Book reviews
http://euro-math-soc.eu/book-reviews
Book reviews published on the European Mathematical Society websiteenPython 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>
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<span class="field field-name-field-review-msc-other field-type-taxonomy-term-reference field-label-hidden">
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<li class="field-item even"><a href="/msc-full/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>
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<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.euStrategy Games to Enhance Problem-Solving Ability in Mathematics
http://euro-math-soc.eu/review/strategy-games-enhance-problem-solving-ability-mathematics
<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>
In the introduction the authors explain the goal of their book. When two opponents are playing a board game they need some strategy to win or at least maximize the chances not to loose the game. Mastering such strategies is a skill that can also be used in solving a (mathematical) problem. They even give a table drawing parallels between playing (and winning) the game versus the steps in solving a problem. I believe this is only superficial and much better and deeper analogies do exist. Winning a game is just another problem, where you have to first understand the goal, learn the rules, and develop some strategy. By repeated playing, one learns which strategies work and most of all which strategies work consistently and are not just a lucky hap. The meta question is then whether this strategy can be generalized, to other problems of larger dimension or when the rules are inverted or only slightly changed etc. This is a general approach to solve any problem, whether the problem is mathematical or not.</p>
<p>
Once this has been made clear, the following chapters are basically an enumeration of games, stating the rules and the goal of the game. There is also what the authors call a "sample simulation" in which some moves or situations are simulated, pointing to some problems or possibilities, making suggestions, and sometimes asking questions to think about.</p>
<p>
The different chapters group games that are similar or just form variations of the same game or at least they have similar goals and thus may require similar strategies. We have a chapter on tic-tac-toe-like games, one chapter is called "blocking games" which can come in many different forms (nim is and example), another chapter deals with games where the strategy has to be continuously updated while playing and finally a "miscellaneous" chapter where, among others, several classic western games are found like checkers, dominoes, battleship,...</p>
<p>
So far, only the problems were formulated and the reader, or rather the players, are supposed to go through the steps that I sketched in the first paragraph: finding and analysing a winning strategy. The last chapter provides answers and hints to the problems in the previous chapters. What are possible strategies? For example what is the best first move to open the game? Sometimes a mathematical proof may exist for the claim that the one who starts (and makes no mistakes) will always win. However there are no mathematics involved here, although there could have been. And these mathematics need not always be connected with game theory.</p>
<p>
In an appendix, illustrations of the (empty) game boards are given, although their geometry should be clear already from the previous chapters. Even if these pages are cut from the book, they may be too small to play on. I do not see the advantage of adding these pages to the printed book. Perhaps an electronic version could be printed with some magnification factor.</p>
<p>
In conclusion, this is a nice collection of board games, and when pupils will play such games, they will develop some winning strategies for these games, and these skills will probably help in cultivating certain attitudes and perhaps working schemes to tackle mathematical problems. However it was certainly not the intention of the authors to involve mathematics in this book. I think however that it would not be very difficult to hook up several mathematical problems to these games, somewhat like what Matthew Lane did for video games in his book <a href="/review/power-unlocking-hidden-mathematics-video-games" target="_blank">Power Up</a>. But that would be a completely different book because here the focus is just the games and learning how to win them mostly by playing them, thereby avoiding all the mathematics and abstract game theory.</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 author's leitmotif in this book is that when two players are trying to win a board game, they will develop a winning strategy which is very similar to the strategies and skills needed to solve other, more mathematical, problems. So they describe many of these board games with their rules and urge the reader to play these games several times until they see some strategy emerge. In a final chapter they give some hints about what such strategies may look like for each of these games. There are however no mathematics involved as such.</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/alfred-s-posamentier" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">alfred s. posamentier</a></li>
