Book reviews
http://euro-math-soc.eu/book-reviews
Book reviews published on the European Mathematical Society websiteenHow to Write and Publish a Scientific Paper (8th ed.)
http://euro-math-soc.eu/review/how-write-and-publish-scientific-paper-8th-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 book has a long history and was initiated by a seminar given by the second author and a paper he wrote. The response was so positive that it was made into a book that has known several translations and is used as a textbook for courses worldwide. Since the sixth edition Barbara Gastel has joined in and with this new edition, she has become the first author since Robert Day has been emeritus for a while now. The evolution of digital publishing has revolutionized the scientific publishing landscape, which made a new revised edition necessary (the previous one is from 2011). New items are for example the ORCID (that is a unique digital identifier distinguishing an author from any other researcher), the archiving of your (published) paper, warnings against predatory journals, digital poster presentations. There is also a new chapter on editing your own work before publishing, which is somehow a summary of what has already been said in previous chapters.</p>
<p>
Barbara Gastel has a position in biomedical sciences, and Robert Day was teaching English. Their backgrounds clearly show in the focus they have put in the book. Even though there are many general guidelines on how to disseminate your research results, and it certainly introduces inexperienced students to the whole process of publishing a research paper, in my opinion the book is very much oriented towards the habits viable in life sciences and there is an emphasis on writing correct English. I am not familiar with publication culture in social sciences, but as far as mathematics is concerned, one should, after reading this book, consult additionally some books or papers that focus on the peculiarities of publishing mathematics. You may find tens if not hundreds of relevant papers and guidelines available on the Web. Most probably your own institution has one. And then there are of course some of the "classics" listed at the bottom of this review.</p>
<p>
Another issue with this book is that this is mainly written for native English speakers/writers and to some extent even for English speaking American students. This is relevant to understand the humor and word play that is included (there are some old and new cartoons for which language is less relevant). Although there is a section on "writing in English as a foreign language", the emphasis there and in the rest of the book is to use correct English sentences and grammar. In fact a lot of attention goes to grammatical issues and common errors. This of course is important in writing in general, hence also in scientific writing</p>
<p>
Another repeated pattern that is used throughout the book is the IMRAD (Introduction, Methods, Results, and Discussion) structure in all writings or presentation, whether it is a paper, a thesis, a seminar, a report, or whatever. To some extent this also applies to mathematical papers, but not as strictly as it is in life sciences. This format is much more suited for empirical papers, and in some journals publishing experimental results, especially in chemistry or biomedical journals, these five words are actually used as section titles. The results section is the main thing and many of the technicalities or formulas are sometimes banned from the paper and are added as "additional material" provided elsewhere. This is not exactly how a mathematical paper should be composed.</p>
<p>
So in this book, guidelines on how to write your paper are following the IMRAD paradigm. After discussing the title, the list of authors, their addresses and e-mails, the I, M (here referring to Methods and Materials), R, and D sections are discussed separately, and the paper is finished with appropriate acknowledgements and references. The intended readership is obviously the community of students who did bot publish before, so the whole process is explained including the selection of a journal, submitting your paper, the refereeing, and how to react to it, and finally the post-refereeing stage of proofreading and publishing. Clearly, besides all the recommendations given, most journals have specific guidelines for authors that should be consulted. This is repeatedly stressed in the book as well. But the book is covering a very broad publishing culture, by discussing also review papers, and letters to the editors, or writing for a general public, composing a conference abstract or report, or how to prepare a poster or an oral presentation, or write a thesis or a project proposal. Once you became an established author you probably are already familiar with how to write a peer review, but there is still some advice given here. Also how to write a book review, give an interview, or write a book proposal. And for the really ambitious, how to become a science communicator.</p>
<p>
So there are many general guidelines on writing. Certainly the part on writing correct English is extensive but not exactly connected to science writing. There are no particular guidelines for writing mathematical papers. The only place where mathematics is explicitly mentioned is when it is discussed in what order the authors should be listed. It is said that sometimes the order is alphabetical "like for example in mathematics". It is almost standard that mathematical papers are written in LaTeX and somewhat less generally accepted that references are managed with BibTeX. These tools are not even mentioned. The role of arXiv, Zentralblatt, and MathSciNet and the Mathematical Subject Classification (MSC) are not discussed. Neither do they mention the UDC classification. But the book is not only about writing or communication in a strict sense, there is also a discussion about ethics, plagiarism but the pitfalls of self-plagiarism are not highlighted. In this respect, I cannot resist to mention this tendency to multiply the number of papers using a process that is somewhat stimulated by this IMRAD structure: just modify the method or the materials and repeat what has been done already in other papers, and in this way you can produce many carbon copies of just one skeleton paper. Such an objectionable publication policy is less common in mathematics, but it can be a problem for numerical computing papers where a slight variation in the method or the equation to which it is applied can duplicate existing papers. This is of course the consequence of the equally disputable policy of evaluating researchers by counting their papers. In this perspective, it is also remarkable that the book does not discuss impact factors. There is only a distinction between "primary" and "secondary" publications. The impact factors for biomedical journals are so much larger than for mathematical journals that this may be a lesser issue there. Anyway, impact factors reduce mathematics to a negligible section in the science publishing landscape. The authors restrict themselves to give as many generally applicable practical guidelines as possible, but they rightfully avoid points that may raise some controversy since such discussion need not be included in an (under)graduate course. Another recent issue that is not discussed is the data life cycle management (DLM) which should ensure that data, results, software, etc. are still available in the long run. An issue of quickly rising importance in a digital age of fake news.</p>
<p>
The book ends with several appendices. The first appendix is a list of abbreviations for words used in journal titles. "Math." is there, but "Comput." for "computer" or "computational" is not. For the benefit of mathematical students I should mention here the useful AMS <a href="http://www.mathontheweb.org/mathweb/annser_f/annser_frames.html">list of journals and abbreviations</a>. The second appendix is a list of jargon words to be avoided with a preferred alternative. That is certainly useful, also for mathematics. Next are lists of magnitudes (from atto to exa) and of many helpful websites, a glossary of terms used in the book, and a and extensive list of references (but the ones below are not in the list), and finally a subject index.</p>
<p>
Conclusion: there are a lot of general guidelines for undergraduates who never published a paper before to learn about the process. Especially the guidelines for using correct English are quite useful. For mathematics one may want to read some extra, more specific, guidelines. Of course, as is also mentioned in this book, much can be learned by consulting (good) examples and by imitation.</p>
<h3>
<strong>Some references relevant for mathematical writing</strong></h3>
<ul><li>
N. Steenrod, P. Halmos, M. Schiffer, J. Dieudonné <em>How to Write Mathematics</em> l'Enseignement Mathématique, vol. 16, 1970 and <a href="http://bookstore.ams.org/hwm">AMS booklet</a> 1973<br />
in particular P. Halmos' paper of about 30 pages is still recommended.</li>
<li>
S. Krantz, <a href="https://arxiv.org/abs/1612.04888"><em>A Primer on Mathematical Writing</em></a>. AMS, 1996.</li>
<li>
S. Krantz. <a href="http://bookstore.ams.org/matpub/"><em>Mathematical Publishing, A Guidebook</em></a>. AMS, 2005.</li>
<li>
S. Krantz. <a href="http://www.ams.org/notices/200711/tx071101507p.pdf" target="_blank">How to write your first paper</a>. Notices of the AMS, vol. 54, no. 11, 2007.</li>
<li>
N. Higham. <a href="http://epubs.siam.org/doi/book/10.1137/1.9780898719550"><em>Handbook of Writing for the Mathematical Sciences</em></a>. SIAM, 1998.</li>
<li>
T. Tao. <a href="https://terrytao.wordpress.com/advice-on-writing-papers/" target="_blank">On Writing</a>. blog, retrieved October 10, 2017. </li>
</ul></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 textbook giving practical guidelines for preparing a paper or for general scientific communication. The new edition pays attention to recent issues such as ORCID, archiving, digital presentation, electronic submission, etc. The focus is on communication in biomedical science, and less on mathematical reporting.</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/barbara-gastel" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">Barbara Gastel</a></li>
