Calculus Math Quotes

I don't want just a night or a week or a month with you. I want you all the time. I like you better than calculus, and math is the only thing that unites the universe.

Calculus was not math. It was a fucking science experiment gone wrong.

I think scientists have a valid point when they bemoan the fact that it's socially acceptable in our culture to be utterly ignorant of math, whereas it is a shameful thing to be illiterate.

I like you better than calculus, and maths is the only thing that unites the universe.

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

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?

Looking at numbers as groups of rocks may seem unusual, but actually it's as old as math itself. The word "calculate" reflects that legacy -- it comes from the Latin word calculus, meaning a pebble used for counting. To enjoy working with numbers you don't have to be Einstein (German for "one stone"), but it might help to have rocks in your head.

Incidentally, the little book Calculus Made Easy, by Silvanus Thompson, has helped generations of students master the subject.

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.

My sub doesn't pay for me,” he says, pulling me to my feet. “That just doesn't happen.” “But we ordered so much,” I say helplessly. “It made you happy,” he says simply. “Now I get to play with you. And that makes me happy.” “I don't think it's that simple an equation.” “Maybe not,” he concedes. “But then, if if sex were the same thing as math, a lot more people would be lining up to take calculus.

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.

That is what is marvelous about school, she realized: when you are in school, your talents are without number, and your promise is boundless. You ace a math test: you will one day work for NASA. The choir director asks you to sing a solo at the holiday concert: you are the next Mariah Carey. You score a goal, you win a poetry contest, you act in a play. And you are everything at once: actor, astronomer, gymnast, star. But at a certain point, you begin to feel your talents dropping away, like feathers from a molting bird. Cello lessons conflict with soccer practice. There aren't enough spots on the debating team. Calculus remains elusive. Until the day you realize that you cannot think of a single thing you are wonderful at.

... I succeeded at math, at least by the usual evaluation criteria: grades. Yet while I might have earned top marks in geometry and algebra, I was merely following memorized rules, plugging in numbers and dutifully crunching out answers by rote, with no real grasp of the significance of what I was doing or its usefulness in solving real-world problems. Worse, I knew the depth of my own ignorance, and I lived in fear that my lack of comprehension would be discovered and I would be exposed as an academic fraud -- psychologists call this "imposter syndrome".

[All phenomena] are equally susceptible of being calculated, and all that is necessary, to reduce the whole of nature to laws similar to those which Newton discovered with the aid of the calculus, is to have a sufficient number of observations and a mathematics that is complex enough.

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.

Everyone hated Calculus. Quadratic equations, parabolas, logarithms, trigonometry - you name it. It was like floating in an endless, frictionless void traveling at x miles per hour at a descension rate of one half the speed of gravity. Solve for x.

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?

ahh, calculus. the mathematics of change

Math has a tendency to reward you if you respect its symmetries" (Essence of Calculus, Chapter 1)

Math is a weave of many threads: the formal and the intuitive, the simple and the profound, the momentary and the eternal. Love the thread you love. But never mistake it for the tapestry.

Right. I don't believe in the idea that there are a few peculiar people capable of understanding math, and the rest of the world is normal. Math is a human discovery, and it's no more complicated than humans can understand. I had a calculus book once that said, 'What one fool can do, another can.' What we've been able to work out about nature may look abstract and threatening to someone who hasn't studied it, but it was fools who did it, and in the next generation, all the fools will understand it. There's a tendency to pomposity in all this, to make it deep and profound.

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]

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...

To a scholar, mathematics is music.

Stupid entropy ruins everything.

Nature—cue the theme from The Twilight Zone—somehow knows calculus.

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

Weight Watchers points is a beautiful system for someone who is absentminded about food. They aren’t the greatest for someone who has had eating disorders all her life. The world became numbers to me and I was doing more math than I ever had before. I got off Weight Watchers and went back to just counting calories. The world became different kinds of numbers, the old, familiar kind. This is how I eat now. The world is still numbers, but it is algebra, not calculus.

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.

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.

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.

