1.1 Two hundred years of algebra
In this section we recapitulate two hundred or so years of mathematical thought.
Let us start with a familiar type of brain teaser.
Example 1.1.1 Sally and Martin go to The Olde Tea Shoppe. Sally buys three cream buns and two bottles of pop for thirteen shillings, whilst Martin buys two cream buns and four bottles of pop for fourteen shillings. How much does a cream bun cost and how much does a bottle of pop cost?
Solution. If Sally had bought six cream buns and four bottles of pop, then she would have bought twice as much and it would have cost her twenty six shillings. Similarly, if Martin had bought six cream buns and twelve bottles of pop, then he would have bought three times as ...