<li class="field-item odd"><a href="/author/robert-day" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">Robert A. Day</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/cambridge-university-press" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">cambridge 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">2017</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">9781316640432 (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">£ 24.99 (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">344</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.amazon.co.uk/How-Write-Publish-Scientific-Paper/dp/1316640434" title="Link to web page">https://www.amazon.co.uk/How-Write-Publish-Scientific-Paper/dp/1316640434</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/97-mathematics-education" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">97 Mathematics education</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/97-01" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">97-01</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/97b20" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">97B20</a></li>
</ul>
</span>
Fri, 13 Oct 2017 11:29:07 +0000adhemar47933 at http://euro-math-soc.euThe Mathematics of Various Entertaining Subjects volume 2
http://euro-math-soc.eu/review/mathematics-various-entertaining-subjects-volume-2
<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>
Recreational mathematics, puzzles and games have by now a long tradition and there are many books, papers, and columns devoted to these topics. Many love the challenges of the puzzles and games and solving the problem is rewarded with a dopamine rush when a solution is finally reached. They love it as a pastime or a hobby. However, solving the problem in a systematic way may require some more serious mathematical research. With the increasing popularity of recreational mathematics new mathematical challenges emerged which transcended the recreational aspect. In fact, historically speaking, some well established branches of mathematics like for example probability theory and graph theory, grew out of trying to solve a recreational problem. Another example mentioned by the editors in their foreword is the development of a theory for combinatorial games which have led Elwyn Berlekamp, John Conway and Richard Guy to compiling their multivolume work <em>Winning Ways for Your Mathematical Plays</em>.</p>
<p>
In 2013 the first MOVES (<em>Mathematics Of Various Entertaining Subjects</em>) conference was organized, which was the start of a series of biennial meetings with an increasing number of participants. This is volume two, a sequel to the book with the same title. The first book can be considered as a kind of proceedings for the 2013 MOVES conference and the present one collects nineteen research papers most of which were presented at the 2015 conference. Berlekamp, Conway and Guy were all three participating as invited speakers then. The difference with the usual books collecting papers about this subject is that here the authors have included the "serious mathematics" behind the recreational aspect. The contributions are organized in five different parts: (1) Puzzles and brain teasers, (2) Geometry and topology, (3) Graph theory, (4) Games of chance, and (5) Computational complexity. Those familiar with recreational mathematics will recognize that most of the problems they know will fall under one (or more) of these headings. One may miss logic as a popular subject, but that falls under the first category. Among the contributors are some well known names:. R. Guy, J. Rosenhouse, P. Stockmeyer, E. and M. Demaine, J. Conway, N. Elkies, and many others.</p>
<p>
In order to give an idea of the type of contributions, let me discuss some examples. I will pick one from each of the five parts. In the part about Puzzles and brain teasers, Tanya Khovanova wrote about <em>Dragons and kasha</em>. The setting is as follows: On each face of a cube sits a four armed dragon with a bowl of kasha. Each minute they grab one fourth of the kasha from the bowls of their four neighbours. Given an initial distribution of kasha in the six bowls, what is the asymptotic distribution? The problem is not difficult to solve and the result is that each dragon will end up with the same amount of kasha, whatever the initial distribution. The nice thing about the paper is that it relates the solution to Markov chains, random walks, eigenvalue problems, but the real purpose is by defining a "stealing operator" and replacing kasha by complex numbers, this can be linked to intertwining operators, group actions, and group representations. The added value of this paper is that such abstract concepts are introduced in an easily accessible and playful way. This is an example of a paper that is playful and does not require much mathematical skills from the reader.</p>
<p>
Jill Bigley Dunham and Gwyneth R. Whieldon have a paper in the Geometry and topology part on counting the solutions to a paper cutting and folding problem proposed by Martin Gardner. Given is a square piece of paper subdivided by a regular 3 x 3 gird. It is black on one side and white on the other. Cutting and folding is allowed only along grid lines, and the cutting should not result in disjoint pieces. The challenge is by cutting and folding to wrap this around a 1 x 1 cube showing black faces on all sides. The problem is not so difficult to solve, but many much more complicated variants can be imagined. The way in which the nine grid squares are connected can be represented by a graph: each 1 x 1 square is a vertex and vertices are connected by an edge when the squares are connected. A cut between two neighbouring grid squares corresponds to removing an edge in the graph. Cutting and folding structures and wrapping sequences can be enumerated and programmed. Because the number of possibilities, given the constraints, is not too large, all possibilities can be checked. By this enumeration, a theorem can be proved: A wrapping solution exists for a cutting pattern if and only if there exists a non-self-intersecting sequence of four moves to adjacent squares starting at the centre square. Some patterns allowed several wrappings, some of them are mono-coloured other mix black and white. Thus a complete enumeration of all possible solutions and a list of cutting patterns that do not allow any solution can be listed by a computer program.</p>
<p>
More graph theory in the paper by Dominic Lanphier from the part on Graphs. Suppose you are attending a sequential duel, which means that duelist 1 aims at duelist 2 and fires. If he misses (with probability 1 − <em>p</em>, then number 2 fires at number 1 and hits with probability <em>q</em>. If he misses, the first duelist fires again etc. The problem is to find out which one has the most chance to survive. The problem can be made more complicate if more than two shooters fire at each other in some order, which could be cyclic or not. What if after one has been shot, the survivors have to continue until there is only one survivor. If you are one of the shooters in a large pool, you better learn the necessary statistics, generating functions and asymptotics discussed in this paper to maximize your chance to survive. It requires some more mathematics and computations than the two previous examples, but it is still very accessible for anyone who would need it. More advanced mathematics is needed for the paper by Noam Elkies from the same part in which the number of crossings in a complete graph is computed. If in a planar graph every vertex is connected to every other vertex, the edges will necessarily cross a minimal number of times. Counting these crossings in not so difficult when it concerns plane graphs, but it is less trivial if these graphs live on another topology like a sphere, a toroid, a projective plane, a Moebius strip,...</p>
<p>
When in part four chance and probability become an essential element in the game, then dice naturally come to the foreground. They literally do in the first contribution of this part authored by Robert Bosch, Robert Fathauer and Henry Segerman. If it is true that for fair dice every face has an equal chance to land on top, then we could number faces in any configuration. In practice however they are always numerically balanced, that is they always have opposite faces numbered (1,6), (2,5) and (3,4). In the paper this phenomenon is investigated for the 20-sided (icosahedral) dice where opposite sides sum to 21. Each of the 12 vertices is common to five triangular faces. Optimal numerical balancing could consider not only the opposite sides, but also the vertex sum (the sum of the 5 adjacent faces), or the face sum (the sum of the 3 adjacent faces) with or without including the number on the face itself, or the sum of the equatorial bands (the sum of the 10 faces on the equator if two opposite vertices are selected as north and south pole). Solving such problems requires integer constrained programming to find a solution and is related to magic squares. Generalisations from d20 to d30 and d120 dice are also considered.</p>
<p>
