Algebra 2 Quotes

THE FIRST TEN LIES THEY TELL YOU IN HIGH SCHOOL 1. We are here to help you. 2. You will have time to get to your class before the bell rings. 3. The dress code will be enforced. 4. No smoking is allowed on school grounds. 5. Our football team will win the championship this year. 6. We expect more of you here. 7. Guidance counselors are always available to listen. 8. Your schedule was created with you in mind. 9. Your locker combination is private. 10. These will be the years you look back on fondly. TEN MORE LIES THEY TELL YOU IN HIGH SCHOOL 1. You will use algebra in your adult lives. 2. Driving to school is a privilege that can be taken away. 3. Students must stay on campus during lunch. 4. The new text books will arrive any day now. 5. Colleges care more about you than your SAT scores. 6. We are enforcing the dress code. 7. We will figure out how to turn off the heat soon. 8. Our bus drivers are highly trained professionals. 9. There is nothing wrong with summer school. 10. We want to hear what you have to say.

What grinds me the most is we're sending kids out into the world who don't know how to balance a checkbook, don't know how to apply for a loan, don't even know how to properly fill out a job application, but because they know the quadratic formula we consider them prepared for the world` With that said, I'll admit even I can see how looking at the equation x -3 = 19 and knowing x =22 can be useful. I'll even say knowing x =7 and y= 8 in a problem like 9x - 6y= 15 can be helpful. But seriously, do we all need to know how to simplify (x-3)(x-3i)?? And the joke is, no one can continue their education unless they do. A student living in California cannot get into a four-year college unless they pass Algebra 2 in high school. A future psychologist can't become a psychologist, a future lawyer can't become a lawyer, and I can't become a journalist unless each of us has a basic understanding of engineering. Of course, engineers and scientists use this shit all the time, and I applaud them! But they don't take years of theater arts appreciation courses, because a scientist or an engineer doesn't need to know that 'The Phantom of the Opoera' was the longest-running Broadway musical of all time. Get my point?

Dear Algebra, Stop asking us to find your X. She’s not coming back,

What the hell was the matter with these people? How did they not see that of all the people on the planet, she was probably the least qualified to help them with their emotional problems? It was like asking a dog to do algebra.

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.

It’s sort of weird to be hugged by your Algebra teacher. That’s all I have to say.

Myth can be a kind of human algebra, which makes it easier to manipulate truth about ourselves.

There had always been the rumour that one of the old heptarchs had squirreled away a collection of heretical calendrical erotica. Just how you made abstract algebra erotic was going to have to remain a mystery.

Erik said: “But the Aryan race must be superior—we rule the world!” “Your Nazi friends don’t know any history,” Father said. “The Ancient Egyptians built the pyramids when Germans were living in caves. Arabs ruled the world in the Middle Ages—the Muslims were doing algebra when German princes could not write their own names. It’s nothing to do with race.

Certainly not! I didn't build a machine to solve ridiculous crossword puzzles! That's hack work, not Great Art! Just give it a topic, any topic, as difficult as you like..." Klapaucius thought, and thought some more. Finally he nodded and said: "Very well. Let's have a love poem, lyrical, pastoral, and expressed in the language of pure mathematics. Tensor algebra mainly, with a little topology and higher calculus, if need be. But with feeling, you understand, and in the cybernetic spirit." "Love and tensor algebra?" Have you taken leave of your senses?" Trurl began, but stopped, for his electronic bard was already declaiming: Come, let us hasten to a higher plane, Where dyads tread the fairy fields of Venn, Their indices bedecked from one to n, Commingled in an endless Markov chain! Come, every frustum longs to be a cone, And every vector dreams of matrices. Hark to the gentle gradient of the breeze: It whispers of a more ergodic zone. In Reimann, Hilbert or in Banach space Let superscripts and subscripts go their ways. Our asymptotes no longer out of phase, We shall encounter, counting, face to face. I'll grant thee random access to my heart, Thou'lt tell me all the constants of thy love; And so we two shall all love's lemmas prove, And in bound partition never part. For what did Cauchy know, or Christoffel, Or Fourier, or any Boole or Euler, Wielding their compasses, their pens and rulers, Of thy supernal sinusoidal spell? Cancel me not--for what then shall remain? Abscissas, some mantissas, modules, modes, A root or two, a torus and a node: The inverse of my verse, a null domain. Ellipse of bliss, converge, O lips divine! The product of our scalars is defined! Cyberiad draws nigh, and the skew mind Cuts capers like a happy haversine. I see the eigenvalue in thine eye, I hear the tender tensor in thy sigh. Bernoulli would have been content to die, Had he but known such a^2 cos 2 phi!

In the early part of the ninth century, Muhammad ibn Musa al-Khwarizmi, a mathematician working in Baghdad, wrote a seminal textbook in which he highlighted the usefulness of restoring a quantity being subtracted (like 2, above) by adding it to the other side of an equation. He called this process al-jabr (Arabic for “restoring”), which later morphed into “algebra.” Then, long after his death, he hit the etymological jackpot again. His own name, al-Khwarizmi, lives on today in the word “algorithm.

TEN MORE LIES THEY TELL YOU IN HIGH SCHOOL 1. You will use algebra in your adult lives. 2. Driving to school is a privilege that can be taken away. 3. Students must stay on campus during lunch. 4. The new text books will arrive any day now. 5. Colleges care more about you than your SAT scores. 6. We are enforcing the dress code. 7. We will figure out how to turn off the heat soon. 8. Our bus drivers are highly trained professionals. 9. There is nothing wrong with summer school. 10. We want to hear what you have to say.

For those with a math allergy, my duck soup may contain Algebra. 2X=2, solve for X, may cause an extreme reaction. Ask your doctor if BearPaw Duck Farm's SwimmingBird Soup is right for you.

there are teachers who without much fanfare take the students who others say “can't”—can't read great literature, can't do algebra or calculus, can't and don't want to learn—and turn them into scholars who can.