Considering how many fools can calculate, it is surprising that it should be thought either a difficult or a tedious task for any other fool to learn how to master the same tricks. Some calculus-tricks are quite easy. Some are enormously difficult. The fools who write the textbooks of advanced mathematics - and they are mostly clever fools - seldom take the trouble to show you how easy the easy calculations are. On the contrary, they seem to desire to impress you with their tremendous cleverness by going about it in the most difficult way. Being myself a remarkably stupid fellow, I have had to unteach myself the difficulties, and now beg to present to my fellow fools the parts that are not hard. Master these thoroughly, and the rest will follow. What one fool can do, another can.

One other thing to keep in mind, though, is that Cantor's transfinite math will end up totally undercutting Aristotelian objections like the above (b) to Dedekind's proof, since Cantor's theory will constitute direct evidence that actually-infinite sets can be understood and manipulated, truly handled by the human intellect, just as velocity and acceleration are handled by calculus. So one thing to appreciate up front is that, however abstract infinite systems are, after Cantor they are most definitely not abstract in the nonreal/unreal way that unicorns are.

Come find us at lunch. We sit at the back table next to the biggest window.” She turns away without waiting for an answer, blond hair sweeping across her shoulders. Ezra watches them leave with a bemused expression, then turns to me. “I have a really strong feeling that on Wednesdays, they wear pink.” Ezra and I have most of the same classes that morning, except for right before lunch, when I head to AP calculus and Ezra goes to geometry. Math isn’t his strong suit. So I end up going to the cafeteria on my own. I make my way through the food line assuming that he’ll join me at any minute, but when I exit with a full tray, he’s still nowhere in sight.

If you're now noticing a certain family resemblance among this no-successive-instant problem, Zeno's Paradoxes, and some of the Real Line crunchers described in Paragraph 2c and -e, be advised that this is not a coincidence. They are all facets of the great continuity conundrum for mathematics, which is that (Infinity)-related entities can apparently be neither handled nor eliminated. Nowhere is this more evident than with 1/(Infinity)s. They're riddled with paradox and can't be defined, but if you banish them from math you end up having to posit an infinite density to any interval, in which the idea of succession makes no sense and no ordering of points in the interval can ever be complete, since between any two points there will be not just some other points but a whole infinity of them. Overall point: However good calculus is at quantifying motion and change, it can do nothing to solve the real paradoxes of continuity. Not without a coherent theory of (Infinity), anyway.

There are several different frameworks one could use to get a handle on the indeterminate vs. determinate question. The math version is calculus vs. statistics. In a determinate world, calculus dominates. You can calculate specific things precisely and deterministically. When you send a rocket to the moon, you have to calculate precisely where it is at all times. It’s not like some iterative startup where you launch the rocket and figure things out step by step. Do you make it to the moon? To Jupiter? Do you just get lost in space? There were lots of companies in the ’90s that had launch parties but no landing parties. “But the indeterminate future is somehow one in which probability and statistics are the dominant modality for making sense of the world. Bell curves and random walks define what the future is going to look like. The standard pedagogical argument is that high schools should get rid of calculus and replace it with statistics, which is really important and actually useful. There has been a powerful shift toward the idea that statistical ways of thinking are going to drive the future.” —PETER THIEL

Two mathematicians were having dinner. One was complaining: ‘The average person is a mathematical idiot. People cannot do arithmetic correctly, cannot balance a checkbook, cannot calculate a tip, cannot do percents, …’ The other mathematician disagreed: ‘You’re exaggerating. People know all the math they need to know.’ Later in the dinner the complainer went to the men’s room. The other mathematician beckoned the waitress to his table and said, ‘The next time you come past our table, I am going to stop you and ask you a question. No matter what I say, I want you to answer by saying “x squared.”‘ She agreed. When the other mathematician returned, his companion said, ‘I’m tired of your complaining. I’m going to stop the next person who passes our table and ask him or her an elementary calculus question, and I bet the person can solve it.’ Soon the waitress came by and he asked: ‘Excuse me, Miss, but can you tell me what the integral of 2x with respect to x is?’ The waitress replied: ‘x squared.’ The mathematician said, ‘See!’ His friend said, ‘Oh … I guess you were right.’ And the waitress said, ‘Plus a constant.

