Berkeley Scientific Journal

Envision the underwater world: vibrant coral, swaying seaweed, and lively creatures abound. However, the postcards and National Geographic covers that try to capture the beauty of this picturesque habitat can only represent it at one moment in time -- in reality, the landscape is hardly static, since many of its animals are capable of body modifications to change their shape and color. To understand the coloration and color vision of sea creatures, UC Berkeley Professor Roy L. Caldwell researches various marine animals such as stomatopods and cephalopods. In an interview with Professor Caldwell on December 13, 2012 BSJ had an opportunity to discuss different aspects of color vision and color change in sea animals with respect to behavioral ecology.

In this essay, we study and comment on two number theoretical applications on prime cyclotomic fields (cyclotomic fields obtained by adjoining a primitive p-th root of unity to Q, where p is an odd prime). We begin by giving a simplified proof of Kummer's case of Fermat's Last Theorem obtained by linking different versions of the proof in different textbooks. We finally modernize Dirichlet's solution to Pell's Equation.