<li class="field-item odd"><a href="/author/stephen-krulik" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">Stephen Krulik</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-scientfic" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">World Scientfic</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">978-981-3146-341 (pbk)</div></div></div><div class="field field-name-field-review-price field-type-text field-label-inline clearfix"><div class="field-label">Price: </div><div class="field-items"><div class="field-item even">GBP 20.00</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">136</div></div></div><div class="field field-name-field-review-website field-type-text field-label-hidden"><div class="field-items"><div class="field-item even"><a href="http://www.worldscientific.com/worldscibooks/10.1142/10187" title="Link to web page">http://www.worldscientific.com/worldscibooks/10.1142/10187</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/97a20" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">97A20</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/00a08" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">00a08</a></li>
<li class="field-item odd"><a href="/msc-full/91a05" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">91A05</a></li>
</ul>
</span>
Fri, 23 Jun 2017 11:37:34 +0000adhemar47737 at http://euro-math-soc.euThe Canterbury Puzzles
http://euro-math-soc.eu/review/canterbury-puzzles
<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>
Henry Dudeney (1857-1930) was an English mathematician who is best remembered for his logic puzzles and games. He published several books that collected sets of his puzzles that appeared in magazines before and to which he added some new material. <em>The Canterbury Puzzles</em> (1907) was his first collection. The title refers to the fact that the first set of the puzzles are presented as if formulated by characters from Chaucer's <em>Canterbury Tales</em>. Ten years later he had another collection published <em>Amusements in Mathematics</em> (1917). In the 1920's two more collections were published and more came out posthumously.</p>
<p>
The <em>Canterbury Puzzles</em> and the <em>Amusements in Mathematics</em> are two classics and have been available as Dover Publications for some time now. More recently they were also available on ebook repositories such as <em>Project Gutenberg</em> and others. The present book is a pocket edition by Penguin that reproduces a 1919 edition of the <em>Canterbury Puzzles</em> published by Thomas Nelson and Sons. So this edition is from after <em>Amusements in Mathematics</em> was published. Although the two books contain a largely disjunct set, some of the puzzles in the <em>Canterbury Puzzles</em> are related to or are variations of puzzles that also appeared in the <em>Amusements in Mathematics</em>, so for some of the discussions, Dudeney refers in this edition to that book for some extra information or related puzzles.</p>
<p>
The book consists of several chapters in which the puzzles are formulated and at the end of the book the solutions are given. The chapters merely differ by the context in which the puzzles are placed, not by the kind of puzzles they contain. The first chapter has the same title as the title of the book and one should be prepared to read some Chaucer's Middle English. Some of the subsequent chapters are also placed in the same realm of medieval castles and monasteries. Later it moves to a more "modern" decorum (recall though that this is written some hundred years ago at the dawn of the 20th century, which obviously is somewhat reflected in the wording and the style, and certainly in the many illustrations). There are puzzles of all sorts to be found in each chapter, geometric as well as combinatorial or even crime mysteries that have to be solved like in a whodunit mystery. Almost all of the problems are illustrated, not only to formulate the problem or the solution when it is geometric, but also with the scenes in which monks, lords, pilgrims, or other persons are figuring. Also the degree of difficulty is rather diverse. Mathematical education is not really needed, simple counting suffices. The problems primarily rely on creative and careful logic thinking. The keywords in the index that was added to this 1919 edition should make it possible to look up a certain (type of) puzzle among the 114 items that the book contains.</p>
<p>
One of the puzzles is the famous Haberdasher puzzle that was formulated by Dudeney in 1902. The problem is to cut up an equilateral triangle into four pieces that have to be rearranged to form a square. The solution given by Dudeney is in the form of a hinged dissection puzzle. Hinged dissections became later a particular type of puzzles. Gregg Frederickson published a couple of books on this kind of problems. Also Martin Gardner has discussed it and he wrote a tribute to Dudeney in his <em>Scientific American</em> columns. Of course Gardner also published several collections of his puzzles. The Haberdasher problem also features in <em>The Penguin book of curious and interesting puzzles</em> (1992) by David Wells which is another collection of classical puzzles. <em>The Moscow puzzles</em> (1956) by Boris Kordemsky is yet another classic that was very popular in the Soviet Union. It will also be republished by Penguin. And nowadays there are of course many more collections available on the book market of popular science and mathematics.</p>
