There is a pleasure in the pathless woods; There is a rapture on the lonely shore; There is society, where none intrudes, By the deep sea, and music in its roar: I love not man the less, but Nature more… - Lord Byron

To solve a problem is a very human undertaking, and more than a little mystery remains about how we best guide ourselves to the discovery of original solutions. Still, as George Pólya and others have taught us, there are principles of problem solving. With practice and good coaching we can all improve our skills. Just like singers, actors, or pianists, we have a path toward a deeper mastery of our craft.

“ In mathematics, you don’t understand things, you just get used to them.” - John von Neumann

Free flight is one of the most common subjects of sweet dreams; just as falling is the frequent stuff of nightmares. And yes, we learned to fly; we achieved the dream and it has proved dust and ashes. Ironically enough, everything about human flying is the antithesis of what we dream of. Aeroplanes are noisy, cramped, polluting – they scratch the surface of the blue ceiling and break up the silence of the night.

] Prof.Trefethen David Bau Prof Lloyd N.Trefethen and his student, David Bau have neatly organized all aspects of numerical linear algebra in to a set of 40 lectures. Each lecture revolves around one specific idea. I will try to summarize the key points of these lectures. Every person who has solved any real life math fin problem knows that the classic numerical algebra is dead. Iterative methods are almost always used for finite difference methods, solving pde’s, optimization.