When I threw the stick at Jamie, I hadn't intended to hit him with it. But the moment it left my hand, I knew that's what was going to happen. I didn't yet know any calculus or geometry, but I was able to plot, with some degree of certainty, the trajectory of that stick. The initial velocity, the acceleration, the impact. The mathematical likelihood of Jamie's bloody cheek. It had good weight and heft, that stick. It felt nice to throw. And it looked damn fine in the overcast sky, too, flying end over end, spinning like a heavy, two-pronged pinwheel and (finally, indifferently, like math) connecting with Jamie's face. Jamie's older sister took me by the arm and she shook me. Why did you do that? What were you thinking? The anger I saw in her eyes. Heard in her voice. The kid I became to her then, who was not the kid I thought I was. The burdensome regret. I knew the word "accident" was wrong, but I used it anyway. If you throw a baseball at a wall and it goes through a window, that is an accident. If you throw a stick directly at your friend and it hits your friend in the face, that is something else. My throw had been something of a lob and there had been a good distance between us. There had been ample time for Jamie to move, but he hadn't moved. There had been time for him to lift a hand and protect his face from the stick, but he hadn't done that either. He just stood impotent and watched it hit him. And it made me angry: That he hadn't tried harder at a defense. That he hadn't made any effort to protect himself from me. What was I thinking? What was he thinking? I am not a kid who throws sticks at his friends. But sometimes, that's who I've been. And when I've been that kid, it's like I'm watching myself act in a movie, reciting somebody else's damaging lines. Like this morning, over breakfast. Your eyes asking mine to forget last night's exchange. You were holding your favorite tea mug. I don't remember what we were fighting about. It doesn't seem to matter any more. The words that came out of my mouth then, deliberate and measured, temporarily satisfying to throw at the bored space between us. The slow, beautiful arc. The spin and the calculated impact. The downward turn of your face. The heavy drop in my chest. The word "accident" was wrong. I used it anyway.

Explaining evolution to a fundamentalist Christian is like trying to explain Calculus to someone with absolutely no grasp of Maths.

A few books that I've read.... Pascal, an Introduction to the Art and Science of Programming by Walter Savitch Programming algorithms Introduction to Algorithms, 3rd Edition (The MIT Press) Data Structures and Algorithms in Java Author: Michael T. Goodrich - Roberto Tamassia - Michael H. Goldwasser The Algorithm Design Manual Author: Steven S Skiena Algorithm Design Author: Jon Kleinberg - Éva Tardos Algorithms + Data Structures = Programs Book by Niklaus Wirth Discrete Math Discrete Mathematics and Its Applications Author: Kenneth H Rosen Computer Org Structured Computer Organization Andrew S. Tanenbaum Introduction to Assembly Language Programming: From 8086 to Pentium Processors (Undergraduate Texts in Computer Science) Author: Sivarama P. Dandamudi Distributed Systems Distributed Systems: Concepts and Design Author: George Coulouris - Jean Dollimore - Tim Kindberg - Gordon Blair Distributed Systems: An Algorithmic Approach, Second Edition (Chapman & Hall/CRC Computer and Information Science Series) Author: Sukumar Ghosh Mathematical Reasoning Mathematical Reasoning: Writing and Proof Version 2.1 Author: Ted Sundstrom An Introduction to Mathematical Reasoning: Numbers, Sets and Functions Author: Peter J. Eccles Differential Equations Differential Equations (with DE Tools Printed Access Card) Author: Paul Blanchard - Robert L. Devaney - Glen R. Hall Calculus Calculus: Early Transcendentals Author: James Stewart And more....

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

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

Unfortunately, calculus can epitomize what’s wrong with math education. Most lessons feature contrived examples, arcane proofs, memorization and abstract symbol manipulation that body slam our intuition and enthusiasm before they can put on their gloves. It really shouldn’t be this way.

Is there an evolutionary consequence to this distinctive quality of story? Researchers have imagined so. We prevailed, in large part, because we are an intensely social species. We are able to live and work in groups. Not in perfect harmony, but with sufficient cooperation to thoroughly upend the calculus of survival. It is not just safety in numbers. It is innovate, participate, delegate, and collaborate in numbers. And essential to such successful group living are the very insights into the variety of human experience we’ve absorbed through story. As psychologist Jerome Bruner noted, “We organize our experience and our memory of human happenings mainly in the form of narrative,”37 leading him to doubt that “such collective life would be possible were it not for our human capacity to organize and communicate experience in narrative form.”38 Through narrative we explore the range of human behavior, from societal expectation to heinous transgression. We witness the breadth of human motivation, from lofty ambition to reprehensible brutality. We encounter the scope of human disposition from triumphant victory to heartrending loss. As literary scholar Brian Boyd has emphasized, narratives thus make “the social landscape more navigable, more expansive, more open with possibilities,” instilling in us a “craving for understanding our world not only in terms of our own direct experience, but through the experiences of others—and not only real others.”39 Whether told through myths, stories, fables, or even embellished accounts of daily events, narratives are the key to our social nature. With math we commune with other realities; with story we commune with other minds.

