I know the notation, and learned it in math classes required for a computer science degree at a US university. But I wouldn't expect most US programmers to know it, since most of the people in my major did not like math. On hearing "Big O" these days, some of them would probably be thinking "giant robot". For my own use I sometimes use mathematical notations because they are concise and precise.

I agree. Windows 8 has a lot of great features, even game-changing improvements. Microsoft is running in the right direction. Running sideways and backwards, sometimes, but still moving mostly the right way. Windows 8 has most of the pieces needed to be a truly great operating system. Getting there is more a matter of tweaking what they have than rebuilding. I like that my phone and my tablet have so much in common in how they operate. I think that phone, tablet and desktop should all work basically the same way. There will be differences brought about by the limitations of each form factor, but the OS doesn't necessarily need to be different for each case. Having appropriate settings available (and installed with defaults based on the device) should be able to take care of the problems while allowing single-path development. Imagine having the same control type render differently based on device type, but working the same way behind the scenes. You might need to have extra code based on whether or not touch and or mouse were available, and would have to account for different screen sizes - but one build would apply to phones, tablets and desktops instead of having one different build for each. It might take a couple more years, but I think Windows will get there. And when they do, let's hope they allowing installing your own software on your own computer.