Department van Wiskundige Wetenskappe

Wiskunde

Resources

So you need to give a Wiskus talk, and you don’t know what to talk about? Where do you start? Have a look at the following great books:

  • William Dunham, Journey through Genius – The great theorems of mathematics. Available in the library.
    This is a great book; each chapter goes through a famous theorem from history at an easy level and explains it nicely while also explaining the historical background. Just one of these chapters will be fantastic for a Wiskus talk! The chapters are:

    • Hippocrates quadrature of the line (440 BC)
    • Euclid’s proof of the Pythagorean theorem (300 BC)
    • Euclid and the infinitude of primes (300 BC)
    • Archimedes’ determination of circular area (225 BC)
    • Heron’s formula for triangular area (75 AD)
    • Cardano and the solution of the cubic (1545) (Ed: that’s a 1500 year gap…see what the Dark Ages did..!!)
    • A gem from Isaac Newton (late 1660′s)
    • The Bernoullis and the Harmonic series (1689)
    • The extraordinary sums of Euler (1734)
    • A sampler of Euler’s number theory (1736)
    • The non-denumerability of the continuum (1874)
    • Cantor and the transfinite realm (1891)
  • Kenji Ueno, Koji Shiga and Shigeyuki Morita, A mathematical gift I-III: the interplay between topology, functions and geometry. Available in the library.
    pic of book
    This is a fantastic series of three books and consists of lectures given to high school students in Japan. Yes that’s right, high school students, so don’t think it’s too hard for you! Each lecture is something you can cover in a Wiskus talk. There’s stuff in there about the “curvature” of a surface, “What is dimension?”, a nice lecture about trigonometry, the Poncelet theorem, scissors-congruent polygons, and lots more.
  • Ross Honsberger, Ingenuity in mathematics. Available in the library.Ross Honsberger has written a whole bunch of books explaining little mathematical gems, such as Ingenuity in mathematicsMathematical gems I-IIIMathematical delights, and a few more. They are all available in the library, and are full of excellent topics for a Wiskus talk.
  • Ian Stewart, Professor Stewart’s hoard of mathematical treasures. Available in the library.Ian Stewart is a great explainer of maths. See his video on symmetry on YouTube! In this book you can find all sorts of interersting things to talk about at Wiskus, mostly along the lines of “recreational mathematics”. Things like hexaflexagons, swallowing elephants, magic circle, by the numbers of babylon, why toast always falls buttered-side-down, for a start!
  • Martin Gardner, Hexaflexagons and other mathematical diversions. Available in the library.picMartin Gardner is the legendary figure who wrote the Mathematical Games column for the Scientific American from 1956-1981. He died in 2010. He collected his columns into books, and there are loads of them (the one above is just one of them!). They are all absolutely fantastic. Each chapter is about some interesting mathematical fact, game, puzzle or paradox. Highly recommended.
  • Clifford Pickover, The Math Book – From Pythagoras to the 57th dimension, 250 milestones in the history of mathematics. Available in the library.Another book going through maths history, picking out the coolest stories and theorems. Things like the Mobius strip, proof of the Prime number theorem, Tetris is NP-complete, Checkers is solved, the Hairy Ball theorem. Really good.
  • Peter Winkler, Mathematical mind-benders. Available in the library.picA nice book on puzzles, etc. For example, “At what age will the average child be half the height that he or she will be as an adult?”. Or “Curves on Potatoes”.