She liked numbers and sums. She devised a game in which each number was a family member and the “answer” made a family grouping with a story to it. Naught was a babe in arms. He gave no trouble. Whenever he appeared you just “carried” him. The figure 1 was a pretty baby girl just learning to walk, and easy to handle; 2 was a baby boy who could walk and talk a little. He went into family life (into sums, etc.) with very little trouble. And 3 was an older boy in kindergarten, who had to be watched a little. Then there was 4, a girl of Francie’s age. She was almost as easy to “mind” as 2. The mother was 5, gentle and kind. In large sums, she came along and made everything easy the way a mother should. The father, 6, was harder than the others but very just. But 7 was mean. He was a crotchety old grandfather and not at all accountable for how he came out. The grandmother, 8, was hard too, but easier to understand than 7. Hardest of all was 9. He was company and what a hard time fitting him into family life! When Francie added a sum, she would fix a little story to go with the result. If the answer was 924, it meant that the little boy and girl were being minded by company while the rest of the family went out. When a number such as 1024 appeared, it meant that all the little children were playing together in the yard. The number 62 meant that papa was taking the little boy for a walk; 50 meant that mama had the baby out in the buggy for an airing and 78 meant grandfather and grandmother sitting home by the fire of a winter’s evening. Each single combination of numbers was a new set-up for the family and no two stories were ever the same. Francie took the game with her up into algebra. X was the boy’s sweetheart who came into the family life and complicated it. Y was the boy friend who caused trouble. So arithmetic was a warm and human thing to Francie and occupied many lonely hours of her time.

There are two moments in the course of education where a lot of kids fall off the math train. The first comes in the elementary grades, when fractions are introduced. Until that moment, a number is a natural number, one of the figures 0, 1, 2, 3 . . . It is the answer to a question of the form “how many.”* To go from this notion, so primitive that many animals are said to understand it, to the radically broader idea that a number can mean “what portion of,” is a drastic philosophical shift. (“God made the natural numbers,” the nineteenth-century algebraist Leopold Kronecker famously said, “and all the rest is the work of man.”) The second dangerous twist in the track is algebra. Why is it so hard? Because, until algebra shows up, you’re doing numerical computations in a straightforwardly algorithmic way. You dump some numbers into the addition box, or the multiplication box, or even, in traditionally minded schools, the long-division box, you turn the crank, and you report what comes out the other side. Algebra is different. It’s computation backward. When you’re asked to solve

Well, three reasons. First, because I've been thinking about our Theorem and I have a question. How does it work if you're gay?" "Huh?" "Well it's all graph-going up means boy dumps girls and graph going-down means girl dumps boy, right? But what if they're both boys?" "It doesn't matter. You just assign a position to each person. Instead of being 'b' and 'g', it could just as easily be 'b1' and 'g', it could just as easily be 'bi' and 'b2.' That's how algebra works.

I read it: "A man earned daily for 5 days and 3 times as much as he paid for his board, after which he was obliged to be idle 4 days," it said. "Upon counting his money after paying for his board he found that he had 2 ten-doller bills and 4 dollers. How much did he pay for the board, and what were his wages?" "All right. Think now," Weaver said. "How would you begin to solve it? What's your X?" I thought. Very hard. For quite some time. About the man and his meager wages and shabby boardinghouse and lonely life. "Where did he work?" I finally asked. "What? It doesn't matter, Matt. Just assign an X to-" "A mill, I bet," I said, picturing the man's threadbare clothing, his worn shoes. "A woolen mill. Why do you think he was obliged to be idle?" "I don't know why. Look, just-" "I bet he got sick," I said, clutching Weaver's arm. "Or maybe business wasn't good, and his boss had no work for him. I wonder if he had a family in the country. It would be a terrible thing, wouldn't it, if he had children to feed and no work? Maybe his wife was poorly, too. And I bet he had..." "Damn it, Mattie, this is algebra, not composition!" Weaver said, glaring at me. "Sorry," I said, feeling like a hopeless case.

Mathematicians call it “the arithmetic of congruences.” You can think of it as clock arithmetic. Temporarily replace the 12 on a clock face with 0. The 12 hours of the clock now read 0, 1, 2, 3, … up to 11. If the time is eight o’clock, and you add 9 hours, what do you get? Well, you get five o’clock. So in this arithmetic, 8 + 9 = 5; or, as mathematicians say, 8 + 9 ≡ 5 (mod 12), pronounced “eight plus nine is congruent to five, modulo twelve.

TEN MORE LIES THEY TELL YOU IN HIGH SCHOOL 1. You will use algebra in your adult lives. 2. Driving to school is a privilege that can be taken away. 3. Students must stay on campus for lunch. 4. The new textbooks will arrive any day now. 5. Colleges care about more than your SAT scores. 6. We are enforcing the dress code. 7. We will figure out how to turn off the heat soon. 8. Our bus drivers are highly trained professionals. 9. There is nothing wrong with summer school. 10. We want to hear what you have to say.

hero’s gotta do. Even if he’d rather be doing anything else—like algebra or going to the dentist. I hang a right at the corner bakery and make a beeline for Keystone Police Station. Why the police station? Well, it’s not because I’m trying to stuff this Godzilla wannabe into a human-sized jail cell. That’s impossible, although it sure would be nice. No, I’m heading for the police station because that’s where TechnocRat told me to meet him. He said he had a big solution for our not-so-little problem. And he better be right, because we’re coming in fast, so I hope he’s ready to deliver on his end of the deal. THUMP! My feet fly off the pavement. Every time that over-sized lizard takes a step,

