Book of the Month: Journey Through Genius

The May Book of the Month is Journey Through Genius: The great theorems of mathematics by William Dunham, first published by John Wiley in 1990, and republished in Penguin Paperback in 1991.

Dunham places each theorem within its historical context and explores the life of the creator — from Archimedes to Gerolamo Cardano to Georg Cantor. He also provides step-by-step proofs for the theorems, each easily accessible to readers with no more than a knowledge of high school mathematics. His approach is to present this material as a work of art like music or literature.

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Site of the Month: Mathematics News

ScienceDailyMay’s Site of the Month is: ScienceDaily – Mathematics News

This site is part of the ScienceDaily website. Here are updated articles that give short overviews of recent applications of mathematics. The entries are backed up with references for further reading.

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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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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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