In Chapter 1, we have seen how the algebra of the polynomial rings k [x1,..., xn] and the
geometry of affine algebraic varieties are linked. In this chapter, we will study the method of …

This book covers the development of reciprocity laws, starting from conjectures of Euler and
discussing the contributions of Legendre, Gauss, Dirichlet, Jacobi, and Eisenstein. Readers …

In introducing his essays on the study and understanding of nature and e-lution, biologist
Stephen J. Gould writes:[W] e acquire a surprising source of rich and apparently limitless …

Résumé Une étude approfondie des manuscrits de Sophie Germain sur le dernier théorème
de Fermat, révèle que l'on doit réévaluer ses travaux en théorie des nombres. En effet, on …

Gauss's quadratic reciprocity theorem is among the most important results in the history of
number theory. It's also among the most mysterious: since its discovery in the late eighteenth …

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This thesis establishes the following three claims:(1) Experience with mechanical curve
drawing devices played a role of fundamental historic and conceptual importance of in the …

Our upper-level university honors course, entitled Great Theorems: The Art of Mathematics,
views mathematics as art and examines selected mathematical masterpieces from antiquity …

There is not much that can be said for all $ x $ and for all $ n $ about the sum\[\sum_ {k= 1}^
n\frac {1}{|\sin k\pi x|}.\] However, for this and similar sums, series, and products, we can …

Solving Quadratic equation is one of the intrinsic interests as it is the simplest nonlinear
equations. A novel approach for solving Quadratic Equation based on Genetic Algorithms …