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          by Frederick Pocklock - Mon, 13 Jul 2015 23:37:34 EST ID:rBg8Fq2S No.14815 Ignore Report Reply Quick Reply
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How do you measure intelligence?
Jack Wubbernene - Tue, 14 Jul 2015 02:39:02 EST ID:i84x+n57 No.14816 Ignore Report Quick Reply
With an IQ test. /thread

In reality, intelligence is much more subtle than this. But IQ tests are the best we have and will give a rough estimate relative to the general population.
Nakura !xMsGPnYjBI - Tue, 14 Jul 2015 15:06:10 EST ID:NAU1L+Of No.14817 Ignore Report Quick Reply
Intelligence Scientists are working to improve IQ tests, remember, there's actually many different IQ tests, but only a few in wide use. Along with EQ (Emotional Intelligence) tests. IQ tests are a fantastic way to measure intelligence, although crude compared to the actual complexity of the intelligence of a human being.

I've seen people have intense chess games, losing their minds, battling to settle who loses an IQ point, dark games, for brilliant young minds. Computers are people too.
Molly Pedgeham - Fri, 21 Aug 2015 16:34:45 EST ID:uAPhVfTX No.14862 Ignore Report Quick Reply

>Computers are people too.

Computers aren't people, but people are computers.
Jack Peddlewill - Wed, 09 Sep 2015 10:23:07 EST ID:BG0DExq5 No.14884 Ignore Report Quick Reply
I have a strange view of intelligence. I think if you're a genius at making music or doing math, you might not even be that intelligent, because at that point you're a complex machine that excels at doing a job. I find myself defining intelligence in terms of how stupid you're not. What I mean exactly is this: I define intelligence as how good you are at induction. I think that's strange because solid reasoning is not inductive. On the other hand, if you're a human in a world as complex as this, you're almost never able to get all the information you need in order to acquire an accurate understanding of something. I think your ability to reach a correct understanding with incomplete information is a measure of how intelligent you are. For example, if game changing advances in solar technology happen every few months, and you have a cousin that thinks any real advance in solar technology would be followed by the government assassinating a scientist, your cousin isn't very intelligent. (True story).

Greatest Mathematical Achievements by Samuel Fanfuck - Wed, 27 May 2015 00:57:30 EST ID:So3FHAh7 No.14750 Ignore Report Reply Quick Reply
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In today's world, what's the greatest achievement a mathematician can reach?

What's the greatest "honor" a mathematician can receive?
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Priscilla Blingerlin - Sat, 01 Aug 2015 00:22:09 EST ID:mJf1tiy7 No.14837 Ignore Report Quick Reply

Before they die, aging mathematicians are racing to save the Enormous Theorem's proof, all 15,000 pages of it, which divides existence four ways
ASEEMINGLY ENDLESS VARIETY OF FOOD WAS SPRAWLED OVER SEVERAL TABLES at the home of Judith L. Baxter and her husband, mathematician Stephen D. Smith, in Oak Park, Ill., on a cool Friday evening in September 2011. Canapes, homemade meatballs, cheese plates and grilled shrimp on skewers crowded against pastries, pates, olives, salmon with dill sprigs and feta wrapped in eggplant. Dessert choices included -- but were not limited to -- a lemon mascarpone cake and an African pumpkin cake. The sun set, and champagne flowed, as the 60 guests, about half of them mathematicians, ate and drank and ate some more.
The colossal spread was fitting for a party celebrating a mammoth achievement. Four mathematicians at the dinner- Smith, Michael Aschbacher, Richard Lyons and Ronald Solomon -- had just published a book, more than 180 years in the making, that gave a broad overview of the biggest division problem in mathematics history.
Their treatise did not land on any best-seller lists, which was understandable, given its title: The Classification of Finite Simple Groups. But for algebraists, the 350-page tome was a milestone. It was the short version, the CliffsNotes, of this universal classification. The full proof reaches some 15,000 pages- some say it is closer to 10,000 -- that are scattered across hundreds of journal articles by more than 100 authors. The assertion that it supports is known, appropriately, as the Enormous Theorem. (The theorem itself is quite simple. It is the proof that gets gigantic.) The cornucopia at Smith's house seemed an appropriate way to honor this behemoth. The proof is the largest in the history of mathematics.
And now it is in peril. The 2011 work sketches only an outline of the proof. The unmatched heft of the actual documentation places it on the teetering edge of human unmanageability. "1 don't know that anyone has read everything," says Solomon, age 66, who studied the proof his entire career. (He retired from Ohio State University two years ago.) Solomon and the other three mathe…
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Priscilla Blingerlin - Sat, 01 Aug 2015 00:23:10 EST ID:mJf1tiy7 No.14838 Ignore Report Quick Reply