In the computational complexity part, we find a relatively long paper by Aviv Adler, Erik Demaine and others who give a proof of the fact that Clickomania is a hard problem even if there are only two colours and two columns. The game is a popular computer game that starts with a rectangular grid tiled with coloured squares. With one click you can remove a connected structure of tiles with the same colour. The empty space is filled with tiles higher up in the same column. Isolated singletons can not be removed and empty columns collapse so that their left and right neighbours join. Either the target is to remove all tiles or to get the highest possible score. Each click adds to your score which is about the square of the number of tiles you remove in that click. The theorem says that if the target is to remove all tiles, then this is an NP-complete problem, unless we have the trivial situation of only one column and one colour. The score variant is NP-complete if there is more than one column and more than one colour, and trivial (and hence in complexity class P) if there is only one colour. Proving this theorem requires first of all a speed course in complexity theory to define the terminology and the process of reduction has to be explained, that is how a problem, known to be NP-complete, can be transformed (in polynomial time) into another one, in order to conclude that the latter will be NP-complete too. Given all this basic material, then the proof itself is far from trivial. And if the problem is indeed NP-complete, then one still wants to find a good approximation. Such approximations and variants are also discussed and, for the ambitious reader, there are still many open problems left to be solved.</p>
<p>
It should be clear from this selection that the papers cover not only a very diverse set of problems, but also that they are not always at the same level of complication. Nevertheless all authors have attempted to reach a general public with a certain mathematical training. We could conclude that this is a book on recreational mathematics for the mathematician. This does indeed reflect the audience that attended the MOVES conference in 2015. I suppose these participants will be interested in a copy of this book but even more so those who could not be there but would have loved to. They can still get an idea of what kind of problems were discussed.</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 number two in what is probably going to be a series of a sort of proceedings of the biennial MOVES conferences (Mathematics of Various Entertaining Subjects) organized at the MoMath museum in New York. The first book was a selection of papers of the 2013 conference, the current one of the 2015 conference. The papers do not only present the games and puzzles and their fun-aspect, but they connect them to "real mathematics". One could characterize them as books on recreational mathematics for mathematicians. </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/jennifer-beineke" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">Jennifer Beineke</a></li>
<li class="field-item odd"><a href="/author/jason-rosenhouse" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">Jason Rosenhouse</a></li>
<li class="field-item even"><a href="/author/eds-1" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">(eds.)</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">2017</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">9780691171920 (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"> £ 70.95 (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">408</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/11171.html" title="Link to web page">https://press.princeton.edu/titles/11171.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/control-theory-and-optimization" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">Control Theory and Optimization</a></li>
<li class="field-item odd"><a href="/imu/geometry" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">Geometry</a></li>
<li class="field-item even"><a href="/imu/mathematical-aspects-computer-science" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">Mathematical Aspects of Computer Science</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>
<li class="field-item even"><a href="/imu/topology" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">Topology</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/00a08" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">00a08</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/05a99" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">05A99</a></li>
<li class="field-item odd"><a href="/msc-full/05c99" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">05C99</a></li>
<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/03d15" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">03D15</a></li>
<li class="field-item even"><a href="/msc-full/51-01" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">51-01</a></li>
<li class="field-item odd"><a href="/msc-full/91-01" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">91-01</a></li>
<li class="field-item even"><a href="/msc-full/97a20" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">97A20</a></li>
</ul>
</span>
Fri, 13 Oct 2017 11:06:35 +0000adhemar47932 at http://euro-math-soc.euThe Great Formal Machinery Works
http://euro-math-soc.eu/review/great-formal-machinery-works
<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>
People identify computers sometimes with their technology: chips ever decreasing in size up to the level of nanostructures, but computer science is so much more about the software that runs on this technology. Since the early digital computers emerged around the middle of the twentieth century, computer science has grown into a mature science requiring rigorous and rather abstract approaches to solve highly challenging problems in for example computer graphics, computational complexity, formal languages, artificial intelligence, program verification, cyber security, and many more. Maturity shows when a theoretical level exists above a more experimental approach. In many of the applications just mentioned, one will recognize in their scientific analysis the same deductive formalism that also mathematicians are used to. In these aspects it can certainly be considered as a branch of (applied) mathematics. On top of the current state of affairs, it is almost certain that Von Neumann, Turing and other founders of the early computer age, would not have developed their fundamental ideas if the time had not been ripe for it. The way scientists were thinking about the foundations of mathematics and logic and their use of formalism in deducing their conclusions were essential elements that triggered mathematicians and engineers to become the computer pioneers who made it all happen.</p>
<p>
Indeed, computers do not think, but need a strict formalism to describe the algorithms that will allow to design compilers, to extract information from big data, to search the web, to render computer animated movies and many more. So the title of the books is most appropriate: The great formal machine works because of the preparatory work on the theories of deduction, logic and the foundation of mathematics as they were at the start of the digital age. In this book the philosopher von Plato sketches in some detail how the concept of a formal proof emerged after a long history of evolution and of competing opinions. The transition from the deductive logic and the syllogistic proofs of Aristotle's time to the logicism of Frege and Russell and the subsequent natural deduction came not overnight but has followed a meandering path, sometimes with great ideological controversies.</p>
<p>
After introducing the Aristotlian model, the book immeditely jumps to the nineteenth century. Two events then started to revolutionize the proof techniques from Greek antiquity that had dominated mathematics for centuries. One is the discovery of non-Euclidean geometry (E. Beltrami, 1868), and the other is the algebraic technique used to formalize calculus and the definition of the natural numbers (H. Grassmann, 1861). Grassmann gave a recursive definition of the natural numbers which later led to the Peano axioms (1889). Still later Dedekind added the real numbers to the system. Hilbert was the one to support and push an axiomatic geometry to the frontline. With the formalization of mathematics also the formalization of the logic deduction came along. Boole algebra (1847) reduced the description of complex circuitry to simple algebraic computations which actually corresponds to the valuation calculus of a logic propositional system. E. Schröder (1890) used an order relation and this was picked up by T. Skolem who brought a lattice theory to logic. But the true father of formal logic is Gottlob Frege. Von Plato makes it very clear that no exegesis of Frege's work can be taken seriously if it does not recognize that his greatest contribution is the inference to generality (he essentially introduced quantifiers) although it was only properly recognized by B. Russell in the <em>Principia Mathematica</em> (1910). Russell's paradox on the other hand revealed the inconsistency of Frege's foundational system of mathematics. The <em>Principia</em> are of course a summit of logic formalism and a direct consequence of the work of Frege, adding the quantifiers to Peano's logic.</p>
<p>
Following Kronecker, Skolem was the 20th century promoter of finitism: something only exist if it can be decided in a finite number of steps. In this spirit, Skolem rejected the use of quantifiers and introduced recursion instead. Intuitionism was introduced in mathematics and logic by Brouwer and his student Heyting in Holland. But David Hilbert in Göttingen was a leading mathematical figure with many followers in his slipstream. Göttingen had a research tradition on foundations in mathematics and logic and Hilbert was strongly opposed to Brouwer's ideas of constructivism. The German approach was explained in several books by Hilbert and Ackermann and Hilbert and Bernays, of which von Plato gives a thorough discussion, even more so as what he did in previous chapters with other publications that were important for the swings of the historical flow. Similarly he also discusses the work of Gödel who, besides several other things proved the completeness of predicate logic and of course his famous incompleteness theorems (1930-31). This of course had a tremendous impact on the community at the time. In the remaining chapters von Plato discusses the work of Gentzen who introduced a system of natural deduction. His sequent calculus formed the basis of current proof analysis and proof search. Both of these contributions by Gentzen are again explained in detail by von Plato. A final chapter is an in depth discussion of an intuitionistic consistency proof of classical arithmetic as it was originally conceived by Gentzen (1934).</p>