<p>
It is fortunate that Penguin republishes these classics and makes them available again. Dudeney was one of the first of what has become a flourishing branch of recreational mathematics and logical games and puzzles, a market that is fuelled by traditional puzzle clubs and currently the more trendy math jams. </p>
</div></div></div></div><div class="field field-name-field-review-reviewer field-type-text field-label-inline clearfix"><div class="field-label">Reviewer: </div><div class="field-items"><div class="field-item even">Adhemar Bultheel</div></div></div><div class="field field-name-field-review-desc field-type-text-long field-label-hidden"><div class="field-items"><div class="field-item even"><div class="tex2jax"><p>
This is a classic puzzle book in which part of the problems are placed in a medieval context and where some characters of Chaucer's book do appear. The original is from 1908, but the text reproduced here is from a revision originally published in 1919. It is one of the earliest puzzle books of its kind. <br />
</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/henry-dudeney" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">Henry Dudeney</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/penguin-michael-joseph" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">Penguin / Michael Joseph</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">9780718187088 (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">£9.99 (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">256</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.penguin.co.uk/books/304828/the-canterbury-puzzles/" title="Link to web page">https://www.penguin.co.uk/books/304828/the-canterbury-puzzles/</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/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/97a20" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">97A20</a></li>
</ul>
</span>
Fri, 23 Jun 2017 11:26:34 +0000adhemar47736 at http://euro-math-soc.euPower-Up: Unlocking the Hidden Mathematics in Video Games
http://euro-math-soc.eu/review/power-unlocking-hidden-mathematics-video-games
<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>
Matthew Lane is a mathematician who maintains an interesting blog <a href="http://www.mathgoespop.com/" target="_blank">Mathematics Goes Pop!</a> where he links mathematics to popular culture, and this book is perfectly in line with that. Six years before, Keith Devlin in his book <em>Mathematics Education for a New Era: Video Games as a Medium for Learning</em> (A K Peters, 2011), already argued that video games could be a tool for (mathematical) education. Devlin, as well as Lane have some sensible ideas about how to make use of the fact that gaming is so popular among youngsters into a tool or an incentive to learn some mathematics. That this can be obtained by especially designed or pimped versions of existing games is rather obvious, but Lane claims here that any game is suitable. Just analysing the winning strategies or the way in which adventurous problems have to be solved in different games can be concrete examples of a mathematical abstraction. Even, just the creativity that goes into exploring the possibilities within the rules of the game and the endurance with which it is played may promote an attitude of trial and error within the rules of mathematics and a culture of perseverance in solving mathematical problems. Anyway, it would be a waste if the popularity of gaming would not be exploited to serve a higher purpose.</p>
<p>
In different chapters, Lane gives examples of how these ideas can be brought into practice by just relying on some popular video games that were <em>not</em> especially designed with an educational purpose in mind.</p>
<p>
The first chapter introduces several games, in which physical reality is overly simplified. Gravitation and inertia are missing and worlds may be even just two-dimensional. However in the game <em>A Slower Speed of Light</em>, as you may have guessed, the speed of light is lowered so that one moves through the landscape and it will be observed just as relativity theory predicts when you are travelling close to the speed of light. In <em>Miegakure</em> the environment is the familiar three-dimensional setting, but one can move into a fourth dimension to avoid obstacles. Moving to a fourth space dimension is not possible in reality, but there is no problem to experience it in a video game. The gamer can experience a mathematical abstraction or a physical observation that is impossible in real life.</p>
<p>
Chapter two is about guessing games like <em>Family Feud</em> where two teams have to guess the five most popular answers to some question. The popularity of these games dropped drastically after a short time because the number of questions was finite, and hence the questions keep repeating after a while. This can be the hook on which to attach some statistics and combinatorics and to design a procedure to avoid repetition as much as possible by attaching weights to questions that have already been asked. This is like interpolating between drawing balls from an urn with and without replacement, something that simply studying combinatorics mathematically does not offer.</p>
