Mathematics

Course summary

In the introduction to The Mathematical Experience, Davis and Hersh write that a naïve definition of Mathematics is The Science of Quantity and Space, before going on to declare that its definition changes with the generations. Jan Gullberg, in his introduction to Mathematics, From the Birth of Numbers despairs that Mathematics is often perceived as little more than arithmetic that will prove useful in life. Rather, it is from the understanding that, far from rote learning, has at its heart an adaptability to acquire and utilise new skills and methodologies. This is much more appreciable in A level; one past student commented that it was at this stage, when Maths no longer seemed to be a just set of rather straightforward rules, that she began to appreciate and enjoy the subject. The great areas of the subject, algebra, analysis, statistics, geometry, and mechanics to name but a few, have arisen from our experience of the world around us. Mathematics is the realm of logical reasoning and creativity, whether solving problems or proving theorems. Mathematics is an expression of the human mind, it reflects the active will, the contemplative reason, and the desire for aesthetic perfection. Its basic elements are logic and intuition, analysis and construction, generality and individuality. Active experience in maths itself alone can answer the question. From the introduction to What is Mathematics? by Robert Courant and Herbert Robins. Mathematics is a wonder. Its historical roots can be traced back to the origins of every civilisation. Its psychological roots are embedded in the most ordinary activities of everyday life. It is more than an art, more than a science, more than a game, the first and purest science, but also a mysteriously and in comprehensively powerful tool for understanding the real world. David Wells.