That loss would be, well, enormous. In a nutshell, the work brings order to group theory, which is the mathematical study of symmetry. Research on symmetry, in turn, is critical to scientific areas such as modern particle physics. The Standard Model -- the cornerstone theory that lays out all known particles in existence, found and yet to be found -- depends on the tools of symmetry provided by group theory. Big ideas about symmetry at the smallest scales helped physicists figure out the equations used in experiments that would reveal exotic fundamental particles, such as the quarks that combine to make the more familiar protons and neutrons.
Group theory also led physicists to the unsettling idea that mass itself -- the amount of matter in an object such as this magazine, you, everything you can hold and see -- formed because symmetry broke down at some fundamental level. Moreover, that idea pointed the way to the discovery of the most celebrated particle in recent years, the Higgs boson, which can exist only if symmetry falters at the quantum scale. The notion of the Higgs popped out of group theory in the 1960s but was not discovered until 2012, after experiments at CERN's Large Hadron Collider near Geneva.
Symmetry is the concept that something can undergo a series of transformations -- spinning, folding, reflecting, moving through time -- and, at the end of all those changes, appear unchanged. It lurks everywhere in the universe, from the configuration of quarks to the arrangement of galaxies in the cosmos.
The Enormous Theorem demonstrates with mathematical precision that any kind of symmetry can be broken down and grouped into one of four families, according to shared features. For mathematicians devoted to the rigorous study of symmetry, or group theorists, the theorem is an accomplishment no less sweeping, important or fundamental than the periodic table of the elements was for chemists. In the future, it could lead to other profound discoveries about the fabric of the universe and the nature of reality.
Except, of course, that it is a mess: the equations, corollaries and conjectures of the proof have been tossed amid more than 500 journal articles, some buried in thick vol…
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Priscilla Blingerlin - Sat, 01 Aug 2015 00:25:22 EST ID:mJf1tiy7 No.14839 Ignore Report Quick Reply

Simple finite groups are analogous to atoms. They are the basic units of construction for other, larger things. Simple finite groups combine to form larger, more complicated finite groups. The Enormous Theorem organizes these groups the way the periodic table organizes the elements. It says that every simple finite group belongs to one of three families-or to a fourth family of wild outliers. The largest of these rogues, called the Monster, has more than 1053 elements and exists in 196,883 dimensions. (There is even a whole field of investigation called monsterology in which researchers search for signs of the beast in other areas of math and science.) The first finite simple groups were identified by 1830, and by the 1890s mathematicians had made new inroads into finding more of those building blocks. Theorists also began to suspect the groups could all be put together in a big list.
Mathematicians in the early 20th century laid the foundation for the Enormous Theorem, but the guts of the proof did not materialize until midcentury. Between 1950 and 1980-a period which mathematician Daniel Gorenstein of Rutgers University called the "Thirty Years' War" -- heavyweights pushed the field of group theory further than ever before, finding finite simple groups and grouping them together into families. These mathematicians wielded 200-page manuscripts like algebraic machetes, cutting away abstract weeds to reveal the deepest foundations of symmetry. (Freeman Dyson of the Institute for Advanced Study in Princeton, N.J., referred to the onslaught of discovery of strange, beautiful groups as a "magnificent zoo.")
Those were heady times: Richard Foote, then a graduate student at the University of Cambridge and now a professor at the University of Vermont, once sat in a dank office and witnessed two famous theorists -- John Thompson, now at the University of Florida, and John Conway, now at Princeton University -- hashing out the details of a particularly unwieldy group. "It was amazing, like two Titans with lightning going between their brains," Foote says. "They never seemed to be at a loss for some absolutely wonderful and totally off-the-wall techniques for doin…
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Priscilla Blingerlin - Sat, 01 Aug 2015 00:26:13 EST ID:mJf1tiy7 No.14840 Ignore Report Quick Reply

