I enjoy this idea of square roots in modular arithmetic. Sometimes when I get a little confused in modular arithmetic I just remind myself what modular arithmetic actually means, and when I put the equation into 'regular' arithmetic it makes more sense. One question I have about the Legendre and Jacobi symbols is regarding their relationships to fractions. Is the fraction notation used just as an arbitrary symbol or is there a connection between the modular arithmetic and fractions? I'm guessing there is a connection but I haven't made it yet.
I became a little confused with the examples. One difficulty for me was that they kept referring to the steps of the Theorem on page 91 in the examples, and I kept having to flip between pages to understand the reasoning. While it may sound trivial, having to flip the pages over and over again made the example much harder to follow. In class we have the advantage of writing the theorem down on one board and doing an example on the other so that they may be seen simultaneously.
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