I teach mathematics at the University of Hertfordshire.

This web site covers mathematics up to 2nd year undergraduate studies and I would appreciate any helpful comments regarding this site. Please send your comments via email to [email protected]

Some mathematicians are birds, others are frogs. Birds fly high in the air and survey broad vistas of mathematics out to the far horizon. They delight in concepts that unify our thinking and bring together diverse problems from different parts of the landscape. Frogs live in the mud below and see only the flowers that grow nearby. They delight in the details of particular objects, and they solve problems one at a time… Mathematics needs both birds and frogs.

Mathematics is rich and beautiful because birds give it broad visions and frogs give it intricate details. Mathematics is both great art and important science, because it combines generality of the concepts with depth of structures. It is stupid to claim that birds are better than frogs because they see further, or that frogs are better than birds because they see deeper. The world of mathematics is both broad and deep, and we need birds and frogs working together to explore it.

Freeman Dyson 1923 – present

Qualities of a good mathematics student:

  • An ability to tackle problems that are not routine variations of textbook or exam questions
  • A sound understanding of mathematical logic, the concept of proof, and counter-example
  • A readiness to explore ideas beyond the confines of the syllabus
  • Knowing standard formulas – without needing a formula sheet
  • Having good numerical skills – without needing a calculator
  • Willing to spend time thinking about a problem whose solution is not immediately obvious
  • Having good geometric insight
  • Being good at algebraic manipulation
  • Knowing that geometry can be used to think of algebraic problems, and algebra can solve geometric problems
  • Able to construct logical proofs
  • Connecting apparently different areas of mathematics Thinking flexibly and creatively