Gorenstein envisioned a series of books that would neatly collect all the disparate pieces and streamline the logic to iron over idiosyncrasies and eliminate redundancies. In the 1980s the proof was inaccessible to all but the seasoned veterans of its forging. Mathematicians had labored on it for decades, after all, and wanted to be able to share their work with future generations. A second-generation proof would give Gorenstein a way to assuage his worries that their efforts would be lost amid heavy books in dusty libraries.
Gorenstein did not live to see the last piece put in place, much less raise a glass at the Smith and Baxter house. He died of lung cancer on Martha's Vineyard in 1992. "He never stopped working," Lyons recalls. "We had three conversations the day before he died, all about the proof. There were no good-byes or anything; it was all business."
THE FIRST VOLUME of the second-generation proof appeared in 1994. It was more expository than a standard math text and included only two of 30 proposed sections that could entirely span the Enormous Theorem. The second volume was published in 1996, and subsequent ones have continued to the present -- the sixth appeared in 2005.
Foote says the second-generation pieces fit together better than the original chunks. "The parts that have appeared are more coherently written and much better organized," he says. "From a historical perspective, it's important to have the proof in one place. Otherwise, it becomes sort of folklore, in a sense. Even if you believe it's been done, it becomes impossible to check."
Solomon and Lyons are finishing the seventh book this summer, and a small band of mathematicians have already made inroads into the eighth and ninth. Solomon estimates that the streamlined proof will eventually take up 10 or 11 volumes, which means that just more than half of the revised proof has been published.
Solomon notes that the 10 or 11 volumes still will not entirely cover the second-generation proof. Even the new, streamlined version includes references to supplementary volumes and previous theorems, proved elsewhere. In some ways, that reach speaks to the cumulative nature of mathematics: every proof is a product not only of its time but of all the thousands of years of thought that came before.
In a 2005 article in the Notices of the American Mathematical Society, mathematician E. Brian Davies of King's College London pointed out that the "proof has never been written down in its entirety, may never be written down, and as presently envisaged would not be comprehensible to any single individual." His article brought up the uncomfortable idea that some mathematical efforts may be too complex to be understood by mere mortals. Davies's words drove Smith and his three co-authors to put together the comparatively concise book that was celebrated at the party in Oak Park.
The Enormous Theorem's proof may be beyond the scope of most mathematicians -- to say nothing of curious amateurs -- but its organizing principle provides a valuable tool for the future. Mathematicians have a long-standing habit of proving abstract truths decades, if not centuries, before they become useful outside the field.
"One thing that makes the future exciting is that it is difficult to predict," Solomon observes. "Geniuses come along with ideas that nobody of our generation has had. There is this temptation, this wish and dream, that there is some deeper understanding still out there."
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James Tillingson - Sat, 01 Aug 2015 20:08:09 EST ID:i84x+n57 No.14843 Ignore Report Quick Reply
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Cool thanks. That's quite the predicament. I hope the other two guys live to see its completion.

please solve my math problem by Edwin Sorryfield - Fri, 24 Jul 2015 09:31:58 EST ID:C4sQWBeJ No.14825 Ignore Report Reply Quick Reply
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Im trying to figure out how much paper I have to pick up at work...
A roll of paper weighing in at 4200 pounds and a diameter of 50". If I have to cut off let's say an inch of paper, how much would that inch weigh?
To tired for math
Simon Pommerhat - Fri, 24 Jul 2015 15:17:28 EST ID:i84x+n57 No.14826 Ignore Report Quick Reply
You'd need to know the length of the roll - knowing the diameter does you no good without knowing the density.
Simon Pommerhat - Fri, 24 Jul 2015 15:37:13 EST ID:i84x+n57 No.14827 Ignore Report Quick Reply
Unless you mean spool off and cut the paper so the diameter of the roll you're cutting from decreases by an inch (this is almost certainly what you mean, so disregard my previous post). In that case, the paper you spool off will weigh [R^2 - (R - r)^2]/R^2×4200 lbs = 329.28 lbs. Here r is the inch and R is 25''.
Simon Pommerhat - Fri, 24 Jul 2015 15:42:18 EST ID:i84x+n57 No.14828 Ignore Report Quick Reply
>diameter of the roll
Meant radius of the roll. FML, apparently forgot my thinking cap today.
Frederick Naddlebet - Sat, 25 Jul 2015 10:35:38 EST ID:Va1A/b0+ No.14829 Ignore Report Quick Reply
Thank you so much for that. Now I can tell my boss how ridiculous it is to pick that up twenty times a day.
Clara Claywell - Sat, 25 Jul 2015 14:55:57 EST ID:i84x+n57 No.14830 Ignore Report Quick Reply
No prob. How were you supposed to lift that much weight? I don't know how giant rolls of paper are usually transported.

dot dot dot by Barnaby Babbleshaw - Sat, 13 Jun 2015 01:58:32 EST ID:F9AJX/Os No.14795 Ignore Report Reply Quick Reply
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So the symbol of ... in mathematics is kind've confusing I've realized. Or an ellipsis. or just "that dot dot dot thing". whatever the hell you wanna call it.


both use the ... symbol, and in very different ways. In the first example, I think most people would say that it means a decimal point followed by an infinite amount of 9s. I would agree.