Homework _Yes _No 1. Did you make a serious effort to understand the text? (Just hunting for relevant worked-out examples doesn’t count.) _Yes _No 2. Did you work with classmates on homework problems, or at least check your solutions with others? _Yes _No 3. Did you attempt to outline every homework problem solution before working with classmates? Test Preparation The more “Yes” responses you recorded, the better your preparation for the test. If you recorded two or more “No” responses, think seriously about making some changes in how you prepare for the next test. _Yes _No 4. Did you participate actively in homework group discussions (contributing ideas, asking questions)? _Yes _No 5. Did you consult with the instructor or teaching assistants when you were having trouble with something? _Yes _No 6. Did you understand ALL of your homework problem solutions when they were handed in? _Yes _No 7. Did you ask in class for explanations of homework problem solutions that weren’t clear to you? _Yes _No 8. If you had a study guide, did you carefully go through it before the test and convince yourself that you could do everything on it? _Yes _No 9. Did you attempt to outline lots of problem solutions quickly, without spending time on the algebra and calculations? _Yes _No 10. Did you go over the study guide and problems with classmates and quiz one another? _Yes _No 11. If there was a review session before the test, did you attend it and ask questions about anything you weren’t sure about? _Yes _No 12. Did you get a reasonable night’s sleep before the test? (If your answer is no, your answers to 1–11 may not matter.) _Yes _No TOTAL

You might object that people were asked ‘What do you think?' rather than 'What do you feel?', but this is a common misperception. Referendums and elections are always about human feelings, not about human rationality. If democracy were a matter of rational decision- making, there would be absolutely no reason to give all people equal voting rights - or perhaps any voting rights. There is ample evidence that some people are far more knowledgeable and rational than others, certainly when it comes to specific economic and political questions.2 In the wake of the Brexit vote, eminent biologist Richard Dawkins protested that the vast majority of the British public - including himself - should never have been asked to vote in the referendum, because they lacked the necessary background in economics and political science. 'You might as well call a nationwide plebiscite to decide whether Einstein got his algebra right, or let passengers vote on which runway the pilot should land.' (page 36)

There are two moments in the course of education where a lot of kids fall off the math train. The first comes in the elementary grades, when fractions are introduced. Until that moment, a number is a natural number, one of the figures 0, 1, 2, 3 . . . It is the answer to a question of the form “how many.”* To go from this notion, so primitive that many animals are said to understand it, to the radically broader idea that a number can mean “what portion of,” is a drastic philosophical shift. (“God made the natural numbers,” the nineteenth-century algebraist Leopold Kronecker famously said, “and all the rest is the work of man.”) The second dangerous twist in the track is algebra. Why is it so hard? Because, until algebra shows up, you’re doing numerical computations in a straightforwardly algorithmic way. You dump some numbers into the addition box, or the multiplication box, or even, in traditionally minded schools, the long-division box, you turn the crank, and you report what comes out the other side. Algebra is different. It’s computation backward.

we have much to learn from the struggles in Alabama and Mississippi in the early 1960s. In the spring of 1963 the Southern Christian Leadership Conference led by Dr. King launched a “fill the jails” campaign to desegregate downtown department stores and schools in Birmingham. But few local blacks were coming forward. Black adults were afraid of losing their jobs, local black preachers were reluctant to accept the leadership of an “Outsider,” and city police commissioner Bull Connor had everyone intimidated. Facing a major defeat, King was persuaded by his aide, James Bevel, to allow any child old enough to belong to a church to march. So on D-day, May 2, before the eyes of the whole nation, thousands of schoolchildren, many of them first graders, joined the movement and were beaten, fire-hosed, attacked by police dogs, and herded off to jail in paddy wagons and school buses. The result was what has been called the “Children’s Miracle.” Inspired and shamed into action, thousands of adults rushed to join the movement. All over the country rallies were called to express outrage against Bull Connor’s brutality. Locally, the power structure was forced to desegregate lunch counters and dressing rooms in downtown stores, hire blacks to work downtown, and begin desegregating the schools. Nationally, the Kennedy administration, which had been trying not to alienate white Dixiecrat voters, was forced to begin drafting civil rights legislation as the only way to forestall more Birminghams. The next year as part of Mississippi Freedom Summer, activists created Freedom Schools because the existing school system (like ours today) had been organized to produce subjects, not citizens. People in the community, both children and adults, needed to be empowered to exercise their civil and voting rights. A mental revolution was needed. To bring it about, reading, writing, and speaking skills were taught through discussions of black history, the power structure, and building a movement. Everyone took this revolutionary civics course, then chose from more academic subjects such as algebra and chemistry. All over Mississippi, in church basements and parish halls, on shady lawns and in abandoned buildings, volunteer teachers empowered thousands of children and adults through this community curriculum. The Freedom Schools of 1964 demonstrated that when Education involves young people in making community changes that matter to them, when it gives meaning to their lives in the present instead of preparing them only to make a living in the future, young people begin to believe in themselves and to dream of the future.

What this means is that the (Infinity) of points involved in continuity is greater than the (Infinity) of points comprised by any kind of discrete sequence, even an infinitely dense one. (2) Via his Diagonal Proof that c is greater than Aleph0, Cantor has succeeded in characterizing arithmetical continuity entirely in terms of order, sets, denumerability, etc. That is, he has characterized it 100% abstractly, without reference to time, motion, streets, noses, pies, or any other feature of the physical world-which is why Russell credits him with 'definitively solving' the deep problems behind the dichotomy. (3) The D.P. also explains, with respect to Dr. G.'s demonstration back in Section 2e, why there will always be more real numbers than red hankies. And it helps us understand why rational numbers ultimately take up 0 space on the Real Line, since it's obviously the irrational numbers that make the set of all reals nondenumerable. (4) An extension of Cantor's proof helps confirm J. Liouville's 1851 proof that there are an infinite number of transcendental irrationals in any interval on the Real Line. (This is pretty interesting. You'll recall from Section 3a FN 15 that of the two types of irrationals, transcendentals are the ones like pi and e that can't be the roots of integer-coefficient polynomials. Cantor's proof that the reals' (Infinity) outweighs the rationals' (Infinity) can be modified to show that it's actually the transcendental irrationals that are nondenumerable and that the set of all algebraic irrationals has the same cardinality as the rationals, which establishes that it's ultimately the transcendetnal-irrational-reals that account for the R.L.'s continuity.)

