Introduction to Classical Mathematics I From the Quadratic Reciprocity Law to the Uniformization Theorem

6Et moi, ..., si j'avait su comment en revenir, One service mathematics has rendered the human mce. It has put common sense back je n'y serais point alle.' Jules Verne where it belongs, on the topmost shelf nCllt to the dusty canister labelled 'discarded non­ sense'. The series is divergent; therefore we may be able to do something with it. Eric T. Bell O. Heaviside Mathematics is a tool for thought. A highly necessary tool in a world where both feedback and non­ linearities abound. Similarly, all kinds of parts of mathematics serve as tools for other parts and for other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One service topology has rendered mathematical physics ...'; 'One service logic has rendered com­ puter science ...'; 'One service category theory has rendered mathematics ...'. All arguably true. And all statements obtainable this way form part of the raison d'etre of this series.