But it would be wrong to assume the same in the second case, as the number I was obviously stating is pi, and as such is irrational therefore doesn't have infinite repeating digits.
Archie Brickleman - Sat, 13 Jun 2015 05:53:14 EST ID:i84x+n57 No.14796 Ignore Report Quick Reply
What's your point? That it's bad notation for certain cases? All it means is that the decimal expansion of a number is nonterminating. To emphasize a repeating decimal, a vinculum (a line) is marked above the string of digits that repeat.

Nakura !xMsGPnYjBI - Tue, 14 Jul 2015 15:37:37 EST ID:NAU1L+Of No.14819 Ignore Report Quick Reply
The (...) in the decimal form of pi represents the decimal sequence continuing in an infinite series of numerals with the complexity state holding at that expected for pi.
Does that make sense?
Martha Nimmledock - Thu, 30 Jul 2015 00:18:21 EST ID:AopNL+nM No.14833 Ignore Report Quick Reply
Only a nerd would complain about something like that.

Math Anxiety (Know the material) by Frederick Megglechere - Thu, 09 Jul 2015 04:44:52 EST ID:oIF65CiW No.14812 Ignore Report Reply Quick Reply
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I have horrible math test anxiety.

Originally, I thought it had to do with failing to practice enough. I never had math anxiety or problems with tests in school up to ~algebra 2 (I never took AP classes, I had to start working.) I will admit, I tried to slack off at first but I knocked it off. You can even find a panic post of mine on this board if you look hard enough. I did alright on that test, but not what I could have done.

That was my wake up call.

I realized, going into college and having not used math, it made sense that I'd have to work harder than others to understand the material at first.

I started doing an insane amount of problems - the homework and then more on top of it. I re-took the class.

No. I get into a Calc test and am fine at first. I browse the whole test and smile because I covered all of the material. I did problems upon problems - I have a stack of printer full of shit (not an entire ream... but a lot), and yet, as I go through, I fall apart. I am slow and the clock ticks, and I can't remember simple concepts. I bomb. I do worse than before I prepared well!

I end up start switching endlessly from problem to problem because I'm missing little factoring issues or I used f'' instead of f'. I mean, for fuck's sake, I couldn't formally derive d/dx(x^1/2) using a limit... it's not difficult in the slightest. It's like I forget how to use LCDs and the simplest crap when I am tested.

I'm almost paranoid that there will just be algebraic tricks I'm not accustomed to and so sometimes I go down the wrong path solving a problem I could have done easily with a method I knew.
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Nathaniel Niggerfuck - Mon, 13 Jul 2015 05:34:55 EST ID:Dk8yywxc No.14813 Ignore Report Quick Reply

Everyone goes through this to a certain extent, some much more so than others. Sadly this is the limitation of the grading system, that someone like you with good understanding will slip through.

My advice is:

1) Slow down with your problems. You might be burning through stacks of problems without taking the time to think about what's going on, memorizing methods without developing any intuition. If you're going too fast or writing illegibly, you could be doing work that the grader can't make sense of, or worse you can't make sense of when you come back to the problem if you need to.

2) Don't be afraid to make mistakes. It's ok to have a shit ton of scratch paper to try again, if you've gone down a fruitless path try something different. I'm not saying half ass a bunch of different approaches, but if something just isn't working move on and come back to it.

3) Read the test, think about how you'll do each problem, then start doing the grunt work. The way math often works is that your brain is confused by a problem at first, but when you come back to it, it may be crystal clear. This is what's happening when you get back to your car, you've primed yourself for the problem on the test and it's then crystal clear when you take the second look at it. There's something subconscious going on, but if you read something and come back to it later you'll find that you have been processing it without noticing.

4) Calm down. It's easy to get worked up about things, it's just a test that you're prepared for and you can do it. Try doing something that calms you down before a test, such as drinking a coffee, reading a favorite short story, sitting under a tree with a cigarette, whatever it is you like.

