Tuesday, 1 October 2013

What should be teach about the reciprocity law for high school for gifted student

What should be teach about the reciprocity law for high school for gifted
student

This autumn I have to teach a mini course for a small group of high school
student (mathematical gifted class) on Quadratic Reciprocity Law (3
lectures in ten hours). This is the requirement of the school for me to
become an assistant lecturer. I have studied thís law in the second year
in university, but that was only a glimpse: the origin, the proof... and
my approach at that time was quite modern. I know that this law is very
beautiful and important in mathematics, but I did know much about its role
and applications.
So,
What are the books/lecture notes/papers should I read for preparing my talk?
What should be teach about this topic for high school student? (May be
like the reciprocity law with a view toward modern number
theory/mathematics?)

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