<p>
The pitfalls of voting systems is another popular, yet tricky business to analyse mathematically. This applies not only to politics but also to games in which the user has to grade some components and also to the scores and the ranking of the users themselves. The way in which the player collects his points can be very complicated, and it may not always be clear what will be the score, positive or negative, that can be earned by their actions. Inverse engineering of your final score is not at all a simple problem. But if you succeed, then it should be possible to detect impossible scores, or perhaps screen configurations revealing partial information that is not possible, given the rules of the game. Of course the latter remotely refers to the consistency of a logical system. There are two chapters devoted to this kind of problems.</p>
<p>
Chapter five is all about chasing and shooting. This is the chapter that is the most mathematical or at least the one with most formulas. As far as shooting is concerned, one may consider two kinds of missiles: those that go in a straight line and bounce off walls or the heat seeking missiles that lock in on the target and adapts its trajectory continuously. In the first case, the mathematics involves some simple trigonometry, but still the moving target complicates things, and it becomes really tricky when there are multiple reflections on walls. This is the part that has most of the formulas. The trajectories of heat seeking missiles are not piecewise linear anymore. They can in principle still hit a target that disappears behind a corner. This is a more involved issue and it is worked out to some extent in an addendum. But even a simple interception problem of an enemy missile moving on a straight line towards a target that has to be neutralised by your own missile, also moving in a straight line, is interesting to investigate. A blast with a certain radius can help you still destroying the enemy missile when the interception point is slightly missed. There are some quite interesting mathematics involved here.</p>
<p>
As we progress in the book, the mathematics and the abstraction is cranked up a bit. The next chapter is about computational complexity and the P vs NP problem. These complexity concepts are introduced by explaining Kevin Beacon numbers. This is the distance of an actor to Kevin Beacon measured in coactor-of-coactorship. It is the analogue of the Erdős number which is the co-authorship distance from Paul Erdős, which is quite popular among mathematicians (I wonder why the Erdős number is not even mentioned). Finding these numbers is a shortest path problem in a graph and that is a problem from class P, but finding the longest path or the path of a certain length between two nodes are known to be NP-complete, i.e. easy to check but difficult to solve. So are some problems related to <em>Tetris</em>. Another well known example is the travelling salesman problem. This is a problem a gamer has to solve when he has to pick up some potions, treasures or weapons at fixed places in a maze. Finding a fast algorithm for solving them will earn you instant fame and a 1 million dollar prize from the Clay Mathematical Institute. Games in the class NP are usually the more challenging and perhaps therefore the more attractive ones. There is however little hope that you will crack the P vs. NP problem by playing video games.</p>
<p>
There is a game called <em>Sims</em> which is all about getting (and keeping) friendship relations. Chapter 7 is about modelling such relations between two persons. Several models are proposed in discrete and in continuous time. The latter involves differential equations. It is not explained how to solve systems of differential equations, but solutions are plotted graphically, so that interpretations can be given. This moves seamlessly to the next chapter where nonlinear elements cause chaotic behaviour. For example when a third person competes with the second for the friendship of the first: a three-body problem. Chaotic trajectories may also result when a shell is fired that behaves like a ball on a billiard table. Even when these tables have simple geometries like squares or ovals or when there are a few obstacles inside.</p>
<p>
In a final chapter Lane reflects on how video games can help in solving pedagogical issues. He explicitly refers to Devlin's book mentioned above and to other publications and reports on experiments that have been conducted at several places.</p>
<p>
From this summary, it is clear that this is not about the mathematics of video games which would be much more involved with modelling the physics of the scenes, and the involved mathematics of computer graphics needed for rendering realistic characters. On the contrary, this is all about relatively simple mathematics and logical questions that the gamer could ask spontaneously or with a little help from his teacher. It's the mathematics hidden behind the game, the one not really explicitly visible. The game or its modes of operation can be the hook on which to hang the meaning of some abstraction or it can justify why a certain mathematical concept is useful. The mathematics itself is not really the focus of the book. Differential equations are mentioned but not their solution method for example. Lane just gives