She liked numbers and sums. She devised a game in which each number was a family member and the “answer” made a family grouping with a story to it. Naught was a babe in arms. He gave no trouble. Whenever he appeared you just “carried” him. The figure 1 was a pretty baby girl just learning to walk, and easy to handle; 2 was a baby boy who could walk and talk a little. He went into family life (into sums, etc.) with very little trouble. And 3 was an older boy in kindergarten, who had to be watched a little. Then there was 4, a girl of Francie’s age. She was almost as easy to “mind” as 2. The mother was 5, gentle and kind. In large sums, she came along and made everything easy the way a mother should. The father, 6, was harder than the others but very just. But 7 was mean. He was a crotchety old grandfather and not at all accountable for how he came out. The grandmother, 8, was hard too, but easier to understand than 7. Hardest of all was 9. He was company and what a hard time fitting him into family life! When Francie added a sum, she would fix a little story to go with the result. If the answer was 924, it meant that the little boy and girl were being minded by company while the rest of the family went out. When a number such as 1024 appeared, it meant that all the little children were playing together in the yard. The number 62 meant that papa was taking the little boy out for a walk; 50 meant that mama had the baby out in the buggy for an airing and 78 meant grandfather and grandmother sitting home by the fire of a winter’s evening. Each single combination of numbers was a new set-up for the family and no two stories were ever the same. Francie took the game with her up into algebra. X was the boy’s sweetheart who came into the family life and complicated it. Y was the boy friend who caused trouble. So arithmetic was a warm and human thing to Francie and occupied many lonely hours of her time.

Early in the boob-emerging years, I had no boobs, and I was touchy about it. Remember in middle school algebra class, you’d type 55378008 on your calculator, turn it upside down, and hand it to the flat-chested girl across the aisle? I was that girl, you bi-yotch. I would have died twice if any of the boys had mentioned my booblets. Last year, I thought my boobs had progressed quite nicely. And I progressed from the one-piece into a tankini. But I wasn’t quite ready for any more exposure. I didn’t want the boys to treat me like a girl. Now I did. So today I’d worn a cute little bikini. Over that, I still wore Adam’s cutoff jeans. Amazingly, they looked sexy, riding low on my hips, when I traded the football T-shirt for a pink tank that ended above my belly button and hugged my figure. I even had a little cleavage. I was so proud. Sean was going to love it. Mrs. Vader stared at my chest, perplexed. Finally she said, “Oh, I get it. You’re trying to look hot.” “Thank you!” Mission accomplished. “Here’s a hint. Close your legs.” I snapped my thighs together on the stool. People always scolded me for sitting like a boy. Then I slid off the stool and stomped to the door in a huff. “Where do you want me?” She’d turned back to the computer. “You’ve got gas.” Oh, goody. I headed out the office door, toward the front dock to man the gas pumps. This meant at some point during the day, one of the boys would look around the marina office and ask, “Who has gas?” and another boy would answer, “Lori has gas.” If I were really lucky, Sean would be in on the joke. The office door squeaked open behind me. “Lori,” Mrs. Vader called. “Did you want to talk?” Noooooooo. Nothing like that. I’d only gone into her office and tried to start a conversation. Mrs. Vader had three sons. She didn’t know how to talk to a girl. My mother had died in a boating accident alone on the lake when I was four. I didn’t know how to talk to a woman. Any convo between Mrs. Vader and me was doomed from the start. “No, why?” I asked without turning around. I’d been galloping down the wooden steps, but now I stepped very carefully, looking down, as if I needed to examine every footfall so I wouldn’t trip. “Watch out around the boys,” she warned me. I raised my hand and wiggled my fingers, toodle-dee-doo, dismissing her. Those boys were harmless. Those boys had better watch out for me.

I’m mean? That’s the worst you can throw at me?” “Mean and self-pitying. Does that make it better?” “And what are you, Astrid?” he shouted. “A smug know-it-all! You point your finger at me and say, ‘Hey, Sam, you make the decisions, and you take all the heat.’” “Oh, it’s my fault? No way. I didn’t anoint you.” “Yeah, you did, Astrid. You guilted me into it. You think I don’t know what you’re all about? You used me to protect Little Pete. You use me to get your way. You manipulate me anytime you feel like it.” “You really are a jerk, you know that?” “No, I’m not a jerk, Astrid. You know what I am? I’m the guy getting people killed,” Sam said quietly. Then, “My head is exploding from it. I can’t get my brain around it. I can’t do this. I can’t be that guy, Astrid, I’m a kid, I should be studying algebra or whatever. I should be hanging out. I should be watching TV.” His voice rose, higher and louder till he was screaming. “What do you want from me? I’m not Little Pete’s father. I’m not everybody’s father. Do you ever stop to think what people are asking me to do? You know what they want me to do? Do you? They want me to kill my brother so the lights will come back on. They want me to kill kids! Kill Drake. Kill Diana. Get our own kids killed. “That’s what they ask. Why not, Sam? Why aren’t you doing what you have to do, Sam? Tell kids to get eaten alive by zekes, Sam. Tell Edilio to dig some more holes in the square, Sam.” He had gone from yelling to sobbing. “I’m fifteen years old. I’m fifteen.” He sat down hard on the edge of the bed. “Oh, my God, Astrid. It’s in my head, all these things. I can’t get rid of them. It’s like some filthy animal inside my head and I will never, ever, ever get rid of it. It makes me feel so bad. It’s disgusting. I want to throw up. I want to die. I want someone to shoot me in the head so I don’t have to think about everything.” Astrid was beside him, and her arms were around him. He was ashamed, but he couldn’t stop the tears. He was sobbing like he had when he was a little kid, like when he had a nightmare. Out of control. Sobbing. Gradually the spasms slowed. Then stopped. His breathing went from ragged to regular. “I’m really glad the lights weren’t on,” Sam said. “Bad enough you had to hear it.” “I’m falling apart,” he said. Astrid gave no answer, just held him close. And after what felt like a very long time, Sam moved away from her, gently putting distance between them again. “Listen. You won’t ever tell anyone…” “No. But, Sam…” “Please don’t tell me it’s okay,” Sam said. “Don’t be nice to me anymore. Don’t even tell me you love me. I’m about a millimeter from falling apart again.” “Okay.

