European Mathematical Society - i. stewart
https://euro-math-soc.eu/author/i-stewart
enHow to Cut a Cake
https://euro-math-soc.eu/review/how-cut-cake
<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>There is an easy way of how to make a fair division of a cake between two persons: one cuts and the other then chooses. If the first one does not cut fairly, then the second one can take the bigger (or the better) half. The analogous task becomes a good deal more difficult when the cake is to be divided between three or even more people. This puzzle, having certain obvious practical applications, leads to a serious mathematical problem mathematicians have been grappling with for more than 50 years. This beautiful book, written by one of the most famous writers of mathematics, gives an amusing description of this problem, its history, false solutions and the correct solution. </p>
<p>Cake-cutting algorithms however occupy just the first chapter of the book and there are nineteen more chapters. Their topics range from sardine tins to chess games and from quasi-crystals to the Sierpinski Gaskets. The book also explains what the portioning of the Moon has got in common with electric circuits. In twenty chapters, the author takes the reader for an amazing journey through a diverse world of mathematics and its applications, pointing out mind-boggling conundrums and mysteries, some with deadly serious applications in practice. As he says in the introduction, this is a book for the fans, the math enthusiasts, the people who actively like mathematics. Being one of those, I can confirm that, for those who do, this book is another must. Make a space for it in your bookcase.</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">lp</div></div></div><span class="vocabulary field field-name-field-review-author field-type-taxonomy-term-reference field-label-inline clearfix"><h2 class="field-label">Author: </h2><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/author/i-stewart" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">i. stewart</a></li></ul></span><span class="vocabulary field field-name-field-review-publisher field-type-taxonomy-term-reference field-label-inline clearfix"><h2 class="field-label">Publisher: </h2><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/publisher/oxford-university-press-oxford" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">oxford university press, oxford</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">2006</div></div></div><div class="field field-name-field-review-isbn field-type-text field-label-inline clearfix"><div class="field-label">ISBN: </div><div class="field-items"><div class="field-item even">0-19-920590-6 </div></div></div><div class="field field-name-field-review-price field-type-text field-label-inline clearfix"><div class="field-label">Price: </div><div class="field-items"><div class="field-item even">GBP 9.99</div></div></div><span class="vocabulary field field-name-field-review-msc field-type-taxonomy-term-reference field-label-hidden"><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/msc/00-general" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">00 General</a></li></ul></span>Fri, 30 Sep 2011 17:06:31 +0000Anonymous39805 at https://euro-math-soc.euGalois Theory, third edition
https://euro-math-soc.eu/review/galois-theory-third-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>This is the third edition of the classic textbook of Galois theory, first published in 1972. But it is not just a reprint of earlier editions. Those who know the first two editions will be surprised by a radical change of presentation. The author reversed the original Bourbakiste approach expressed by a slogan “from general to concrete” and now presents the theory in the direction “from concrete to general”. Thus after a historical chapter, he starts with solutions in radicals of polynomial equations of degree 2, 3, 4, and presents a quintic equation solvable in radicals. Factorization of complex polynomials is developed from theory of polynomials with complex coefficients and the fundamental theorem of algebra. Field extensions of rational numbers follow including the definition of rational expressions and the degree of an extension. As a digression, the author proves non-existence of ruler-and-compass solutions of classical geometric problems of squaring the cube, trisecting the angle and squaring the circle. Then the Galois theory starts. After a short explanation of Galois groups according to Galois, he presents modern definitions of the Galois correspondence, splitting fields, normal and separable extensions, and field automorphisms. The fundamental Galois correspondence between the subfields of a field extension and subgroups of the automorphism group of the extension is proved. An example of the correspondence resulting from a quartic equation is also given. Solvable and simple groups are introduced and the Galois theorem about solvability of equations in radicals is proved. After all this, abstract rings and fields are introduced and the abstract theory of field extensions is developed. The last part of the book contains some applications, e.g., the construction of finite fields, constructions of regular polygons, circle divisions (including cyclotomic polynomials) and an algorithm on how to calculate the Galois group of a polynomial equation. The penultimate chapter is about algebraically closed fields and the last chapter, on transcendental numbers, contains “what-every-mathematician-should-see-at-least-once”, the proof of transcendence of p. The book is designed for the second and third year undergraduate courses. I will certainly use it.</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">jtu</div></div></div><span class="vocabulary field field-name-field-review-author field-type-taxonomy-term-reference field-label-inline clearfix"><h2 class="field-label">Author: </h2><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/author/i-stewart" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">i. stewart</a></li></ul></span><span class="vocabulary field field-name-field-review-publisher field-type-taxonomy-term-reference field-label-inline clearfix"><h2 class="field-label">Publisher: </h2><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/publisher/chapman-hallcrc" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">chapman & hall/crc</a></li></ul></span><div class="field field-name-field-review-pub field-type-number-integer field-label-inline clearfix"><div class="field-label">Published: </div><div class="field-items"><div class="field-item even">2003</div></div></div><div class="field field-name-field-review-isbn field-type-text field-label-inline clearfix"><div class="field-label">ISBN: </div><div class="field-items"><div class="field-item even">1-58488-393-6</div></div></div><div class="field field-name-field-review-price field-type-text field-label-inline clearfix"><div class="field-label">Price: </div><div class="field-items"><div class="field-item even">$44,96</div></div></div><span class="vocabulary field field-name-field-review-msc field-type-taxonomy-term-reference field-label-hidden"><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/msc/12-field-theory-and-polynomials" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">12 Field theory and polynomials</a></li></ul></span>Mon, 12 Sep 2011 15:33:56 +0000Anonymous39692 at https://euro-math-soc.eu