-hidden"><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/msc-full/60g70" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">60g70</a></li></ul></span><span class="vocabulary field field-name-field-review-msc-other field-type-taxonomy-term-reference field-label-hidden"><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/msc-full/60e99-91f10-91b30-91b74-86a17-86a10" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">60e99, 91f10, 91b30, 91b74, 86a17, 86a10</a></li></ul></span>Tue, 06 Mar 2012 15:27:55 +0000Adhemar Bultheel45447 at https://euro-math-soc.euhttps://euro-math-soc.eu/review/calculating-catastrophe#commentsThe Principles of Newtonian and Quantum Mechanics: The Need for Planck's Constant, h
https://euro-math-soc.eu/review/principles-newtonian-and-quantum-mechanics-need-plancks-constant-h
<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 written for both physicists and mathematicians. The topics treated include Newtonian mechanics, semi-classical mechanics, (non-relativistic) quantum mechanics and its Bohmian interpretation. The main tool in the book is symplectic geometry. A study of symplectic rigidity leads to a semi-classical quantization scheme and to the Maslov index. A use of a general Leray index leads to a definition of a wave form on the phase space. The metaplectic group is a double cover of the symplectic group. A study of its representations is used in a treatment of the Schrödinger equation for a class of Hamiltonians and for a definition of certain Feynman path integrals.</p>
</div></div></div></div><div class="field field-name-field-review-reviewer field-type-text field-label-inline clearfix"><div class="field-label">Reviewer: </div><div class="field-items"><div class="field-item even">vs</div></div></div><span class="vocabulary field field-name-field-review-author field-type-taxonomy-term-reference field-label-inline clearfix"><h2 class="field-label">Author: </h2><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/author/m-de-gosson" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">m. a. de gosson</a></li></ul></span><span class="vocabulary field field-name-field-review-publisher field-type-taxonomy-term-reference field-label-inline clearfix"><h2 class="field-label">Publisher: </h2><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/publisher/imperial-college-press" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">imperial college 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">2001</div></div></div><div class="field field-name-field-review-isbn field-type-text field-label-inline clearfix"><div class="field-label">ISBN: </div><div class="field-items"><div class="field-item even">ISBN 1-86094-274-1</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">£50</div></div></div><span class="vocabulary field field-name-field-review-msc field-type-taxonomy-term-reference field-label-hidden"><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/msc/70-mechanics-particles-and-systems" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">70 Mechanics of particles and systems</a></li></ul></span>Wed, 15 Jun 2011 17:21:23 +0000Anonymous39512 at https://euro-math-soc.euEveryday Probability and Statistics. Health, Elections, Gambling and War
https://euro-math-soc.eu/review/everyday-probability-and-statistics-health-elections-gambling-and-war
<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>Information disseminated by newspapers, radio, television and so on brings a lot of data that we can use as support for our decisions. Since the decisions are made in an environment where uncertainty plays an important role, a scientific approach is also based on probability theory. It is easy to misinterpret given data, which leads to the well-known phrase “lies, damned lies and statistics” (L. H. Courtney). As for me, I prefer another phrase: “It is easy to lie with statistics. It is hard to tell truth without statistics” (A. Dunkels). And the author in the introduction correctly writes: “In the 21st century a cultured man should understand something about statistics otherwise he will be led by the nose by those who know how to manipulate statistics for their own ends”. </p>
<p>The book is a very elementary introduction to probabilistic and statistical thinking. The basic ideas are demonstrated on simple examples from everyday life, e.g. how to bet on a horse. There are also non-intuitive problems like the birthday problem and the problem about switching. As a more practical topic we find an application of probability theory to medicine. The elements of statistics presented in the book concern calculations of the mean and variance and normal and Poisson distributions. The book also contains parts devoted to predicting voting preferences, a sampling technique, some statistical tests and building probabilistic models. The author does not assume that the reader is familiar with mathematics. Because of that, an explanation on how to handle expressions like (22)3 is quite long and, similarly, a description of the definition of the number e is also very detailed. Some places in the book deserve critical remarks. The expectation of the normal distribution is called the mean and denoted by the same symbol as the arithmetical mean – this is confusing (p. 117). I cannot agree with the formulation “Assuming that the lifetimes have a normal distribution ...” (p. 120). The lifetimes are nonnegative and so they cannot have a normal distribution. It would be better to say that a normal distribution can be a good approximation to the unknown and perhaps very complicated true distribution of the lifetimes. The book can be recommended to students who are not specialists in mathematics.</p>
</div></div></div></div><div class="field field-name-field-review-reviewer field-type-text field-label-inline clearfix"><div class="field-label">Reviewer: </div><div class="field-items"><div class="field-item even">ja</div></div></div><span class="vocabulary field field-name-field-review-author field-type-taxonomy-term-reference field-label-inline clearfix"><h2 class="field-label">Author: </h2><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/author/m-m-woolfson" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">m. m. woolfson</a></li></ul></span><span class="vocabulary field field-name-field-review-publisher field-type-taxonomy-term-reference field-label-inline clearfix"><h2 class="field-label">Publisher: </h2><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/publisher/imperial-college-press" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">imperial college 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">2008</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">978-1-84816-031-6 </div></div></div><div class="field field-name-field-review-price field-type-text field-label-inline clearfix"><div class="field-label">Price: </div><div class="field-items"><div class="field-item even">GBP 35</div></div></div><span class="vocabulary field field-name-field-review-msc field-type-taxonomy-term-reference field-label-hidden"><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/msc/62-statistics" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">62 Statistics</a></li></ul></span><span class="vocabulary field field-name-field-review-msc-full field-type-taxonomy-term-reference field-label-hidden"><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/msc-full/62-01" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">62-01</a></li></ul></span>Thu, 19 May 2011 09:34:41 +0000Anonymous39125 at https://euro-math-soc.eu