some examples of where a game can be an incentive to engage in a mathematical problem, and these problems go well beyond the cuddling mathematics of kindergarten. Lane is certainly convinced of the idea and he has a broad knowledge of the many different games, probably earned with a lot of experience. He does a good job in making his point and the ideas are not naive and they do make sense. If, as a teacher, you are game-phobic and feel like an alien in this virtual world of your students, don't be afraid of this book. Lane does a marvellous job in explaining what all these games do, or at least you are informed about what you need to know, and the book is amply illustrated. We shall not be teaching all our mathematics using games in the near future, but who knows what will happen when the ideas are elaborated further in games especially designed with an educational purpose. It is not unthinkable that they become standard ingredients in our educational toolboxes.</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 point made in this book is that with little effort video games can be used as a hook on which to hang a mathematical problem and hence they can be used for educational purposes. By directing the interest of the pupil for gaming towards questions about the rules of the game, or the winning strategies, or the models that were used in the design of the game, this can serve as an incentive to study its abstracter version or to analyse the sequence of events or to generalize the problem, hence to illustrate the usefulness and the meaning of mathematics</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/matthew-lane" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">Matthew Lane</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">9780691161518 (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 29.95 (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">264</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/10954.html" title="Link to web page">http://press.princeton.edu/titles/10954.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/00a35" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">00A35</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/97a20" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">97A20</a></li>
<li class="field-item odd"><a href="/msc-full/97a80" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">97A80</a></li>
<li class="field-item even"><a href="/msc-full/97c70" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">97C70</a></li>
<li class="field-item odd"><a href="/msc-full/97m70" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">97M70</a></li>
<li class="field-item even"><a href="/msc-full/97u80" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">97U80</a></li>
</ul>
</span>
Mon, 19 Jun 2017 06:54:14 +0000adhemar47725 at http://euro-math-soc.euProblem-Solving Strategies in Mathematics From Common Approaches to Exemplary Strategies
http://euro-math-soc.eu/review/problem-solving-strategies-mathematics-common-approaches-exemplary-strategies-0
<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/2017_ProblemSolvingStrategies_0.pdf" type="application/pdf; length=25740">2017_ProblemSolvingStrategies.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/alfred-s-posamentier-0" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">Alfred S Posamentier</a></li>
<li class="field-item odd"><a href="/author/stephen-krulik" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">Stephen Krulik</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">978-981-4651-63-9 </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">188</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>
Wed, 07 Jun 2017 16:48:59 +0000Eugenia47703 at http://euro-math-soc.euLarge Truncated Toeplitz Matrices, Toeplitz Operators, and Related Topics
http://euro-math-soc.eu/review/large-truncated-toeplitz-matrices-toeplitz-operators-and-related-topics
<div class="field field-name-field-review-review field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><div class="tex2jax"><p>
This book is a volume 259 in the Bikhäuser OT Series <em>Operator Theory Advances and Applications</em>. It contains 30 contributions celebrating Albert Böttcher's 60th birthday.</p>
<p>
Albert Böttcher is a professor of mathematics at the TU Chemnitz in Germany. His main research topic is functional analysis. At his 18th he won the silver medal at the International Math Olympiad in Moscow. He studied mathematics at the TU Karl-Marx-Stadt (now TU Chemnitz) and finished a PhD in 1984 entitled <em>The finite section method for the Wiener-Hopf integral operator</em> under supervision of V.B. Dybin at Rostov-on-Don State University in Russia (this was all while the Berlin wall was still up). Since then he stayed at the TU Chemnitz. At the time of writing he has (co)authored 9 books and over 220 papers. The complete list is in the beginning of the book but one may also consult his <a href="https://www-user.tu-chemnitz.de/~aboettch/" target="_blank">website</a> where he keeps his list of publications up to date.</p>
<p>
The contributions start with reminiscences and best wishes by friends, colleagues and students of Albrecht Böttcher. Besides personal recollections, there is some discussion of his work, some photographs and reproductions of slides he used in presentations to illustrate that he is not only an excellent mathematician but also a passionate teacher and lecturer.</p>
