Integral Equations
In my research I had to solve a bunch of integral equations, and so I took a lot of notes on them. It's a fascinating topic. Fourier and Laplace transforms
figure prominently. The Projection method is of particular interest. Applied math has always been more of an interest to me than 'pure' math, as the latter always
seemed to lack vital interest. But the Projection method is one where the two sides of math really come together, where being fussy and fastidious about seemingly
unimportant details actually yields profoundly useful practical results. Lie groups in differential equations also felt that way to me.
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