calculus

If you put it as 'complex nervous systems' it sounds pretty deflationary. What's so special about a complex nervous system? But of course, that complex nervous system allows you to do calculus. It allows you to do astrophysics_ to write poetry... to fall in love. Put under that description, when asked 'What__ so special about humans...?', I__ at a loss to know how to answer that question. If you don__ see why we__ be special_ because we can do poetry [and] think philosophical thoughts [and] we can think about the morality of our behavior, I__ not sure what kind of answer could possibly satisfy you at that point....I could pose the same kinds of questions of you... So God says, 'You are guys are really, really special.' How does his saying it make us special? 'But you see, he gave us a soul.' How does our having a soul make us special? Whatever answer you give, you could always say_ 'What__ so special about that?

I abandoned the assigned problems in standard calculus textbooks and followed my curiosity. Wherever I happened to be--a Vegas casino, Disneyland, surfing in Hawaii, or sweating on the elliptical in Boesel's Green Microgym--I asked myself, "Where is the calculus in this experience?

You can't teach calculus to a chimpanzee. So just share your banana.

The teacher manages to get along still with the cumbersome algebraic analysis, in spite of its difficulties and imperfections, and avoids the smooth infinitesimal calculus, although the eighteenth century shyness toward it had long lost all point.

It is an unfortunate fact that proofs can be very misleading. Proofs exist to establish once and for all, according to very high standards, that certain mathematical statements are irrefutable facts. What is unfortunate about this is that a proof, in spite of the fact that it is perfectly correct, does not in any way have to be enlightening. Thus, mathematicians, and mathematics students, are faced with two problems: the generation of proofs, and the generation of internal enlightenment. To understand a theorem requires enlightenment. If one has enlightenment, one knows in one's soul why a particular theorem must be true.

He calculated the number of bricks in the wall, first in twos and then in tens and finally in sixteens. The numbers formed up and marched past his brain in terrified obedience. Division and multiplication were discovered. Algebra was invented and provided an interesting diversion for a minute or two. And then he felt the fog of numbers drift away, and looked up and saw the sparkling, distant mountains of calculus.

Nothing takes place in the world whose meaning is not that of some maximum or minimum.

Two writings of al-Hass_r have survived. The first, entitled Kit_b al-bay_n wa t-tadhk_r [Book of proof and recall] is a handbook of calculation treating numeration, arithmetical operations on whole numbers and on fractions, extraction of the exact or approximate square root of a whole of fractionary number and summation of progressions of whole numbers (natural, even or odd), and of their squares and cubes. Despite its classical content in relation to the Arab mathematical tradition, this book occupies a certain important place in the history of mathematics in North Africa for three reasons: in the first place, and notwithstanding the development of research, this manual remains the most ancient work of calculation representing simultaneously the tradition of the Maghrib and that of Muslim Spain. In the second place, this book is the first wherein one has found a symbolic writing of fractions, which utilises the horizontal bar and the dust ciphers i.e. the ancestors of the digits that we use today (and which are, for certain among them, almost identical to ours) [Woepcke 1858-59: 264-75; Zoubeidi 1996]. It seems as a matter of fact that the utilisation of the fraction bar was very quickly generalised in the mathematical teaching in the Maghrib, which could explain that Fibonacci (d. after 1240) had used in his Liber Abbaci, without making any particular remark about it [Djebbar 1980 : 97-99; Vogel 1970-80]. Thirdly, this handbook is the only Maghribian work of calculation known to have circulated in the scientific foyers of south Europe, as Moses Ibn Tibbon realised, in 1271, a Hebrew translation.[Mathematics in the Medieval Maghrib: General Survey on Mathematical Activities in North Africa]

I studied calculus for the first time, which to me was an amazingly empowering experience which I could really see how you could understand all sorts of things, and I decided that chemistry and biology just had too much memory for me to be interested. Physics was very easy.

Whereas Nature does not admit of more than three dimensions ... it may justly seem very improper to talk of a solid ... drawn into a fourth, fifth, sixth, or further dimension.

The ultimate goal of a meteorologist is to set up differential equations of the movements of the air and to obtain, as their integral, the general atmospheric circulation, and as particular integrals the cyclones, anticyclones, tornados, and thunderstorms.

Normal. She wanted normal and so did I. "You know what's normal?""What?" She wiped away her remaining tears. "Calculus.

Being kidnapped and abused by the undead was worse than calculus, but not by a wide margin.

The analytical geometry of Descartes and the calculus of Newton and Leibniz have expanded into the marvelous mathematical method__ore daring than anything that the history of philosophy records__f Lobachevsky and Riemann, Gauss and Sylvester. Indeed, mathematics, the indispensable tool of the sciences, defying the senses to follow its splendid flights, is demonstrating today, as it never has been demonstrated before, the supremacy of the pure reason.

I will never listen to ocean waves or view a beautiful sunset in quite the same way again. That is perhaps the greatest gift one can gain by delving into calculus: It is a whole new way of looking at the world, accessible only through the realm of mathematics.