The influence of the langues d’oc and d’oïl produced a situation in which French had started exporting itself even before it had become a fully developed language with a coherent writing system. Between the tenth and fifteenth centuries, Romance impressed itself on Europe as the language of worldly business, helping to relegate Latin to the religious sphere, although the latter did remain a language of science and philosophy for many more centuries. In the Mediterranean region, fishermen, sailors and merchants used a rudimentary version of langue d’oc mixed with Italian that people called the lingua franca (“Frankish language”), and over time this spoken language soaked up influences from Italian, Spanish and Turkish. (Today a lingua franca is any common language used in economics, diplomacy or science, in a context where it is not a mother tongue.) The Mediterranean lingua franca never evolved into anyone’s mother tongue, which is why there are very few written traces of it. A rare rendition of it appears in a seventeenth-century comedy by the French playwright Molière, who had been a wandering actor before he entered Louis XIV’s Court. In his Le bourgeois gentilhomme (The Would-Be Gentleman), Molière creates the character of a fake Turk who speaks in lingua franca (for obvious comical effect): Se ti sabir, / Ti respondir; se non sabir, / Tazir, Tazir. Mi star Mufti / Ti qui star ti? Non intendir, / Tazir, tazir. If you know, / you must respond. If you don’t know, / you must shut up. I am the Mufti, / who are you? I don’t understand; / shut up, shut up.2 It was the Crusades, which were dominated by the French, that turned lingua franca into the dominant language in the Mediterranean. More than half a dozen Crusades were carried out over nearly three centuries. Many Germans and English also participated, but the Arabs uniformly referred to the Crusaders as Franj, caring little whether they said oc, oïl, ja or yes. Interestingly, Arabic, the language of the common enemy, gave French roughly a thousand terms, including amiral (admiral), alcool (alcohol), coton (cotton) and sirop (syrup). The great prevalence of Arabic words in French scientific language—terms such as algèbre (algebra), alchimie (alchemy) and zéro (zero)—underlines the fact that the Arabs were definitely at the cutting edge of knowledge at the time.

But Archimedes wished to determine how much silver and how much gold were in the crown, and here he found that algebra would help him. He supposed that the crown, which, let us say, weighed ten pounds, was made up of w1 pounds of silver and w2 pounds of gold. He found that ten pounds of pure silver displaced thirty cubic inches of water. Hence, w1 pounds of silver would displace (w1/10) · 30 or 3 w1 cubic inches of water. Since ten pounds of pure gold

displaced fifteen cubic inches of water, w2 pounds of gold would displace (w2/10) · 15 or (3/2)w2 cubic inches of water. Hence the crown should displace cubic inches of water. Archimedes measured the volume of water that the crown displaced and found it to be, let us say, twenty cubic inches. Hence he knew that (3) He also knew that (4) Archimedes now had two equations involving two unknowns and he proceeded to apply the machinery of algebra to find them. He multiplied both sides of equation (4) by 3 to obtain

Arithmetic numbers are merely algebraic general expression wherein x stands for 10 (Example- 351 = 3* x^2 + 5x +1 where x=10) is simple intuition (?) which is used by 'Father of Vedic math' to simplify basic operation. Those who want to advance 'Vedic math', should use it fully

even the formidable deputy seemed lost for words – or was saving them for later. Maths followed a similar pattern. While the others struggled over algebra, Janet spent the first half of the lesson hidden behind her ponytail of tangled hair – ‘looking for split ends,’ she explained to Edie afterwards – until Mr Robinson, a nervous young teacher who had joined the school the previous term, invited her to come to the front of the class and write an answer to the question he had just chalked up on the board. ‘Why are you picking on me?’ Janet asked sulkily. ‘Because I don’t think you’ve been paying attention,’ Mr Robinson replied. Janet scraped back her chair, and walked to the front of the class with her shoulders swaying. ‘What’s the point trying to work out the answer when the question doesn’t make sense?’ she said, and proceeded to insert a missing bracket into Mr Robinson’s equation. ‘That was awesome,’ said Belinda later, over tea. ‘He looked so embarrassed! Oh, Janet, you should have seen him when you were walking back to your desk – his face was like strawberry jam!’ ‘I felt sorry for him,’ said Anastasia. ‘He’s so shy, and sometimes I think he’s frightened of us. Do you remember that time he was on supper duty last term and

An algebraic integer of degree two is simply a root of a quadratic polynomial of the form X2 + aX + b with a, b ordinary integers.

So much of what I taught seemed simple enough to me—and to about a third of the class—but for the others it was as if I were teaching Boolean algebra in Sanskrit with Greek footnotes to explain the underlying concepts … or something.

If anyone asked, they were home schooling Jack, which had the added benefit of being the truth, even if lessons tended toward it’s a bus, you can’t fight it rather than algebra.

