Basic Calculus Quotes

Okay, so I may use basic math for doing my checking account, the percent-off sales on my favorite shoes, and other mundane things, but Calculus? When the hell would I ever use this?

G. W. Leibniz, codiscoverer of calculus and a towering intellect of eighteenth-century Europe, wrote: “The first question which should rightly be asked is: Why is there something rather than nothing?”[1] In other words, why does anything at all exist? This, for Leibniz, is the most basic question that anyone can ask. Like me, Leibniz came to the conclusion that the answer is to be found, not in the universe of created things, but in God. God

The most fundamental, a major shift from the ape brand of sociality, was the human nuclear family, which gave all males a chance at procreation along with incentives to cooperate with others in foraging and defense. A second element, developed from an instinct shared with other primates, was a sense of fairness and reciprocity, extended in human societies to a propensity for exchange and trade with other groups. A third element was language. And the fourth, a defense against the snares of language, was religion. All these behaviors are built on the basic calculus of social animals, that cooperation holds more advantages than competition.

I spent the next year basically killing time, as if I were creating an alibi. Instead of attending cram school to prepare to retake the exam, I hung out at the local library, plowing my way through thick novels. But, hey, that's life. I found it a lot more enjoyable to read all of Balzac than to delve into the principles of calculus.

As soon as she releases me, Galen grabs my hand and I don’t even have time to gasp before he snatches me to the surface and pulls me toward shore, only pausing to dislodge his pair of swimming trunks from under his favorite rock, where he had just moments before taken the time to hide them. I know the routine and turn away so he can change, but it seems like no time before he hauls me onto the beach and drags me to the sand dunes in front of my house. “What are we doing?” I ask. His legs are longer than mine so for every two of his strides I have to take three, which feels a lot like running. He stops us in between the dunes. “I’m doing something that is none of anyone else’s business.” Then he jerks me up against him and crushes his mouth on mine. And I see why he didn’t want an audience for this kiss. I wouldn’t want an audience for this kiss, either, especially if the audience included my mother. This is our first kiss after he announced that he wanted me for his mate. This kiss holds promises of things to come. When he pulls away I feel drunk and excited and nervous and filled with a craving that I’m not sure can ever be satisfied. And Galen looks startled. “Maybe I shouldn’t have done that,” he says. “That makes it about fifty times harder to leave, I think.” He tucks my head under his chin and I wrap my arms around him until both our breathing returns to normal. I take the time to soak in his scent, his warmth, the hard contours of his-well, his everything. It’s really not fair that he has to leave when he’s only just gotten back. We didn’t have much time to talk on the way back home. We haven’t had much time for anything. “Emma,” he murmurs. “The water isn’t safe for you right now. Please don’t get in it. Please.” “I won’t.” I really won’t. He said please, after all. He lifts my chin with the crook of his finger. His eyes hold all the gentleness and love in the world, with a pinch of mischief. “And take good notes in calculus, or I’ll be forced to cheat off you and for some weird reason that makes me feel guilty.” I wonder what Grom the Triton king would think of that. That Galen basically just stated his intention to keep doing human things. Galen pushes his lips against my forehead, then disentangles himself from me and leads me back toward the water. My body feels ten degrees cooler when his arms fall, and it’s got nothing to do with the temperature outside. We reach the others just in time to see Rayna all but throw herself at Toraf. I can’t help but smile as they kiss. It’s like watching Beauty and the Beast. And Toraf’s not the Beast.

The overall structure of the calculus is simple. The subject is defined by a fantastic leading idea, one basic axiom, a calm and profound intellectual invention, a deep property, two crucial definitions, one ancillary definition, one major theorem, and the fundamental theorem of the calculus. The fantastic leading idea: the real world may be understood in terms of the real numbers. The basic axiom: brings the real numbers into existence. The calm and profound invention: the mathematical function. The deep property: continuity. The crucial definitions: instantaneous speed and the area underneath a curve. The ancillary definition: a limit The major theorem: the mean value theorem. The fundamental theorem of the calculus is the fundamental theorem of the calculus. These are the massive load-bearing walls and buttresses of the subject.

As the sensations of motion and discreteness led to the abstract notions of the calculus, so may sensory experience continue thus to suggest problem for the mathematician, and so may she in turn be free to reduce these to the basic formal logical relationships involved. Thus only may be fully appreciated the twofold aspect of mathematics: as the language of a descriptive interpretation of the relationships discovered in natural phenomena, and as a syllogistic elaboration of arbitrary premise.

I took 17 computer science classes and made an A in 11 of them. 1 point away from an A in 3 of them and the rest of them didn't matter. Math is a tool for physics,chemistry,biology/basic computation and nothing else. CS I(Pascal Vax), CS II(Pascal Vax), Sr. Software Engineering, Sr. Distributed Systems, Sr. Research, Sr. Operating Systems, Sr. Unix Operating Systems, Data Structures, Sr. Object Oriented A&D, CS (perl/linux), Sr. Java Programming, Information Systems Design, Jr. Unix Operating Systems, Microprocessors, Programming Algorithms, Calculus I,II,III, B Differential Equations, TI-89 Mathematical Reasoning, 92 C++ Programming, Assembly 8086, Digital Computer Organization, Discrete Math I,II, B Statistics for the Engineering & Sciences (w/permutations & combinatorics) -- A-American Literature A-United States History 1865 CLEP-full year english CLEP-full year biology A-Psychology A-Environmental Ethics

If whole numbers and their ratios couldn’t even measure something as basic as the diagonal of a perfect square, then all was not number. This deflating letdown may explain why later Greek mathematicians always elevated geometry over arithmetic. Numbers couldn’t be trusted anymore. They were inadequate as a foundation for mathematics.