<p>
That leaves about 700 pages of original research papers all of which relate from far or near to subjects that Böttcher has worked on. The Toeplitz operators and Toeplitz matrices of the title are indeed well represented, but there are all the other "Related Topics" which are close to his work too. About fifty renowned authors are involved.</p>
<p>
The Toeplitz operator (and hence also its spectrum) is characterized by a function, which is called its symbol. It features in a multiplication or convolution in the definition of the operator. With respect to a standard monomial basis, Toeplitz operators are represented by (infinite) Toeplitz matrices that have constant entries along diagonals. Of course the spectral and other properties of truncations of the infinite matrices to large finite ones relate to corresponding properties of Toeplitz operators, and similarly it can be related to other operators such as convolution and Wiener-Hopf operators. These matrices and operators have applications in differential and integral equations, systems and control, signal processing, and many more. Depending on the application the symbol may get an interpretation of transfer function of a system, power spectrum or autocorrelation of a signal, the kernel of an integral equation, or just a weight function in a Hilbert space. So, Toeplitz matrices and operators are also related to numerical methods for solving functional equations after discretization. Or to orthogonal polynomials (on the unit circle), which then in turn links to (trigonometric) moment problems, quadrature, and approximation theory (on the unit circle, but in a similar way also to analogs on the real line).</p>
<p>
Obviously this is not the place to discuss every paper in detail. The table of contents is available on the publisher's website and for convenience the research papers are also listed below. From the titles you will recognize the papers on determinants and eigenvalues for Toeplitz matrices, in particular their asymptotic behaviour as their size goes to infinity. Of course circulant and Hankel operators and combinations of these as operators or matrices are not far off the central theme and they are thus also treated in some of the chapters. The majority of the papers present new results. Note that most of them are (functional) analysis. Only a few exceptions are more linear algebra or make a link to physics or explicitly discuss numerical aspects (see [14, 16, 18, 23, 25, 27] below).</p>
<p>
Some of the papers are quite long (more than 30 pages and some even up to 50 pages). They are basically true research papers, sometimes a bit more expository, but they are not of the introductory broad survey type. So this is not the book you should read to be introduced to the subject, but is is more a sketch of the state-of-the-art for who is already famiiar. The style of course depends on the authors, but the book is homogeneous because of the subjects that all somehow relate to Böttcher's work. These topics discussed here are also close to the core idea of this book series <em>Operators Theory Advances and Applications</em>, founded by Israel Gohberg as a complement to the journal <em>Integral Equations and Operator Theory</em>. Only one of Böttcher's books appeared in this series though (<em>Convolution Operators and Factorization of Almost Periodic Matrix Functions </em> (2002) authored with Yu. I. Karlovich, and I. M. Spitkovsky appeared as volume 131) but several of his books are with Springer / Birkhäuser. That these topics are still a main focus of research is illustrated by the successful annual IWOTA conferences (<em>International Workshop on Operator Theory and its Applications</em>), the proceedings of which are also published in this OT series. The IWOTA 2017 is organized by A. Böttcher, D. Potts and P. Stollmann at the TU Chemnitz.</p>
<p>
Thus for anyone interested in the general topics of this book series, this collection will be a worthy addition. For those who are more selective, there is of course still the possibility to get some separate chapters, which is the advantage of having it also available as an ebook.</p>
<p>
Here are the titles and authors of the research papers in this volume:</p>
<p>
<br />
7. <em>Asymptotics of Eigenvalues for Pentadiagonal Symmetric Toeplitz Matrices, </em> Barrera, M. (et al.), Pages 51-77<br />
8. <em>Echelon Type Canonical Forms in Upper Triangular Matrix Algebras, </em> Bart, H. (et al.), Pages 79-124<br />
9. <em>Asymptotic Formulas for Determinants of a Special Class of Toeplitz + Hankel Matrices, </em> Basor, E. (et al.), Pages 125-154<br />
10. <em>Generalization of the Brauer Theorem to Matrix Polynomials and Matrix Laurent Series, </em> Bini, D.A. (et al.), Pages 155-178<br />
11. <em>Eigenvalues of Hermitian Toeplitz Matrices Generated by Simple-loop Symbols with Relaxed Smoothness, </em> Bogoya, J.M. (et al.), Pages 179-212<br />
12. <em>On the Asymptotic Behavior of a Log Gas in the Bulk Scaling Limit in the Presence of a Varying External Potential II, </em> Bothner, T. (et al.), Pages 213-234<br />
13. <em>Useful Bounds on the Extreme Eigenvalues and Vectors of Matrices for Harper's Operators, </em> Bump, D. (et al.), Pages 235-265<br />