<p>
In this review, I have spent quite a few lines on the historical events that have led to the eventual work of Gödel. I do not want to leave here the wrong impression that this is the main part of this book. On the contrary, von Plato starts with the ideas of Hilbert and his co-workers when the book is about half way. It is clear that with this book, which is based on notes for his lectures, he wants to push the students towards a study of primary sources. He discusses them in depth, lifting those elements that are important for this historical line of thoughts with references to pages, paragraphs and formulas. He also uses the formal notation that is used there, rather than translating everything to a uniform modern standard notation. Thus readers should have a strong interest and preferably an certain education in formal logic and/or the foundations of mathematics and maybe some philosophical interest as well. I am not aware of any publication that covers this particular subject in any depth as it is developed here. The book definitely fills a gap. Even though this book is based on mostly primary sources, it is still quite readable, not letting the quotations dominate and obscure the historical trail that has led to the eventual consistency proof in the last chapter. On the other hand, it is a research text, focussing on the foundations of mathematics and logic. The sources used are historic, but it is not just a history book either. We are not informed about biographical data of the mathematicians or the unfortunate fate of mathematics in Göttingen during the Nazi regime. The fact that Gentzen collaborated is utterly irrelevant for his scientific achievements. So you probably will not want to read this if you are looking for an easy reading text such as a popular history or science book. I should also warn computer scientists that this is about foundations that have led to computer science and that are still relevant in some of the more abstract branches of theoretical computer science, but it is not about computer science in an engineering or applied sense. There is no cryptography, computer graphics, networks, etc. and not even the P vs NP problem. Turing, for example, is present but only as a bit player while others take the main stage,</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 foundations of mathematics, formalism in logic, and proof theory were essential for the start of the information age and computer science. In this book von Plato sketches how the old Aristotlian ideas were revolutionized starting in the nineteenth century by an advancing algebraic formalism in logic and by rattling the axioms of Euclidean geometry. From the historical rapids that followed till around the 1940's, the names of Peano, Frege, Russell, Hilbert, Gödel, and others are the ones that are still resounding in any book reflecting on foundations of mathematics and logic. Their work and the historical link connecting them is discussed with care and insight by von Plato.</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/jan-von-plato" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">Jan von Plato</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">2017</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">9780691174174</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 35.00</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">400</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://press.princeton.edu/titles/10979.html" title="Link to web page">http://press.princeton.edu/titles/10979.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-aspects-computer-science" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">Mathematical Aspects of Computer Science</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/68-computer-science" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">68 Computer science</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/68-03" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">68-03</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/03-03" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">03-03</a></li>
<li class="field-item odd"><a href="/msc-full/03b70" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">03B70</a></li>
</ul>
</span>
Wed, 20 Sep 2017 12:13:18 +0000adhemar47871 at http://euro-math-soc.euWetting of Real Surfaces
http://euro-math-soc.eu/review/wetting-real-surfaces
<div class="field field-name-field-review-review field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><div class="tex2jax"><p>Something as apparently simple as the shape of the water droplets on the wall after a shower may hide intriguing mathematical questions. In this book, the author provides a comprehensive exposition of the problems concerning the shape and dynamics of liquid droplets on surfaces as well as some of the applications that these issues entail.<br />
The work is organized into nine chapters. They begin with the fundamentals of the Physics of liquid-air liquid-solid interfaces (surface and line tensions, free energy…). Then the problem of droplets on atomically flat, chemically homogeneous, isotropic, insoluble, nonreactive and non-deformed solid surfaces is tackled. This idealistic situation is useful for the contents of the following chapters, where more realistic surfaces are introduced: rough, heterogeneous or non-flat surfaces. This explain the title of the book. At the end of each chapter, the reader will appreciate the so-called bullets: a collection of short paragraphs giving the key points of that chapter.<br />
The main mathematical machinery used by the author is Variational Calculus. Since the shape of droplets minimizes the free energy, some of the classical tools are applied, mainly for the determination of the liquid-solid contact angle. From this, hydrophilic, hydrophobic and other situations are analyzed.<br />
Although the book does not contain sophisticated Mathematics, and taking into account that the book is intended to MSc or PhD students in Physics, Chemical Engineering or Material Sciences, a mathematician may still enjoy and take advantage of this work, specially if he/she is interested in modelization of interface phenomena.</p>
</div></div></div></div><div class="field field-name-field-review-reviewer field-type-text field-label-inline clearfix"><div class="field-label">Reviewer: </div><div class="field-items"><div class="field-item even">Marco Castrillon Lopez</div></div></div><div class="field field-name-field-review-desc field-type-text-long field-label-hidden"><div class="field-items"><div class="field-item even"><div class="tex2jax"><p>In this book, a panoramic study of the shape of liquid droplets on surfaces is given. Starting from an idealistic surface, the chapters explores the case where more realistic situations are introduced.</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/edward-yu-bormashenko" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">Edward Yu. Bormashenko</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/walter-de-gruyter-berlin-boston" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">Walter de Gruyter Berlin-Boston.</a></li>
</ul>
</span>
<div class="field field-name-field-review-pub field-type-number-integer field-label-inline clearfix"><div class="field-label">Published: </div><div class="field-items"><div class="field-item even">2013</div></div></div><div class="field field-name-field-review-isbn field-type-text field-label-inline clearfix"><div class="field-label">ISBN: </div><div class="field-items"><div class="field-item even">978-3-11-025853-0</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">170</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-science-and-technology" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">Mathematics in Science and Technology</a></li>
</ul>
</span>
Wed, 13 Sep 2017 17:14:27 +0000mcastri47860 at http://euro-math-soc.euAn Informal Introduction to stochastic Calculus with Applications
http://euro-math-soc.eu/review/informal-introduction-stochastic-calculus-applications
<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 spectacular development of Stochastic Calculus in the last decades has not been accompanied by an increasing presence in Science courses. As a consequence, many scientists, engineerings and economists, even with a good mathematical background, oftem find themselves in the situation where they have to learn the foundations of this discipline from the very beginning, sometimes struggling with a not very helpful literature. The book under review can be an excellent source for these people. This does not mean that the book cannot be used as a course manual. It is indeed an excellent manual. But the spirit seems to be close to people already possessing a mathematical maturity on which one can build with rigour the basic ideas on Stochastic Calculus and its Applications. From this point of view, senior undergraduate students or graduate students can also benefit from this book.<br />
The book is organized in eleven chapters: starting from the fundamentals of Probability and random variables, going to the definition and main properties of Stochastic Processes, providing the definition and properties of Ito integral and Stochastic Differential Equations, and giving, at the end, a rich collection of applications. Every chapter includes many examples and exercices that are very useful to put in practise, step by astep, the ideas, notions and properties that are introduced. The final chapter provides solutions and hints to all these exercices. A good bibliography is provided at the end for those who want to go deeper.<br />
The point of view is clear and rigurous, but avoiding unnecessary machinery. This probably justifies the title of the work. The result is a good reference book that is completely recommendable to anyone who want to enter Stochastic Calculus with the idea of really understanding the foundations.</p>
