Learning group theory, integrals of logarithms, continued fractions, mathematical analysis, undergraduate math problems,

and some paintings ... sharing my personal interests!
 

Welcome to John Coffey's page of interesting finds in mathematics.

This website is for maths students and amateurs who enjoy exploring maths as a hobby.  I am not a professional mathematician, so there are no high-powered research papers here -- just the work of an enthusiast.

Recently I have been working on the article on continued fractions, adding my account of the Lagrange-Markoff Spectrum.  I hope readers find it more clear and straightforward than some accounts in the literature.

Two new sections were added in 2011

Sequences and Series is an introduction to mathematical analysis.   Analysis is that vast area of maths concerned with rigorous proof of the existence of limits of sequences, tests for convergence, continuity of functions, differentiability, and integration.   Here are the full texts of two books on analysis by my colleague Dr John Reade of the University of Manchester.  They are an undergraduate introduction to analysis, and a new, previously unpublished book on uniform convergence.

Continued Fractions is a study still in preparation, but I am working on it so here are the first 120 pages or so -- the rest is still being edited and developed.   Continued fractions were much studied in the 19th century, but now are largely forgotten.  They have many intriguing properties and applications in number theory.  The latest section I've edited is Section 11 on approximation by rational numbers.

Other established sections are:

  • Group Theory has interactive programs to 'teach-yourself' the basics of mathematical group theory.  The programs, called PermGroups and Word Groups, come with detailed instructions and fully worked examples.  Great for first year undergraduates who want to 'get a feel' for finite groups and representation theory.
  • Integrals of log(x) is a study of definite integrals of rational functions involving the logarithm, log(x), and polynomials, using complex variables.   Many fully worked examples of complex contour integration.  Useful for undergraduates who want to practice complex contour integration.
  • Puzzles and Problems are maths challenge problems with my solutions.
  • Paintings: I also paint pictures when I find time, mainly portraits.
  • Music: I enjoy European classical music.  Here are three short pieces I have written
        i)  this is me live, playing a Baroque-style two part invention (mp3, 1.3 MB).
       ii)  a fugue played on flute, oboe and vibes and marimba.
      iii)  a more modern piece for oboe and piano -- "Chase".

Join in by e-mailing me your views and your own interesting finds in maths.

John Coffey, Cheshire, England, February 20112

e-mail comments to johnc@mathstudio.co.uk