Distribution theory was one of the two great revolutions in mathematical analysis in the 20th century. It can be thought of as the completion of differential calculus, just as the other great revolution, measure theory (or Lebesgue integration theory), can be thought of as the completion of integral calculus. There are many parallels between the two revolutions. Both were created by young, highly individualistic French mathematicians (Henri Lebesgue and Laurent Schwartz). Both were rapidly assimilated by the mathematical community, and opened up new worlds of mathematical development. Both forced a complete rethinking of all mathematical analysis that had come before, and basically altered the nature of the questions that mathematical analysts asked.

Distribution theory was one of the two great revolutions in mathematical analysis in the 20th century. It can be thought of as the completion of differential calculus, just as the other great revolution, measure theory (or Lebesgue integration theory), can be thought of as the completion of integral calculus. There are many parallels between the two revolutions. Both were created by young, highly individualistic French mathematicians (Henri Lebesgue and Laurent Schwartz). Both were rapidly assimilated by the mathematical community, and opened up new worlds of mathematical development. Both forced a complete rethinking of all mathematical analysis that had come before, and basically altered the nature of the questions that mathematical analysts asked.

Radicals and exponents (also known as roots and powers) are two common — and oftentimes frustrating — elements of basic algebra.

Mathematics main goal is to describe the relationship between the points on the numberline by internationally recognized symbols. The most basic symbol involving the numberline is the equal sign (=).

Yet, as Brandon explained with a mixture of bitterness and regret, college proved to be the start of a long series of disappointments. Unable to pass calculus or physics, he switched his major from engineering to criminal justice. Still optimistic, he applied to several police departments upon graduation, excited about a future of “catching crooks.” The first department used a bewildering lottery system for hiring, and he didn’t make the cut. The second informed him that he had failed a mandatory spelling test (“I had a degree!”) and refused to consider his application. Finally, he became “completely turned off to this idea” when the third department disqualified him because of a minor incident in college in which he and his roommate “borrowed” a school-owned buffing machine as a harmless prank. Because he “could have been charged with a felony,” the department informed him, he was ineligible for police duty. Regrettably, his college had no record of the incident. Brandon had volunteered the information out of a desire to illustrate his honest and upstanding character and improve his odds of getting the job. With “two dreams deferred,”2 Brandon took a job as the nightshift manager of a clothing chain, hoping it would be temporary. Eleven years later, he describes his typical day, which consists of unloading shipments, steaming and pricing garments, and restocking the floor, as “not challenging at all. I don’t get to solve problems or be creative. I don’t get to work with numbers, and I am a numbers guy. I basically babysit a team and deal with personnel.” When his loans came out of deferment, he couldn’t afford the monthly payments and decided to get a master’s degree—partly to increase his earning potential and partly to put his loans back into deferment. After all, it had been “hammered into his head” that higher education was the key to success. He put on twenty-five pounds while working and going to school full-time for three years. He finally earned a master’s degree in government, paid for with more loans from “that mean lady Sallie Mae.”3 So far, Brandon has still not found a job that will pay him enough to cover his monthly loan and living expenses. He has managed to keep the loans in deferment by continually consolidating—a strategy that costs him $5,000 a year in interest. Taking

An essential pedagogic step here is to relegate the teaching of mathematical methods in economics to mathematics departments. Any mathematical training in economics, if it occurs at all, should come after students have at the very least completed course work in basic calculus, algebra and differential equations (the last being one about which most economists are woefully ignorant). This simultaneously explains why neoclassical economists obsess too much about proofs and why non-neoclassical economists, like those in the Circuit School, experience such difficulties in translating excellent verbal ideas about credit creation into coherent dynamic models of a monetary production economy.

The construction of a "problem calculus" in the sense of Heyting and Kolmogoroff yields a model of logic in which the theorem of the excluded middle does not appear among the basic formulas. The study of such a logic widens our insight into the basic elements of mathematics and, in particular, points out the special position of the so-called indirect proofs within mathematics.

We assume familiarity with programming, a basic understanding of computational performance issues, complexity theory, introductory level calculus and some of the terminology of graph theory.

Fortunately for investors, two substantial funds management organizations adhere to high fiduciary standards, adopted in the context of corporate cultures designed to serve investor interests. Vanguard and TIAA-CREF both operate on a not-for-profit basis, allowing the companies to make individual investor interests paramount in the funds management process. By emphasizing high-quality delivery of low-cost investment products, Vanguard and TIAA-CREF provide individual investors with valuable tools for the portfolio construction process. Ultimately, a passive index fund managed by a not-for-profit investment management organization represents the combination most likely to satisfy investor aspirations. Following Mies van der Rohe’s famous dictum—“less is more”—the rigid calculus of index-fund investing dominates the ornate complexity of active fund management. Pursuing investment with a firm devoted solely to satisfying investor interests unifies principal and agent, reducing the investment equation to its most basic form. Out of the enormous breadth and complexity of the mutual-fund world, the preferred solution for investors stands alone in stark simplicity.