</div></div></div></div><div class="field field-name-field-review-reviewer field-type-text field-label-inline clearfix"><div class="field-label">Reviewer: </div><div class="field-items"><div class="field-item even">Marco Castrillon Lopez</div></div></div><div class="field field-name-field-review-desc field-type-text-long field-label-hidden"><div class="field-items"><div class="field-item even"><div class="tex2jax"><p>The goal of this book is to introduce elmentary Stocgastic Calculus to readers with some Mathematical backgroud .</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/ovidiu-calin" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">Ovidiu Calin</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/world-scientific-publishing-co-pte-ltd" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">World Scientific Publishing Co. Pte. Ltd.</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">978-9814678933</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">315</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/probability-and-statistics" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">Probability and Statistics</a></li>
<li class="field-item odd"><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>
Fri, 18 Aug 2017 17:49:45 +0000mcastri47818 at http://euro-math-soc.euPython for Scientists (2nd edition)
http://euro-math-soc.eu/review/python-scientists-2nd-edition
<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>
Python is a young flexible scripting language of growing popularity for scientific computing. As the language is still evolving, also the books introducing the language do evolve along. John M. Stewart retired as a member of the Relativity and Gravitation group from the Department of Applied Mathematics and Theoretical Physics at the University of Cambridge in 2010. After his retirement he started working on his book introducing <em>Python for Scientists</em> of which the first edition appeared in 2014 which was reviewed <a href="/review/python-scientists" target="_blank">here</a> earlier. He passed away shortly after he finished this revised second edition.</p>
<p>
Since the first edition has been reviewed in some detail, it suffices here to discuss the differences. The basic structure and concept is retained, except for a new extra chapter 7 in which the new native Python computer algebra system (CAS) <em>SymPy</em> is discussed. <em>Maple</em> and <em>Mathematica</em> are the most widespread such systems. The <em>SymPy</em> library has similar possibilities like combinatorics, calculus, linear algebra, orthogonal polynomials and special functions, and solving differential equations. Although it is still developing and expanding, it is already a viable alternative for the topics mentioned. Combined with the plotting possibilities, and the graphical interface this is an important instrument for educational as well as for research purposes.</p>
<p>
For the rest the text is mainly the same as it was in the first edition. The chapter about plotting is slightly extended. Where it had before 2D and 3D plotting sections, now the 3D discussion is extended and discusses multidimensional plotting. Another novelty is that the users interface to Python was a command-line driven <em>IPython</em> which used basically a text terminal with pop-up graphics, it has now the possibility to handle notebooks which, like Maple and Mathematica notebooks, use a graphical browser to interact and which allows to mix the maple commands with text that can be introduced with section headers and a LaTeX kind of typesetting for the formulas. Instead of text oriented version of <em>IPython</em>, one has to open the IPython notebook with another tool called <em>Jupyter</em>. This does not influence the code snippets of the previous edition, but it is a much nicer users interface. Most of the snippets that are given in this book are now made available online in the form of an elementary notebook in <a href="http://www.ctc.cam.ac.uk/news/code.txt" target="_blank">txt</a> format or as a <a href="http://www.ctc.cam.ac.uk/news/code.pdf" target="_blank">pdf</a> file.</p>
<p>
In other words, this second edition is just a logical evolution, following the evolution of Python, while retaining its original concept and quality, Requiring only an increase from 220 to 257 pages, I still think the conciseness of the book is a major asset. It provides just enough to get you started with the language if you are already familiar with some computer programming or with a system like Maple or Mathematica. You might consider switching to Python to use it in either your design of scientific software, or, now with the nice notebook flexibility available, you might want to use it as a tool in teaching calculus or numerical analysis. It allows to generate on online interactive version of your course.</p>
<p>
The dynamism in the evolution and the succession of Python releases is a blessing and a curse. A blessing because with every release, the possibilities and the quality does increase, but also a curse because there is no standard for the language yet, and therefore it is not guaranteed that what works in some release will still work in the next one. As a consequence, one usually has to install different versions. This is done in a protected environment (basically confining a Python version to a directory) generated by a command <em>virtualenv env</em>. The necessary libraries are then installed there using the proper version dependency. This is achieved by using some command like for example <em>pip install jupyter</em> to install the <em>Jupyter</em> module. Stewart gives some explanation about the installation of Python, but that is rather minimal. There is nothing about virtual environments and pip install's. Also installing some packages on a computer where you do not have admin permission, can be problematic. Fortunately Python, its environment and all its satellite modules are well documented on the internet, and it is all open software. So you might need some external help to get started, but once you have an operational Python system, this book is still and excellent starting point to put you on the tracks to master the language and enjoy the marvels of the latest version of Python.</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 the second edition of the book for which the first edition was reviewed <a href="/review/python-scientists">here</a>, three years ago. The text has been rewritten to better reflect the <em>IPython</em> notebook style with graphical interface using <em>Jupyter</em> and a new chapter is added about <em>SymPy</em> (a library for symbolic mathematics). The number of code snippets has also been increased and most of them are now available online in an elementary 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/john-m-stewart" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">John M. Stewart</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/cambridge-university-press" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">cambridge 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">2017</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">9781108120241 (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"> € 29.99 (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">271</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.cambridge.org/be/academic/subjects/mathematics/computational-science/python-scientists-2nd-edition" title="Link to web page">http://www.cambridge.org/be/academic/subjects/mathematics/computational-science/python-scientists-2nd-edition</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-science-and-technology" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">Mathematics in Science and Technology</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/68-computer-science" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">68 Computer science</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/68n15" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">68N15</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/68-04" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">68-04</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/97n80" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">97N80</a></li>
<li class="field-item odd"><a href="/msc-full/97u70" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">97U70</a></li>
</ul>
</span>
Fri, 11 Aug 2017 09:31:22 +0000adhemar47806 at http://euro-math-soc.euSignificant Figures
http://euro-math-soc.eu/review/significant-figures
<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>
Ian Stewart has found yet another way to bring mathematics to a broad public. After over 40 books in his well known entertaining style, he is now writing a selective history of mathematics, not using the numbers or the mathematics as the main players, but this time it are the mathematicians of all ages that are the significant figures in this case.</p>
<p>
He has selected 25 mathematicians starting with Archimedes and ending with William Thurston. The thread connecting both consist of an impressive list of names all of them identifying famous mathematicians. Since most popular books on the history of mathematics are European-centered, perhaps the first names following Archimedes are a bit less familiar. The jump is usually made from the Greek whose work came to us in the form of Arab translations to Fibonacci. The latter also popularized the positional number system brought to us by work of al-Khwarizmi. This Fibonacci is just a stepping stone to bring us to the Renaissance with Italian, French, and German mathematicians whose more familiar names are echoing in the formulas and theorems that are still in use today.</p>
<p>
