alderssc
Without this common language, we would have a specialized language for every field, allowing little "cross-pollination". As an example, in evolutionary biology, take the NK model of epistatic interactions which models gene interactions. It just so happens that this model is extremely similar to a thing in statistical physics called a spin-glass. Without mathematics the biologist would have to sit and work out all the details of these epistatic interactions before getting to actually do biology. So in short, mathematics saves you time by expressing common patterns or ideas.
A mathematician, like a painter or a poet, is a maker of patterns. If his patterns are more permanent than theirs, it is because they are made with ideas.
as did Bertrand Russell (one of my favorite quotes):
Mathematics, rightly viewed, possesses not only truth, but supreme beauty—a beauty cold and austere, like that of sculpture, without appeal to any part of our weaker nature, without the gorgeous trappings of painting or music, yet sublimely pure, and capable of a stern perfection such as only the greatest art can show.
I suspect many mathematicians view themselves, at least to some extent, as creative types similar to poets.
Eichmann was responsible for over-seeing the trains that sent Jews to concentration camps. He tried, to no avail, to employ the "just following orders" defense. If anyone is interested, definitely check out Hannah's book.
The former because it's an excellent introduction to one of the west's most influential figures (Socrates). As a testament to that influence, any philosopher before him is called 'pre-Socratic'. Not to mention Socrates' tale of traveling around Athens questioning the populace after visiting the Oracle is a great story. It wouldn't hurt to follow up with the dialogue Phaedo next, which details the end of Socrates.
The latter for many reasons. The Republic is the most complete statements of Plato's philosophy, in addition to being beautifully written (Plato's writing seems to shine through in just about any translation that I've seen, but the Allan Bloom translation is particularly enjoyable).
Plato, and this book in particular, have been extremely influential in western thought. Indeed, one philosopher wrote that "the safest general characterization of the European philosophical tradition is that it consists of a series of footnotes to Plato." And here in America, the founding fathers often quoted Plato in their pamphlets prior to seceding.
Following the dialogues in the book will take you from discussions on the nature of justice and reality, to the best mode of governance. It serves as a wonderful introduction to what it means to do philosophy and hopefully you find it as enjoyable as I have.
If you are familiar with the Quaternions, take a look at the 3D rotation group SO(3). This group apparently has applications in computing where one needs a way to perform rotations in three dimensions. According to the Wikipedia article, https://secure.wikimedia.org/wikipedia/en/wiki/Quaternions_a..., this method of representation has certain important advantages over other methods, including being numerically stable and avoiding a problem called gimbal lock, where rotation about one of the possible axes is no longer possible.
The sign of the first derivative only gives you the present rate of adoption/abandonment of the platform, while integrating gives you a measure of success over the platform's entire existence.