QuoteOriginally posted by: flairplayQuoteOriginally posted by: CuchulainnQuoteThe Russians used to write just about the best books on mathematics, chattychatty Russians?? which books did you read?I have hardly ever read any books to be honest. I might have a quick dip in, but I find thinking out an issue or topic, little thoughts pieced together, helps the most.Anyway chatty not in the style of science fiction or books for laymen, but a certain pedagogical style. Some simple motivating examples and illustrations take you easily into useful topics. A couple of examples would be "Differential and Integral Calculus" by Piskunov and "Intro to Topology" by Borisovich et al. In the former, you are even taken into stability of ODE's and Lyapunov exponents without much a do, and the latter has a clean motivating chapter followed by point set and algrebraic topology. Contrast this with any American text book in calculus, or the standard Munkres' texts on General and Algebraic Topology.Of course in the end it is personal preference. There are people who belong to the Bourbaki school, feeling that the difficulty and pain of learning describes the sophistication of content. Undoubtedly there is some correlation. Nevertheless, in the end it is how much sticks and retains that matters. Here cleanliness and simplicity of exposition counts as well. And I think not many people would regard the Bourbaki school as very useful, at least for pedagogical content.The Russian write-ups were in a spirit very different from Bourbaki. I would have thought this is not so unknown.Clear. Nice post. The nice thing is that the theory is motivated by real world example (e.g. like in PDE). For example, motivating group theory by rotations and other geometric transformations of a cube. How does Bourbaki motivate groups?
Last edited by Cuchulainn
on February 12th, 2007, 11:00 pm, edited 1 time in total.