Book of the Month: Unsolved Problems in Number Theory

NumberTheoryMarch Book of the Month is Unsolved Problems in Number Theory by Richard Guy, first published by Springer Verlag in 1981. Third edition (nearly three times the size!!) published in 2004.

These problems are mostly very easy to understand, but are as yet unsolved. Guy gives an account of the problems, and the progress made on them. He does this in such a way that they provide food for thought and avenues for exploration for mathematicians at varying levels of maturity in number theory.

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Book of the Month: Unsolved Problems in Number Theory

NumberTheoryMarch Book of the Month is Unsolved Problems in Number Theory by Richard Guy, first published by Springer Verlag in 1981. Third edition (nearly three times the size!!) published in 2004.

These problems are mostly very easy to understand, but are as yet unsolved. Guy gives an account of the problems, and the progress made on them. He does this in such a way that they provide food for thought and avenues for exploration for mathematicians at varying levels of maturity in number theory.

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The Wolfram MathWorld List of Unsolved Problems

TheHappyEndProblemMarch Site of the Month: The Wolfram MathWorld List of Unsolved Problems

This updated list explains the most famous unsolved problems in mathematics and progress made on each, with references for further reading.

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Famous Problems in Mathematics

JUngelösteProblemeanuary’s Book of the Month is Famous Problems in Mathematics by Heinrich Tietze, first published in German in 1959, and republished in 1990 by DTV. An English translation published by Graylock Press in 1964. The preface contains a beautiful metaphor and explanation of the nature of mathematical learning.

The original work is entitled Gelöste und ungelöste mathematische Probleme aus alter und neuer Zeit.
The full English translation has the title Famous Problems of Mathematics: Solved and Unsolved Mathematical Problems from Antiquity to Modern Times.

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Site of the Month: Famous Problems in the History of Mathematics

HistoryOfMathJanuary’s Site of the Month is Famous Problems in the History of Mathematics.

This site is part of NCTM’s MathForum and continues the problems theme of recent Sites and Books of the Month.

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Hilbert’s Problems

hilbertDecember’s Site of the Month is Hilbert’s 2000 Lecture.
At the International Congress of Mathematicians in 1900, David Hilbert presented ten important unsolved problems. When his lecture was published it contained 23 problems, several of which have now been solved (see the Wikipedia site for more historical information).
This month’s site is a copy of the published lecture–it was presented in the Mathematics Education part of the congress, and so is addressed to teachers of mathematics.

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+Plus Magazine

plusNovember’s Site of the Month is +Plus.
+Plus is an internet magazine from Cambridge University that is now connected to the Millenium Mathematics Project which “aims to help people of all ages and abilities share in the excitement of mathematics and understand the enormous range and importance of its applications to science and commerce”.
Several links from last month’s site are to articles in +Plus.

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Applications of Mathematics

applicationmathOctober’s Site of the Month is Applications of Mathematics.
This is part of the Mathigon website, directed at resources for schools. However the Applications of Mathematics section has links to several references for each application where the reader can access the mathematics behind the application.

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The Pythagorean Theorem

pythagoreantheoremDecember’s Book of the Month is The Pythagorean Theorem: A 4000-year History by Eli Moar, published in 2007 by Princeton Science Library.

This is the third book that celebrates a famous equation, in this case one that is so well known that it needs little introduction. However, its history pre-dates Pythagoras by over 1000 years, and traces through many cultures.

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Euler’s Gem: The Polyhedron Formula and the Birth of Topology

eulersgemNovember’s Book of the Month is Euler’s Gem: The Polyhedron Formula and the Birth of Topology by David Richeson, published in 2008 by Princeton University Press.
(Adapted from the Amazon description)
Leonhard Euler’s polyhedron formula describes the structure of many objects–from soccer balls and gemstones to Buckminster Fuller’s buildings and giant all-carbon molecules. From ancient Greek geometry to today’s cutting-edge research, Euler’s Gem celebrates the formula’s far-reaching impact on topology, the study of shapes. David Richeson tells how Descartes almost discovered it but fell short; how nineteenth-century mathematicians widened the formula’s scope for use with higher dimensional shapes; and how twentieth-century mathematicians discovered that every shape has its own Euler’s formula.

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