
Inequalities between Binomial Coefficients in a Needlessly Fancy Way
Most high school students already know far more about the binomial coefficients than they need to, and one of the things that they might know is the fact that if $k < \frac{n}{2}$, then $$ \binom{n}{k} \le \binom{n}{k+1}.
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Braid Codes
The fields of information theory and group theory intersect in a wide variety of places; finite fields are fundamental in the development of error correcting codes, and groups appear in a number of encryption schemes.
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