At first, calculus was mainly directed toward the study of physics, and many of the great seventeenth- and eighteenth-century mathematicians were also physicists.

I sat down before I could de something stupid, like trip on the math homework scattered all over my floor and fall out my window. Death by calculus. I couldn’t imagine a worse way to go.

But formal mathematics without common sense—without the constant interplay between abstract reasoning and our intuitions about quantity, time, space, motion, behavior, and uncertainty—would just be a sterile exercise in rule-following and bookkeeping. In other words, math would actually be what the peevish calculus student believes it to be.

Calculus is the mathematics of change. It describes everything from the spread of epidemics to the zigs and zags of a well-thrown curveball. The subject is gargantuan—and so are its textbooks.

My junior year, I tested into the honors Advanced Math class—a hybrid of trigonometry, advanced algebra, and pre-calculus. The class’s instructor, Ron Selby, enjoyed legendary status among the students for his brilliance and high demands. In twenty years, he had never missed a day of school. According to Middletown High School legend, a student called in a bomb threat during one of Selby’s exams, hiding the explosive device in a bag in his locker. With the entire school evacuated outside, Selby marched into the school, retrieved the contents of the kid’s locker, marched outside, and threw those contents into a trash can. “I’ve had that kid in class; he’s not smart enough to make a functioning bomb,” Selby told the police officers gathered at the school. “Now let my students go back to class to finish their exams.

What she [Winterer] said was, in a way, not that different from what Ivonne had heard from Ileana after her last two tests: Things really aren't equal. They really aren't fair. You really are way behind where you deserve to be, and it really is going to be vary hard to catch up. Where Winterer's message diverged from Ileana's was in what she said to Ivonne next: Where you stand in calculus right now has nothing to do with who you really are. Who you really are is a mathematician. It's not your fault that you're behind. And it's not your destiny. It is going to be hard to erase the disparity between your math knowledge and Marco's. But if you want that knowledge, you can get it. And if you decide you do want to get it, I'm here to help.

Mathematics consists of processes independent of the number. You must remove the number from your thinking and instead dwell on the idea and process of the underlying logic. The faster you do this, the quicker math will begin to make sense to you. Then maybe your life, but defiantly your grade, will get better.

Many school programs seem to offer either The Cultural Literacy Track or The Vocational Track. The Cultural Literacy programs are designed for the “smart kids” who are going to go on to ever-higher levels of both education and financial success. This track, with no pretense of being real world, includes classes on classics, foreign languages, and math theory (such as calculus). It is a curriculum based on “teach what has been taught.” The Vocational programs are for the “remedial kids” who are going to have only blue-collar futures if they are in high school (taking classes such as wood working) or inflexible paraprofessional paths if they are in college (such as degrees in physical therapy). This two-tier approach is an immoral sorting system with crippling consequences. Maybe worse, it also presents a false dichotomy. Instead, true wisdom comes from a synthesis of those two perspectives and more. The

My math teacher sucked as a kid in school. I'd ask him why do you do the problem that way and he would say "because the book says to do it." Later I learned algebra and advanced calculus because a guy explained the application to me. I now know that “If you can't explain it to a six-year-old, you don't understand it yourself.

I have always had an uncomfortable relationship with math. I don’t like numbers for the sake of numbers. I am not impressed by fancy formulas that have no real-world application. I particularly disliked high school calculus for the simple reason that no one ever bothered to tell me why I needed to learn it. What is the area beneath a parabola? Who cares?

That’s calculus in a nutshell. It takes a problem that can’t be done with regular math because things are constantly changing — the changing quantities show up on a graph as curves — it zooms in on the curve till it becomes straight, and then it finishes off the problem with regular math.