However, what the Arabs brought was not only the Greek tradition. They also inherited from Chinese and Indian mathematical culture. Hence Stewart rightfully introduces two exponents of these cultures too. Liu Hui (3rd century) was one of the most important Chinese mathematicians of his time. The Chinese also had geometry, including the Pythagorean Theorem and they knew a rather accurate approximation of <em>π</em>. Al-Khwarizmi lived around 780-850 and his <em>al-jabr</em> is the origin of our name for algebra. Even though that stands nowadays mainly for symbolic manipulation of mathematical quantities, the al-jabr was verbal and arguments were mostly geometric. India is represented by Madhava of Sangamagrama (1350-1425). He is the founder of the Kerala school, in the South-West of India. They had trigonometry and infinite series. Kerala was a common stopping place for long distance navigation. There is no evidence though that their mathematical ideas were directly brought to Europe by sea travelling traders. In any case, they had results that were only discovered by European mathematicians much later.</p>
<p>
The early mathematics of the East and their influence on European mathematics were exposed only recently by the books of George Gheverghese Joseph, in particular <em>The Crest of the Peacock</em> (2010). Of course the names discussed in Stewart's book are just representing a whole culture and he does not restrict to just these particular men, but also comments on their background, some of their contemporaries, and their heritage. The same holds for the other "figures" in the chain connecting Archimedes and Thurston. The account given for each of them is forced to be fragmentary. With an average of about 10 pages for each, not much room is given for an extensive biography and a discussion of their mathematical contribution. So we get some executive summary for Cardano, Fermat, Newton, Euler, Fourier, Gauss, Lobachevsky, Galois, Ada Lovelace, Boole, Riemann, Cantor, Sofia Kovalevskaia, Poincaré, Hilbert, Emmy Noether, Ramanujan, Gödel, Turing, Mandelbrot, and ending with Thurston.</p>
<p>
This list of names is disputable of course. Every selection is subject to controversy. And what is told about each of them is again just a selection, because there exist much more extensive biographies for each of them. Stewart lists them at the end of the book as references for further reading. The mathematician is situated, sometimes introduced with a short sketch (Gauss deciding to choose for mathematics instead of languages after detecting how to divide a circle in 17 equal pieces with ruler and compass, the newspaper announcing the death of Galois after a duel, Hardy receiving his first letter from Ramanujan,...), followed by a short biographic summary, and some discussion of his or her work. In some cases, for the more prolific specimen, discussing only some particular element of it.</p>
<p>
There is a lot of folklore floating around about historical facts. Stewart is very good in busting several of these myths. In this respect he discusses the motive and the opponent in Galois' duel about which there is some controversy. He unravels the dispute about the priority of discovering and the disclosure of the formula for solving the cubic equation between Cardano and Niclolo Fontana (known as Tartaglia, the stammerer). There is also the story about the taxicab number. Hardy claimed that 1729, the number of his taxi, was boring and thus a bad omen. But Ramanujan immediately recognized it as the first number that can be written as the sum of two cubes in two different ways. Stewart claims that this was probably a set-up by Hardy, trying to cheer up his sick friend. For a mathematician, especially for a number theorist like Ramanujan, it would not be difficult to immediately recognize 1728 as the cube of 12 and that this number is also 1000 (10 cubed) plus 729 (9 cubed). And Stewart places question marks after some other myths.</p>
<p>
Of course all of these figures stand out in one way or another. After reading what they have achieved, one can only sit back in awe. There are throughout the ages mathematicians of all sorts. Some were poor, some were rich, some were religious, other were politically engaged, some were child prodigies, and some blossomed at later age. Some were not even professional mathematicians like Fermat, who was a lawyer, just fond of mathematics. Some were very applied, others worshipped the pure stuff. With this sample (although limited) of great mathematical minds it is tempting to ask whether there is some common ground, some way of stimulating the development of extraordinary mathematical skills. Stewart concludes there is none that we could influence. Some just have it, others don't.</p>
<p>
This is a wonderful read authored by one of the best in this genre. Mathematical knowledge is not explicitly needed, but the reading will be best appreciated if there is a minimal background (certainly for the mathematicians active in the 19th and 20th century) but with some love for mathematics and a bit of interest in its history you will savour the text from the first till the last page.</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 significant figures in this book are 25 important mathematicians starting with Archimedes and ending with William Thurston. With a short biography and a framing of (some of) their work, Stewart illustrates why they were important and at the same time we get a fragmented sketch of the history of mathematics. With this selective yet diverse sample of significant mathematicians, Stewart concludes that education or socio-cultural background is not a common requirement to create a great mathematician. It's more the personality and the unconventional creativity of the (wo)man that generates the genius.</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/ian-stewart" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">ian stewart</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">2017</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 178125429 5 (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">£20 (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">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/significant-figures-hb.html" title="Link to web page">https://profilebooks.com/significant-figures-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/history-mathematics" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">History 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/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/01-01" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">01-01</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/00a09" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">00a09</a></li>
</ul>
</span>
Thu, 20 Jul 2017 08:03:32 +0000adhemar47775 at http://euro-math-soc.euMathematics in Ancient Egypt-A Contextual History
http://euro-math-soc.eu/review/mathematics-ancient-egypt-contextual-history
<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"> </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="http://euro-math-soc.eu/sites/default/files/book-review/MathInAncientEgypt.pdf" type="application/pdf; length=41130">MathInAncientEgypt.pdf</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/annette-imhausen" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">ANNETTE IMHAUSEN</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-princeton" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">princeton university press, princeton</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">978-0-691-11713-3</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">234</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>
Tue, 18 Jul 2017 13:10:22 +0000Raquel Díaz47773 at http://euro-math-soc.euA Mind at Play: How Claude Shannon Invented the Information Age
http://euro-math-soc.eu/review/mind-play-how-claude-shannon-invented-information-age
<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>
According to Yuval Harari, dataism will be the new religion of the <em>Homo Deus</em>, the sequel of the current homo sapiens. This homo deus will be only a small subsystem in a gigantic data processing network. Whether this is where evolution will bring us at the end of the 21st century, well beyond the technological singularity, is still speculative. Nevertheless, it is blatantly clear that already today information and communication has become an essential element of our society. Who controls information and how it is communicated is in control of society. One of the people if not <em>the</em> one who made information and communication the subject of a whole new science is Claude Shannon (1916-2001). Surprisingly enough, until now, no proper book with his full biography existed. His collected works were published and shorter biographies and obituaries did appear, but not a full-size biography like the current book.</p>
<p>
Shannon had a master degree in electrical engineering from MIT. At that time Boole algebra was known and taught, but it was just formal logic belonging to a philosophy course, detached from any practical consideration. It was Shannon, working in the neighbourhood of the differential analyser of Vannevar Bush at MIT who made the link in his master thesis. The machine had hundreds of switches and Shannon saw the connection and used algebra to simplify the circuits. This connection may be obvious to us, but in those days circuit design was more an art than a science. His thesis was a big success. Bush recognized immediately Shannon's qualities and sent him to the Eugenics Record Office where he designed for his PhD an algebra to describe the formation of chromosomes pairs. This however turned out not to be very practical and Shannon gave up all research in this direction.</p>
<p>
Shannon spent a summer visiting Bell Labs and got a grant for the Institute of Advanced Studies in Princeton, an accumulation point for the top notch scientists from all over the world: Einstein, Weyl, von Neumann, Gödel, Oppenheim,... Shannon was more a tinkering engineer than an abstract mathematician and didn't feel at home in Princeton. That's why later he preferred the engineering spirit of AT&T Bell Labs and the freedom of choosing his own research projects over a more secure but also more sterile academic career. Early 1940 when he was finalising his PhD, he married Norma Wolf but that was only for a short while since they divorced late summer 1941, close to the end of his stay in Princeton. Norma claimed that he had a depression. Anyway World War II reached the US and science was switched to a war modus. He got a position at Bell Labs where he worked for the National Defence Research Committee computing ballistic trajectories and doing cryptographic research in the SIGSALY project (a secure speech system based on Bell Lab's vocoder).</p>