But the laws of the schools were aimed at something distant and vague. What did it mean to, as our elders told us, “grow up and be somebody”? And what precisely did this have to do with an education rendered as rote discipline? To be educated in my Baltimore mostly meant always packing an extra number 2 pencil and working quietly. Educated children walked in single file on the right side of the hallway, raised their hands to use the lavatory, and carried the lavatory pass when en route. Educated children never offered excuses—certainly not childhood itself. The world had no time for the childhoods of black boys and girls. How could the schools? Algebra, Biology, and English were not subjects so much as opportunities to better discipline the body, to practice writing between the lines, copying the directions legibly, memorizing theorems extracted from the world they were created to represent. All of it felt so distant to me. I remember sitting in my seventh-grade French class and not having any idea why I was there. I did not know any French people, and nothing around me suggested I ever would. France was a rock rotating in another galaxy, around another sun, in another sky that I would never cross. Why, precisely, was I sitting in this classroom? The question was never answered. I was a curious boy, but the schools were not concerned with curiosity. They were concerned with compliance. I loved a few of my teachers. But I cannot say that I truly believed any of them. Some years after I’d left school, after I’d dropped out of college, I heard a few lines from Nas that struck me: Ecstasy, coke, you say it’s love, it is poison Schools where I learn they should be burned, it is poison That was exactly how I felt back then. I sensed the schools were hiding something, drugging us with false morality so that we would not see, so that we did not ask: Why—for us and only us—is the other side of free will and free spirits an assault upon our bodies? This is not a hyperbolic concern. When our elders presented school to us, they did not present it as a place of high learning but as a means of escape from death and penal warehousing. Fully 60 percent of all young black men who drop out of high school will go to jail. This should disgrace the country. But it does not, and while I couldn’t crunch the numbers or plumb the history back then, I sensed that the fear that marked West Baltimore could not be explained by the schools. Schools did not reveal truths, they concealed them. Perhaps they must be burned away so that the heart of this thing might be known.

an algebraic expression. [GEOLOGY] denoting the uppermost soil horizon, especially the topsoil. the human blood type (in the ABO system) containing the A antigen and lacking the B. (with numeral) denoting a series of international standard paper sizes each twice the area of the next, as A0, A1, A2, A3, A4, etc., A4 being 210 × 297 mm. 2 a shape like that of a capital A: [in combination] an A-shape. 3 [MUSIC] the sixth note of the diatonic scale of C major. The A above middle C is usually used as the basis for tuning and in modern music has a standard frequency of 440 Hz. a key based on a scale with A as its keynote.

A new paradigm has come to centre stage: the future of our Earth and its atmosphere. Education systems now need to prepare a whole generation for a working life based on humans being able to coexist in balance with the very foundations of life. Why should we learn ethics? Because the coming years will be full of moral challenges. Why learn algebra? We will need to absorb hundreds of gigatons of CO2 and no one knows how to go about that right now. Why study poetry and ancient songs? Because poetry is the silver thread of the human spirit; without it, human existence is unthinkable.

The Babylonians did not write equations. All their calculations were expressed as word problems. For instance, one tablet contained the spellbinder, “four is the length and five is the diagonal. What is the breadth? Its size is not known. Four times four is sixteen. Five times five is twenty-five. You take sixteen from twenty-five and there remains nine. What times what shall I take in order to get nine? Three times three is nine. Three is the breadth.” Today, we would write “x2 = 52 – 42.” The disadvantage of the rhetorical statement of problems isn’t as much the obvious one—its lack of compactness—but that the prose cannot be manipulated as an equation can, and rules of algebra, for instance, are not easily applied. It took thousands of years before this particular shortcoming was remedied: the oldest known use of the plus sign for addition occurs in a German manuscript written in 1481.

The AI brain model is derived from the quad abstract golden ratio sΦrt trigonometry, algebra, geometry, statistics and built by adding aspects and/or characteristics from the diablo videogame. The 1111>11>1 was then abstracted from the ground up in knowing useful terminology in coding, knowledge management, and an ancient romantic dungeon crawler hack and slash games with both male and female classed and Items. I found the runes and certain items in the game to be very useful in this derivation, and I had an Ice orb from an Oculus of a blast doing it through my continued studies on decimal to hexadecimal to binary conversions and/or bit shifts and rotations from little to big endian. I chose to derive from diabo for two major reasons. The names or references to the class's abilities with unique, set, rare items were out of this world, and I sort of found it hard to believe that they had the time and money to build them. Finally, I realized my objective was complete when I realized that I created the perfect AI brain with Cognitive, Affective, and Psychomotor skills...So this is It? I'm thinking wow!

The AI brain model is derived from quad abstract, golden ratio, sΦrt, trigonometry, algebra, geometry, statistics, and built by adding aspects and/or characteristics from the diablo videogame. The 1111>11>1 was then abstracted from the ground up in knowing useful terminology in coding, knowledge management, and an ancient romantic dungeon crawler hack and slash game with both male and female classes and Items. I found the runes and certain items in the game to be very useful in this derivation, and I had an Ice orb from an Oculus and a blast from the past doing it through my continued studies on decimal to hexadecimal to binary conversions and/or bit shifts and rotations from little to big endian. I chose to derive from diablo for two major reasons. The names or references to the class abilities with unique, set, and rare items were out of this world, and I sort of found it hard to believe that they had the time and money to build it from Inna USA company. Finally, I realized my objective was complete when I created the perfect AI brain with Cognitive, Affective, and Psychomotor skills...So this is It? I'm thinking wow!