So I went down to register at De Anza and saw that the classes for chemistry, physics, and calculus were all full. What? I couldn’t believe it. Here I was—the star science and math student at my high school and all set to be an engineer—and the three most important courses I needed were locked out. It was horrible. I called the chemistry teacher on the phone, who said if I showed up I could probably get in, but I couldn’t shake this terrible feeling that my future was shutting down. I could see it shutting down right in front of me. I felt my whole academic life was going to be messed up right from the start. And it was right then that I changed my mind, and decided to see if it was still possible to go to Colorado.

Taken together, they laid the future cornerstone of what comes to be called calculus, or the mathematics of infinity (Archimedes was the first mathematician to use the concept of infinity in his work). Without it, modern math and science as we know it would not exist.

The view on the equations was even more stupid--the extraterrestrials thought that because the equations used scientific notation, the imaginary unit, sigma notation, and alphabetical letters that were magically and ironically used in mathematics, they theorized and overall concluded that these equations were indisputably correct, since the hoo-mans (humans) on Earth used a multitude of calculus symbols and large numbers to learn more about the universe.

The word "Formal" in this context is a euphemism for "useless

Aside from hijacking people’s abilities, stereotypes also do damage by making people feel they don’t belong. Many minorities drop out of college and many women drop out of math and science because they just don’t feel they fit in. To find out how this happens, we followed college women through their calculus course. This is often when students decide whether math, or careers involving math, are right for them. Over the semester, we asked the women to report their feelings about math and their sense of belonging in math. For example, when they thought about math, did they feel like a full-fledged member of the math community or did they feel like an outsider; did they feel comfortable or did they feel anxious; did they feel good or bad about their math skills?

Calculus is the mathematics of change. It describes everything from the spread of epidemics to the zigs and zags of a well-thrown curveball. The subject is gargantuan—and so are its textbooks. Many exceed a thousand pages and work nicely as doorstops.

So I went to Case, and the Dean of Case says to us, says, it’s a all men’s school, says, “Men, look at, look to the person on your left, and the person on your right. One of you isn’t going to be here next year; one of you is going to fail.” So I get to Case, and again I’m studying all the time, working really hard on my classes, and so for that I had to be kind of a machine. I, the calculus book that I had, in high school we — in high school, as I said, our math program wasn’t much, and I had never heard of calculus until I got to college. But the calculus book that we had was great, and in the back of the book there were supplementary problems that weren’t, you know, that weren’t assigned by the teacher. The teacher would assign, so this was a famous calculus text by a man named George Thomas, and I mention it especially because it was one of the first books published by Addison-Wesley, and I loved this calculus book so much that later I chose Addison-Wesley to be the publisher of my own book. But Thomas’s Calculus would have the text, then would have problems, and our teacher would assign, say, the even numbered problems, or something like that. I would also do the odd numbered problems. In the back of Thomas’s book he had supplementary problems, the teacher didn’t assign the supplementary problems; I worked the supplementary problems. I was, you know, I was scared I wouldn’t learn calculus, so I worked hard on it, and it turned out that of course it took me longer to solve all these problems than the kids who were only working on what was assigned, at first. But after a year, I could do all of those problems in the same time as my classmates were doing the assigned problems, and after that I could just coast in mathematics, because I’d learned how to solve problems. So it was good that I was scared, in a way that I, you know, that made me start strong, and then I could coast afterwards, rather than always climbing and being on a lower part of the learning curve.

I like you better than calculus, and math is the only thing that unites the universe.

Which was not very smart. Indeed the most giddy of high school cheerleaders, say, managing to be friendly with everyone and therefore universally popular, seemed to Sax to be exercising an intelligence at least as powerful as any awkward brilliant mathematician’s—the calculus of human interaction being so much more subtle and variable than any physics, somewhat like the emerging field of math called cascading recombinant chaos, only less simple. So that there were at least two kinds of intelligence, and probably many more: spatial, aesthetic, moral or ethical, interactional, analytic, synthetic, and so forth. And it was those people who were intelligent in a number of different ways who were truly exceptional, who stood out as something special.

calculus

The modulus (%) and the floor division (//) operations are not valid for complex numbers.

Because of Stephen King, I began to write. If it weren't because of him, I would have been an engineer--I am very good with math and studied all the calculus courses in college. I loved his stories, so I became a writer.

In the cubicle facing him, Anita was writing a story about a fifth-grade math whiz who had recently won a master’s-studies-level multivariable calculus competition.