<p>
Making long days at the Bell Labs, his true work was done at home after working hours. It of course was related to elements that showed up in his work in the Labs. Nyquist and Hartley were the first trying to capture the information content in a message. It however required the genius mind of Shannon to add statistics to their ideas. Messages are often redundant. If a part (e.g. a letter or a word) can be predicted with high probability, its information content is low, while an unexpected element has a high information value. This idea is captured in the formula $H=-\sum_i p_i \log_2 p_i$ that Shannon came up with. In this formula $p_i$ is the probability of the $i$th symbol occurring. A new unit of information had to be invented which became the bit in the binary case. When it was recognized that this formula corresponded to what is called entropy in physics, its realm became even bigger. Indeed, it did not only describe the information content of a message but it governed the whole physical reality we live in. Once the information content of the parts of a message are obtained, it becomes clear which parts can be removed without much harming the information content of the message. Hence it is the basis for encoding. A message can be represented in a more compact form by removing redundancy and it can be applied to any form of information that can be transformed into a string of bits: written text, audio, images, whatever. This is what made today's Internet possible. His paper was published in 1948 followed shortly by another one dealing with channel capacity, i.e., the maximal number of bits per second that can be safely sent over a noisy channel: $C=B\log_2(1+S)$ ($B$ is the bandwidth and $S$ is the signal-to-noise ratio). Together with Warren Weaver, Shannon also published his results in the form of a book <em>A Mathematical Theory of Communication</em> in 1949 which gradually conquered the world and became a big success. Shannon was not the best of marketeers, and this is how Weaver came in. Although the essence is Shannon's finding, people referred (and they sometimes still do) to the Shannon-Weaver theory.</p>
<p>
These papers and his book, although not immediately, settled Shannon's fame. He just turned 32. Doob, in those days the pope of statistics, wrote a bad review of their book in <em>Mathematical Reviews</em> reproaching the authors a lack of mathematical exactness. Also Wiener claimed to have this theory earlier in his <em>Cybernetics</em> book. They were both proved to be wrong in the end. Part was also due to the reservation of Shannon, the tinkerer par excellence who was more interested in new challenges than in publishing papers. Anyway Shannon was eventually recognized for his contributions, got invitations, prizes and solicitations. He preferred to stay at Bell Labs and did what he liked to do most: tinker and do some freewheeling research and occasionally turn his tinkering results into papers. Most famous is Theseus, the mechanical mouse that could learn to find its way out of a maze and also his useless machine (a box with a switch on top; when the switch was turned on, a mechanical hand appeared from the box to turn off the switch and disappeared back in the box). Nevertheless such playful experiments led to meaningful research and papers on artificial intelligence.</p>
<p>
Meanwhile Shannon remarried in 1949. With his wife Betty he formed a happy couple for the rest of his life. They had three children. In 1959 MIT did an offer that could not be refused and Shannon became after all a university professor, but with great freedom in teaching and research. He also loved juggling and riding a monocycle. He even prepared a paper on juggling, which never got published though. During the 1980's the first signs of Alzheimer showed. He died in 2001.</p>
<p>
The authors of this book are not mathematicians or engineers as they admit in their acknowledgements. This shows a bit because Shannon's work after his breakthrough in 1948-49 is only superfluously covered. They did however a very good job in explaining what Shannon did before and how this related to his main achievements and they did explain quite well the meaning of the two formulas I mentioned above. Of course exposing the roots of information theory is the most important incentive of why someone would care to write a biography of Claude Shannon at all. They are however good biographers, and so we get a short biographical sketch of about everyone who is introduced as being related, and hence possibly influential to Shannon. They did interviews with first hand witnesses and family members still alive. They may also have some literary aspirations. I liked the account about the telegraph cable across the Atlantic connecting the two continents in 1858. Another example: At the end of the book there is a set of pictures. One of the pictures shows the young Shannon next to a Piper Cub during his study days in MIT when he was trained as a pilot. His instructor didn't want him at first "because his brain was too valuable to risk", but the president allowed him to take the lessons. The authors write in this context that his flights with "cheap propeller crafts, blades buzzing like an overgrown wasp" always brought him down safely. This description of the propellers doesn't add much to the biography of Shannon, but it are these small additions that make the book all but a dull enumeration of facts and events. This is clearly a biography written for the general public. This is also how professional mathematicians, engineers or historians should read it: not for the mathematics, and not to acquire additional precise historical facts and dates. A somewhat more technical exposition about the interplay between Boole's and Shannon's work can be found in Paul Nahin's <a href="/review/logician-and-engineer-how-george-boole-and-claude-shannon-created-information-age" target="_blank"><em>The Logician and the Engineer. How George Boole and Claude Shannon Created the Information Age</em></a> (2012).</p>
<p>
What we learn most from this biography is how Shannon was as a person: A tinkerer and a loner who preferred to work with his door closed, but kind and patient if one cared to enter. These are the descriptions that prevail throughout the book. Clearly, looking for the solution of a puzzle was an inquisitive play for Shannon. A game he preferred to play on his own and that he liked as much as he liked to play the clarinet. He was not the only one. Feynman did too, although much less of a loner and he played the bongos instead. And there is John Conway who liked to hop around from one mathematical topic to another as if in a toy shop. He constructed mathematical polytopes that hung from the ceiling in his office and just like Shannon, his administration was hopeless and incoming correspondence disappearing in a black hole. So the title of this book is well chosen. The title of Siobhan Roberts' biography on Conway sounds similar: <em> Genius at Play: The Curious Mind of John Horton Conway</em> (2015). However not so much is said about Shannon's family, except that after his father died, he broke with his mother and only kept some contact with his older sister. Not much is said about the family life with Betty and the children, except that Betty was his sound board and that she actually corrected his papers. There is an extensive list of notes and a bibliography, but perhaps a time line would have helped. Sometimes the account of his work obscures a bit the precise sequence of events. This is a recurring problem in biographies: keeping coherence in explaining a scientific idea requires spanning several phases in the life of the person, which may force to give up the exact sequence of events. Many things happen at the same time in a lifetime. Anyway a very readable and human biography that I enjoyed very much reading.</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 the first full-size biography of Claude Shannon, who with his two seminal papers, published in 1948, founded information theory. The book is written for a general public. No mathematical knowledge is required. Some of the work is explained tough: Boole algebra, some elements from cryptography and of course Shannon's entropy formula. The emphasis lies on Shannon as a tinkerer and a loner. He was an (electrical) engineer (his master degree) much more than he was a mathematician (his PhD).</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/jimmy-soni" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">Jimmy Soni</a></li>
<li class="field-item odd"><a href="/author/rob-goodman" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">Rob Goodman</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/simon-schuster" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">Simon & Schuster</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">2017</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">978-1476766683 (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">$27.00 (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">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.simonandschuster.com/books/A-Mind-at-Play/Jimmy-Soni/9781476766683" title="Link to web page">http://www.simonandschuster.com/books/A-Mind-at-Play/Jimmy-Soni/9781476766683</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/history-mathematics" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">History 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/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/94a15" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">94A15</a></li>
<li class="field-item odd"><a href="/msc-full/62b10" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">62B10</a></li>
</ul>
</span>
Thu, 06 Jul 2017 06:27:45 +0000adhemar47758 at http://euro-math-soc.euUnsolved!
