Best 49 quotes in «calculus quotes» category

Thus the required rigor was found in the application of the concept of number, made formal by divorcing it from the idea of geometrical quantity

The mathematical theory of continuity is based, not on intuition, but on the logically developed theories of number and sets of points.

Two writings of al-Hassār have survived. The first, entitled Kitāb al-bayān wa t-tadhkār [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]

To a scholar, mathematics is music.

What music is to the heart, mathematics is to the mind.

Voltaire called the calculus "the Art of numbering and measuring exactly a Thing whose Existence cannot be conceived." See Letters Concerning the English Nation p. 152

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

Yet in another way, calculus is fundamentally naive, almost childish in its optimism. Experience teaches us that change can be sudden, discontinuous, and wrenching. Calculus draws its power by refusing to see that. It insists on a world without accidents, where one thing leads logically to another. Give me the initial conditions and the law of motion, and with calculus I can predict the future -- or better yet, reconstruct the past. I wish I could do that now.

But to us, probability is the very guide of life.

Calculus is one course you can come with to your parents and say, I am dropping it. And they'll understand.

Calculus works by making visible the infinitesimally small.

I am the very model of a modern major general

Every one who understands the subject will agree that even the basis on which the scientific explanation of nature rests is intelligible only to those who have learned at least the elements of the differential and integral calculus, as well as analytical geometry.

Geometric calculus consists in a system of operations analogous to those of algebraic calculus, but in which the entities on which the calculations are carried out, instead of being numbers, are geometric entities which we shall define.

History was easy, but I don't know about the Calculus. It seemed like it was making sense, so that probably means I failed.

Hard to be a physics major at Rice University if you have flunked calculus.

I don’t believe in statistics. I believe in calculus.

I was more interested in skating and the girls and traveling than I was in calculus.

I never failed in mathematics. Before I was fifteen I had mastered differential and integral calculus.

In the calculus of feelings, you never really know how one person's absence will affect you more than another's.

In my free time I do differential and integral calculus.

In the calculus of good deeds you have the most to gain.

I was always very strong in math, physics and calculus.

...magic was ugly—-a hard bargain with the universe, a calculus of pain.

Foreshadowings of the principles and even of the language of [the infinitesimal] calculus can be found in the writings of Napier, Kepler, Cavalieri, Fermat, Wallis, and Barrow. It was Newton's good luck to come at a time when everything was ripe for the discovery, and his ability enabled him to construct almost at once a complete calculus.

Private Victory precedes Public Victory. Algebra comes before calculus.

The English language is more complex than calculus because numbers don't have nuances.

The true Logic for this world is the Calculus of Probabilities, which takes account of the magnitude of the probability.

As its campfires glow against the dark, every culture tells stories to itself about how the gods lit up the morning sky and set the wheel of being into motion. The great scientific culture of the West--our culture--is no exception. The calculus is the story this world first told itself as it became the modern world.

As to the need of improvement there can be no question whilst the reign of Euclid continues. My own idea of a useful course is to begin with arithmetic, and then not Euclid but algebra. Next, not Euclid, but practical geometry, solid as well as plane; not demonstration, but to make acquaintance. Then not Euclid, but elementary vectors, conjoined with algebra, and applied to geometry. Addition first; then the scalar product. Elementary calculus should go on simultaneously, and come into vector algebraic geometry after a bit. Euclid might be an extra course for learned men, like Homer...

Cournot protested that concepts exist in the understanding, independently of the definition which one gives to them. Simple ideas sometimes have complicated definitions, or even none. For this reason he felt that one should not subordinate the precision of such ideas as those of speed or the infinitely small to logical definition. This point of view is diametrically opposed to that which analysis since the time of Cournot has been toward ever-greater care in the formal logical elaboration of the subject. This trend, initiated in the first half of the nineteenth century and fostered largely by Cauchy, was in the second half of that century continued with notable success by Weierstrass.

Probability is the very guide of life.

You burros have calculus in your blood.

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

Carnot, one of a school of mathematicians who emphasized the relationship of mathematics to scientific practice, appears, in spite of the title of his work, to have been more concerned about the facility of application of the rules of procedure than about the logical reasoning involved.

If college admissions officers are going to encourage kids to take the same AP math class, why not statistics? Almost every career (whether in business, nonprofits, academics, law, or medicine benefits from proficiency in statistics. Being an informed, responsible citizen requires a sound knowledge of statistics, as politicians, reporters, and bloggers all rely on "data" to justify positions. [p.98]

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.

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?

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.

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’s so special about humans...?', I’m at a loss to know how to answer that question. If you don’t see why we’d be special… because we can do poetry [and] think philosophical thoughts [and] we can think about the morality of our behavior, I’m 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’s so special about that?

In making the basis of the calculus more rigorously formal, Weierstrass also attacked the appeal to intuition of continuous motion which is implied in Cauchy's expression -- that a variable approaches a limit.

I never joke about calculus homework." - Sam al-Abbas

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.

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.

Mathematics is unable to specify whether motion is continuous, for it deals merely with hypothetical relations and can make its variable continuous or discontinuous at will. The paradoxes of Zeno are consequences of the failure to appreciate this fact and of the resulting lack of a precise specification of the problem. The former is a matter of scientific description a posteriori, whereas the latter is a matter solely of mathematical definition a priori. The former may consequently suggest that motion be defined mathematically in terms of continuous variable, but cannot, because of the limitations of sensory perception, prove that it must be so defined.

Love was actually more like calculus or physics. What was the half-life of love? Did it have cosigns and slopes, or quarks that morphed from wave to particle faster than you could say, please don’t leave?

Mathematics is not just a subject of education system, it is the soul of education system.

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

Most of his predecessors had considered the differential calculus as bound up with geometry, but Euler made the subject a formal theory of functions which had no need to revert to diagrams or geometrical conceptions.