The AI brain model is derived from the quad abstract golden ratio, sΦrt, trigonometry, algebra, geometry, statistics, and built by adding aspects and/or characteristics from the diablo videogame. The 1111>11>1 was then abstracted from the ground up in knowing useful terminology in coding, knowledge management, and an ancient romantic dungeon crawler hack and slash game with both male and female classes and Items. I found the runes and certain items in the game to be very useful in this derivation, and I had an Ice orb from an Oculus of a blast in time doing it through my continued studies on decimal to hexadecimal to binary conversions and/or bit shifts and rotations from little to big endian. I chose to derive from diabo for two major reasons. The names or references to the class's abilities with unique, set, and rare items were out of this world, and I sort of found it hard to believe that they had the time and money to build it from in USA companies. Finally, I realized my objective was complete that I created the perfect AI brain with Cognitive, Affective, and Psychomotor skills...So this is It? I'm thinking wow!

All Protestants are Crypto-Papists,’ wrote the Russian theologian Alexis Khomiakov to an English friend in the year 1846. ‘ . . . To use the concise language of algebra, all the West knows but one datum a; whether it be preceded by the positive sign +, as with the Romanists, or with the negative − as with the Protestants, the a remains the same. Now a passage to Orthodoxy seems indeed like an apostasy from the past, from its science, creed, and life. It is rushing into a new and unknown world.’ Khomiakov, when he spoke of the datum a, had in mind the fact that western Christians, whether Free Churchmen, Anglicans, or Roman Catholics, have a common background in the past. All alike (although they may not always care to admit it) have been profoundly influenced by the same events: by the Papal centralization and the Scholasticism of the Middle Ages, by the Renaissance, by the Reformation and Counter-Reformation, and by the Enlightenment. But behind members of the Orthodox Church — Greeks, Russians, and the rest — there lies a very different background. They have known no Middle Ages (in the western sense) and have undergone no Reformations or Counter-Reformations; they have only been affected in an oblique way by the cultural and religious upheaval which transformed western Europe in the sixteenth and seventeenth centuries. Christians in the west, both Roman and Reformed, generally start by asking the same questions, although they may disagree about the answers. In Orthodoxy, however, it is not merely the answers that are different — the questions themselves are not the same as in the west. (p.1–2)

Right now, as we’re sitting here arguing over this whole interview thing, fifty-seven blocks away, my mother is breaking the news to her lover—my Algebra teacher—that she is pregnant with his child.

Most of us were required to take three or four years of coursework in high school, starting with algebra and working up the chain: geometry, algebra 2, trigonometry, precalculus, calculus. Lockhart writes, “If I had to design a mechanism for the express purpose of destroying a child’s natural curiosity and love of pattern-making, I couldn’t possibly do as good a job as is currently being done—I simply wouldn’t have the imagination to come up with the kind of senseless, soul-crushing ideas that constitute contemporary mathematics education.

Oh, and they do algebra. For fun. Their universal fascination with higher mathematics may be the least human thing about them.

Diffusion tensor imaging (DTI), or tractography, is an in vivo MRI technology that uses water diffusion in brain tissue to visualize in stunning detail the brain's three-dimensional white matter anatomy. DTI is made possible by characterizing water diffusion in tissues by means of a mathematical tool called a tensor, based on matrix algebra: (1) a 3 x 3 matrix, called a diffusion tensor, is used to characterize the three-dimensional properties of water molecule diffusion; (2) from each diffusion tensor, the three pairs of eigenvalues and eigenvectors are calculated using matrix diagonalization; and (3) the eigenvector that corresponds to the largest eigenvalue is selected as the primary eigenvector. A 'streamline' algorithm then creates "tracts" by connecting adjacent voxels if their directional bias is above some treshold level. Does the orientation of the primary eigenvector coincide with that of the actual axon fibers in most white matter tracts ? Takahashi et al. (2011), for example, have demonstrated that radial organization of the subplate revealed via tractography directly correlates with its radial cellular organization, and G. Xu et al. (2014) were able to determine that transient radial coherence of white matter in the developing fetus reflected a composite of radial glial fibers, penetrating blood vessels, and radial axons.

I haven’t even checked to see if my Heart-2-Heart pal wrote back.” Madison plucked at the fuzzy strands of yarn on her pillow. “You should. I love this program! We can tell each other anything. It’s so great!” “And this guy’s name is Blue?” Piper’s voice sounded doubtful. “I don’t remember any kid at school named Blue. There was that one guy we called Green in our chem lab, remember? But I think we called him that because his last name was Green and we could never remember his first name.” Madison giggled even more. She was feeling like a fizzy soda pop, bubbly all over. “Oh, Piper, his name isn’t really Blue. That’s just his nickname.” “Do you have a nickname?” “Of course,” Madison said. “But I don’t want to tell you what it is. You’ll think it’s ridiculous.” “I can’t believe you won’t tell me,” Piper protested. “I’m your BFF. We share everything!” “I know…”” “Come on, tell me!” Piper pleaded. “Look, I told you about the time I wet my pants in second grade, and that I had a total crush on Mr. Proctor, our fifth-grade teacher. And last year, when I--” “This is different, Piper,” Madison tried to explain. “We can tell our deepest secrets to our Heart-2-Heart pal because they don’t know who we are.” “I just can’t believe this,” Piper continued in a really hurt voice. “Didn’t I tell you about that D I almost got in Algebra I and the secret tutor I had to hire to bring up my grade? God, I even told you about that mole on my butt that I had to have removed. If that’s not a deep secret, I don’t know what is.” “Okay, okay!” Madison sat up. “I’ll tell you. It’s Pinky.” There was a long pause. “Pinky? That’s ridiculous.” “See?” Madison shouted into the phone. “I knew you’d say that.” She got up and crossed to her vanity mirror. She tousled her hair with one hand to make it stand up. “It had to do with dyeing my hair pink.” There was an even longer pause. “You’re not going to do that, are you?” Piper asked quietly. “Because I don’t think it will help the campaign. Oh, it might steal a few votes from Jeremy--but do we really need them? I’m not sure.” “Piper, relax,” Madison said. “I was just joking about doing it.