http://euro-math-soc.eu/review/unsolved
<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>
Can you imagine: a book on cryptography that gets you hooked and keeps you reading like you would read a Dan Brown page turner. This is what Craig Bauer achieved with this book. When I had to imagine what a (popular) book about cryptography would look like, I would think about some modulo calculus, the Caesar code, perhaps something about Alan Turing and the Enigma machine, and principles of RSA and public key methods. Well, all of this is here, but it is also Indiana Jones, James Bond, The Name of the Rose, Dan Brown, the X-files, Sherlock Holmes, NCIS and Criminal Minds. You name it. Even though you already know in advance that in the end the problem will remain <em>Unsolved!</em>, you keep on reading, running along the cryptographer who is trying to unravel the mystery, collecting more and more information, trying yet another attack, following a new lead.</p>
<p>
In fact, it gave me a complete new idea about cryptography. I would spontaneously think of it as a tool that was used to communicate a message such that the "enemy" would not be able to read it, like in war situations or when I communicate with my bank about transferring money. However, any message, in any form (text, picture, audio, or a signal from outer space, whatever, even the result of an ordinary experiment or a simulation) contains a message that we need to read and interpret correctly, even though we are not "the enemy". Sometimes this message is accidentally hidden. Usually then cryptography will not be of much help. The more challenging ones are of course the messages that have been deliberately obscured not by steganography but by following certain cryptographic rules. Of course, this is cryptography in a narrow sense where the cryptographer comes in with his or her wit and techniques (often statistical) to decipher the seemingly nonsense message. This is from all ages and all cultures and it has been a constant chase of the encryptor trying to outwit the attacking cryptographer.</p>
<p>
In the early techniques not much mathematics was going on in the encryption process, just several methods of substituting letters or groups of letters or words by others or replacing them by especially designed symbols. Statistical techniques, using the frequencies of letters or groups appearing in some language may help detect what kind of substitution is used. It then remains to try to discover some key which requires wit and guesswork. Usually some modulo calculus, perhaps transposing a rectangular table, or transforming letters in numbers which are submitted to simple numerical transformations before transforming back to letters. But that is about all the mathematics that are needed, until prime number factorization becomes essential in RSA type methods. RSA is explained but it comes only at the very end of this book. This means that a mathematical education is not needed to read it. Nevertheless cryptography is usually considered as part of mathematics or maybe computer science or electrical engineering and it are often mathematicians and the likes who seem to have a knack for cryptography.</p>
<p>
Rather than explaining different cryptographic methods and how to attack them and illustrate these with some examples, Bauer had the marvellous idea of presenting (historical) cases of ciphers which, at the time of writing of the book, have not been solved. This does not mean that they will not be solved in the future. Too often a code was assumed to be unbreakable in the past and yet it was eventually solved, certainly since computers could be employed to test a zillion of possible alternatives. The subtitle says it all: <em>The History and Mystery of the World's Greatest Ciphers from Ancient Egypt to Online Secret Societies</em>. Bauer has the gift of presenting the cases in such a way that you, as a reader, are confronted with a puzzling problem and you are fed with little teaspoons uncovering more information and background and along the way you are also instructed about the method of encryption and the way to attack it. It keeps you on the tip of your chair eager to read on. Obviously all these real life puzzles presented involve some cryptogram and it will turn out in the end that it could not be solved until now.</p>
<p>
For some of the cases we do not know the origin of the cipher, and hence we cannot be absolutely sure that it is not a hoax. For others, we do know who produced it, challenging whoever wanting to know the content. I did not expect that there were so many weirdos trying to communicate with deceased or claiming they will try to get a message across after they die. These are relatively harmless but much more frightening are the serial killers hiding their identity in a cryptogram, claiming yet another murder on their list. Among the manuscripts with unknown origin we read about the much investigated Voynich manuscript from the early 15th century. But there are also Egyptian hieroglyph inscriptions and cryptic Viking rune stones. It helps if we know something about the author of the cryptic message. For example the Dorabella cipher which is a cryptographic letter by Edgar Elnar mailed to Dora Penny. Nevertheless this one could not be decrypted. The Zodiac is a serial killer who committed several murders around 1970 in the California Bay Area identifying himself with cryptic messages. He stands as an example for other similar cases. The Somerton man was found poisoned in Somerton Australia. While trying to identify him, also some cryptogram was involved. The most challenging ciphers come of course from cryptographers. An example is the <em>Krypton</em> sculpture, a piece of art by Jim Sanborn, placed in front of the CIA headquarters in Langley. It has 4 parts with cryptographic texts. The first three have been solved, but the last one is still open. There are treasure hunting cryptographic puzzles (online or not) hiding the identity of the author or the location or nature of the eventual treasure. And there are messages to or from outer space and many more unsolved problems, too many to enumerate them all. As I already mentioned at the end of the book RSA encoding is explained.</p>
<p>
If you have read my review this far, it will be clear that I am blown away by this book. I have never read a non-fiction book before that is so thrillingly entertaining and forces you to read on nearly holding your breath. You are left in awe reading the details of what murderous weirdos are capable of, your curiosity is tickled to the extreme trying to find out the meaning of a strange manuscript, and you are left in admiration for the ingenuity of the cryptographers, and in the latter Bauer has contributed his part. Even though this is a thick book, it could not contain everything. Much material is available on the web and Bauer refers to it in the text and points to the many references to be consulted for further documentation. The last paragraph is entitled "More to Come!". I am already hoping now that there will be more of the same in the future.</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>
Bauer presents several cases of unsolved ciphers. His presentation is most entertaining and it reads like a thriller. The cases are varying over many types. There are classics like the Voynich manuscript from the 15th century, the Krypton sculpture in front of the CIA headquarters in Langley, messages from the Zodiac serial killer, and the unidentified murdered man from Somerton. But also messages to or from the afterlife or from outer space. Along the way he explains some of the cryptographic methods and ways to attack them. The subtitle says it all: <em>The History and Mystery of the World's Greatest Ciphers from Ancient Egypt to Online Secret Societies</em>. A marvellous book!</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/craig-p-bauer" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">Craig P. Bauer</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">2017</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">9780691167671 (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">USD 35.00 (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">624</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://press.princeton.edu/titles/10949.html" title="Link to web page">http://press.princeton.edu/titles/10949.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/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/94a60" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">94A60</a></li>
</ul>
</span>
Wed, 28 Jun 2017 12:54:51 +0000adhemar47748 at http://euro-math-soc.eu