14. <em>Fast Inversion of Centrosymmetric Toeplitz-plus-Hankel Bezoutians, </em> Ehrhardt, T. (et al.), Pages 267-300<br />
15. <em>On Matrix-valued Stieltjes Functions with an Emphasis on Particular Subclasses, </em> Fritzsche, B. (et al.), Pages 301-352<br />
16. <em>The Theory of Generalized Locally Toeplitz Sequences: a Review, an Extension, and a Few Representative Applications, </em> Garoni, C. (et al.), Pages 353-394<br />
17. <em>The Bézout Equation on the Right Half-plane in a Wiener Space Setting, </em> Groenewald, G.J. (et al.), Pages 395-411<br />
18. <em>On a Collocation-quadrature Method for the Singular Integral Equation of the Notched Half-plane Problem, </em> Junghanns, P. (et al.), Pages 413-462<br />
19. <em>The Haseman Boundary Value Problem with Slowly Oscillating Coefficients and Shifts, </em> Karlovich, Yu.I., Pages 463-500<br />
20. <em>On the Norm of Linear Combinations of Projections and Some Characterizations of Hilbert Spaces, </em> Krupnik, N. (et al.), Pages 501-510<br />
21. <em>Pseudodifferential Operators in Weighted Hölder-Zygmund Spaces of Variable Smoothness, </em> Kryakvin, V. (et al.), Pages 511-531<br />
22. <em>Commutator Estimates Comprising the Frobenius Norm - Looking Back and Forth, </em> Lu, Zhiqin (et al.), Pages 533-559<br />
23. <em>Numerical Ranges of 4-by-4 Nilpotent Matrices: Flat Portions on the Boundary, </em> Militzer, E. (et al.), Pages 561-591<br />
24. <em>Traces on Operator Ideals and Related Linear Forms on Sequence Ideals (Part IV), </em> Pietsch, A., Pages 593-619<br />
25. <em>Error Estimates for the ESPRIT Algorithm, </em> Potts, D. (et al.), Pages 621-648<br />
26. <em>The Universal Algebra Generated by a Power Partial Isometry, </em> Roch, S., Pages 649-662<br />
27. <em>Norms, Condition Numbers and Pseudospectra of Convolution Type Operators on Intervals, </em> Seidel, M., Pages 663-680<br />
28. <em>Paired Operators in Asymmetric Space Setting, </em> Speck, F.-O., Pages 681-702<br />
29. <em>Natural Boundary for a Sum Involving Toeplitz Determinants, </em> Tracy, C.A. (et al.), Pages 703-718<br />
30. <em>A Riemann-Hilbert Approach to Filter Design, </em> Wegert, E., Pages 719-740</p>
</div></div></div></div><div class="field field-name-field-review-reviewer field-type-text field-label-inline clearfix"><div class="field-label">Reviewer: </div><div class="field-items"><div class="field-item even">Adhemar Bultheel</div></div></div><div class="field field-name-field-review-desc field-type-text-long field-label-hidden"><div class="field-items"><div class="field-item even"><div class="tex2jax"><p>
This is a collection of papers dedicated to Albrecht Böttcher's 60th birthday. The contributions are by friends, colleagues and students. After the impressive list of his publications, many of which dealing with asymptotics of Toeplitz and related operators, the book has some birthday addresses sketching Böttcher as a person and some of his work. The major part however consists of research papers written on invitation by specialists on topics related by far or near to the work of Böttcher. <br />
</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/dario-bini" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">Dario A. Bini</a></li>
<li class="field-item odd"><a href="/author/torsten-ehrhardt" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">Torsten Ehrhardt</a></li>
<li class="field-item even"><a href="/author/alexei-yu-karlovich" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">Alexei Yu. Karlovich</a></li>
<li class="field-item odd"><a href="/author/ilya-matvey-spitkovsky" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">Ilya Matvey Spitkovsky</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>
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<li class="field-item even"><a href="/publisher/birkh%C3%A4user-basel" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">birkhäuser basel</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">978-3-319-49180-6 (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">174,89 € (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">766</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.springer.com/gp/book/9783319491806" title="Link to web page">http://www.springer.com/gp/book/9783319491806</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/analysis-and-its-applications" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">Analysis and its Applications</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/47-operator-theory" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">47 Operator theory</a></li>
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<span class="field field-name-field-review-msc-full field-type-taxonomy-term-reference field-label-hidden">
<ul class="field-items">
<li class="field-item even"><a href="/msc-full/47b35" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">47B35</a></li>
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<li class="field-item even"><a href="/msc-full/30e05" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">30e05</a></li>
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<li class="field-item even"><a href="/msc-full/47a57" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">47A57</a></li>
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Sat, 20 May 2017 12:07:31 +0000adhemar47678 at http://euro-math-soc.eu