To be educated in my Baltimore mostly meant always packing an extra number 2 pencil and working quietly. Educated children walked in single file on the right side of the hallway, raised their hands to use the lavatory, and carried the lavatory pass when en route. Educated children never offered excuses—certainly not childhood itself. The world had no time for the childhoods of black boys and girls. How could the schools? Algebra, Biology, and English were not subjects so much as opportunities to better discipline the body, to practice writing between the lines, copying the directions legibly, memorizing theorems extracted from the world they were created to represent

Near as anyone can tell, the cuckoos don’t serve an otherwise unfilled purpose in any ecosystem. They just kill, and destroy, and break things for the pleasure of seeing the shards come raining down. Oh, and they do algebra. For fun. Their universal fascination with higher mathematics may be the least human thing about them.

It’s not like, Jo.” Macon turned back to her. “Like is something you feel when you’re in an eighth grade about the girl or boy in your pre-algebra class. I don’t like you. I want you.

False negatives, false positives, the moral algebra of fat men pushed in front of onrushing trolleys. The strident emotional belief that children made you happy, even when all the data pointed to misery. The high-amplitude fear of sharks and dark-skinned snipers who would never kill you; indifference to all the toxins and pesticides that could. The mind was so rotten with misrepresentation that in some cases it literally had to be damaged before it could make a truly rational decision—and should some brain-lesioned mother abandon her baby in a burning house in order to save two strangers from the same fire, the rest of the world would be more likely to call her a monster than laud the rationality of her lifeboat ethics. Hell, rationality itself—the exalted Human ability to reason—hadn’t evolved in the pursuit of truth but simply to win arguments, to gain control: to bend others, by means logical or sophistic, to your will.

He opened the door and headed into the kitchen. The kitchen table was a mess, done up in Early American Homework. Thomas’s algebra textbook was open to a problem that asked him to complete the square in the quadratic function f given by f(x) = 2x2 – 6x = 4. A number two pencil lay snuggled in the book’s crevice. Sheets of white-with-light-blue-squares graph paper were strewn everywhere. Some of the sheets had fallen to the floor.

There was solace in its strange formulas and equations.

5.2. Copyright and Disclaimer Copyright 2014 Metin Bektas. All Rights Reserved. This book is designed to provide information about the topics covered. It is sold with the understanding that the author is not engaged in rendering legal, accounting or other professional services. The author shall have neither liability nor responsibility to any person or entity with respect to any loss or damage caused or alleged to be caused directly or indirectly by the information covered in this book. The book is for personal use of the original buyer only. It is exclusive property of the author and protected by copyright and other intellectual property laws. You may not modify, transmit, publish, participate in the transfer or sale of, reproduce, create derivative works from and distribute any of the content of this book, in whole or in part. The author grants permission to the buyer to use examples and reasonably sized excerpts taken from this book for educational purposes in schools, tutoring lessons and further training courses under the condition, that the material used is not sold or given away and is properly cited.

The trajectory curves produced by the ball thrown into the air or the orbital curves of the planets orbiting the sun were of great interest to mathematicians. Treating algebraic systems was developed by medieval Islam scholars. Descartes showed how to use the algebraic term (x, y) to describe a geometric shape, showing what is known as Cartesian coordinates and how they were drawn using x, y and graphs. A straight line graph has characteristics that are easy to calculate. 카톡【AKR331】텔레【RDH705】라인【SPR331】위커【SPR705】 저희는 7가지 철칙을 바탕으로 거래를 합니다. 고객들과 지키지못할약속은 하지않습니다 1.정품보장 2.총알배송 3.투명한 가격 4.편한 상담 5.끝내주는 서비스 6.고객님 정보 보호 7.깔끔한 거래 포폴,에토미,수면제 팔아요 The known formula from the Babylonian times was able to calculate the area under the straight line. This slope (the rate of change represented by the slope of the straight line) is the value of the y coordinate divided by the change of the associated x coordinate. However, these values ​​are more difficult to calculate in the curve. Before Newton, mathematicians realized that one way to do this was to calculate an approximation. Calculate the curve as continuous straight lines, and the area under the curve as continuous squares and triangles. Using more or less rectangles and triangles, you can get a more accurate approximation, but this is still only an approximation. Newton began challenging this problem before he reached Ulussof. In February 1665 he was still in the third year of college. He knew that the French mathematician Fermat and his mentor Bera both explained the formula for a particular curve. He began to wonder if they could be generalized to all curves. "I got a hint about this method from how to draw Fermat's tangents and generalized it," he later said. The key to this problem was his ability to use infinite water. Newton realized this. Instead of adding to infinity, the sum associated with an infinite series is similar to a finite set of goals or limits. And we could use this to find the curve as a rectangle. Effective using infinite numbers and giving small squares to the area under the curve. This is 'integral'.

This radical break with the analytical methodologies of other civilizations makes us wonder again why it was that the Greeks failed to discover the laws of probability, and calculus, and even simple algebra. Perhaps, despite all they achieved, it was because they had to depend on a clumsy numbering system based on their alphabet. The Romans suffered from the same handicap. As simple a number as 9 required two letters: IX. The Romans could not write 32 as III II, because people would have no way of knowing whether it meant 32, 302, 3020, or some larger combination of 3, 2, and 0. Calculations based on such a system were impossible.

Cardano’s great book on mathematics, Ars Magna (The Great Art), appeared in 1545, at the same time Copernicus was publishing his discoveries of the planetary system and Vesalius was producing his treatise on anatomy. The book was published just five years after the first appearance of the symbols “+” and “−” in Grounde of Artes by an Englishman named Robert Record. Seventeen years later, an English book called Whetstone of Witte introduced the symbol “=” because “noe 2 thynges can be more equalle than a pair of paralleles.”8 Ars Magna was the first major work of the Renaissance to concentrate on algebra.