5) After you do a practice problems, don't just do an entirely different set the next time you study. Try looking back over your work, think about why you did something and whether it could have been better, reflect not only on the method itself but why you chose that particular method for the problem at hand.
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Jack Peddlewill - Wed, 09 Sep 2015 10:44:18 EST ID:BG0DExq5 No.14886 Ignore Report Quick Reply
Fucking quality advice. The only advice I have is based on my personal experience. My friends and I were in calculus (I never imagined in a million years I'd be in calculus but I was a high school stoner and the hard classes were the trippiest. I'm doing my 4th year of a physics degree now. Crazy how drugs can affect your life.), and we realized that our math ability was extremely lacking, so we had to take over our own math education in order to be comfortable with ourselves. The thing that changed me forever was taking over mathematics, because it's something that belongs to me. I think crazy and natural thoughts in private, I listen to Terence Mckenna and random psychedelic nonsense and I just own math. It's mine now. So when I sit in front of an exam, I'm totally shocked; because somehow my private hobby is showing up at school. Also, if you're someone who cares about math, nothing is more amazing than an exam. Think about it, you MUST sit there for 3 hours and do math with no distractions. There's no way out. That's the fastest 3 hours of your life, and if you identify math as being home, it's funny. That's the only way I can describe it. How dare you challenge me in my home turf. (Not very modest but if you're dealing with math anxiety, fuck all modesty). I'm not even very mathematically talented, but if you want to get rid of math anxiety, you need to make it a part of your world that you're fond of.

Helpful Youtube channels by Cyril Gebblecocke - Thu, 04 Jun 2015 09:55:27 EST ID:jNXUmpxk No.14775 Ignore Report Reply Quick Reply
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Hey /math/,

I'm taking a satistics course this summer to fulfill my last credit for community college, and I was wondering if you guys know of any good Youtube channels to help me out through. We're currently going over probability, and it flew right over my head.

Cyril Gebblecocke - Thu, 04 Jun 2015 09:57:20 EST ID:jNXUmpxk No.14776 Ignore Report Quick Reply
help me through this*

tired, sorry
Nicholas Bundlekire - Thu, 04 Jun 2015 21:08:37 EST ID:7QJ+5Rkj No.14777 Ignore Report Quick Reply
khan academy
Nicholas Ducklock - Thu, 02 Jul 2015 09:35:59 EST ID:kOuj74f1 No.14810 Ignore Report Quick Reply
this guy help me a lot last summer when i was studing statistics.

Good Ideas Thread by Nakura !xMsGPnYjBI - Sun, 28 Jun 2015 17:45:04 EST ID:NAU1L+Of No.14808 Ignore Report Reply Quick Reply
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Fourier analysis applied to violent events and plotted on a complex plane could assist in finding the root cause of violent events and prevent their occurence in the future. Wave dispersion field devices, in the future, could prevent violent behavior, by taking advantage of wavelengths determined by psychodynamical theory and data, and influencing neuronal firing patterns in the brain. It would work similarly to how radios already work, but calibrated much more carefully.
Frederick Nullyman - Mon, 29 Jun 2015 23:19:30 EST ID:rS9AJec8 No.14809 Ignore Report Quick Reply

>the root cause of violent events

jolly african-americans.

>prevent their occurence in the future

Remove watermelon.

Passed test slayer by Martha Pullerkitch - Sun, 17 May 2015 12:48:46 EST ID:muTtSqY/ No.14736 Ignore Report Reply Quick Reply
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What's up /math/, I just got 84% on a test I was really worried about fuck yeah. But one question I couldn't answer, it seems like it's insoluble, can you help me out?

A rocket is traveling through space at a speed of 7500 m/s. If in one second it burns 710 kg of fuel, what is the change in momentum during this time interval in kg m/s.

Don't you need the exhaust velocity of the rocket to solve this? Thanks
Nathaniel Fuckingwell - Fri, 29 May 2015 15:50:41 EST ID:i84x+n57 No.14762 Ignore Report Quick Reply
Maybe because of an opposing pull of gravity, the velocity of the rocket doesn't change at all. The deceleration from gravity could exactly cancel the acceleration due to thrust. Whatever the case, whoever made the question wants you to assume the change in velocity is negligible and that the change in mass is all that contributes to the change in momentum. So (delta p) = (delta m)*v.
Matilda Pockcocke - Wed, 17 Jun 2015 00:15:37 EST ID:sPd/0oB/ No.14799 Ignore Report Quick Reply
This doesn't mean much without the exhaust velocity, really.
In fact I'm not sure the speed of the rocket is relevant to calculate the momentum change. Speed related to what? In which direction?

Looks like a trick question at best.
Jarvis Bardson - Wed, 17 Jun 2015 18:05:29 EST ID:x6xydNWl No.14800 Ignore Report Quick Reply
Guys, look at the units. Momentum is Mass x velocity. Velocity is fixed, change in mass is given. Find change in momentum.

Unless I'm missing something, this seems like a straightforward elementary physics problem.
Jarvis Bardson - Wed, 17 Jun 2015 18:08:54 EST ID:x6xydNWl No.14801 Ignore Report Quick Reply
Nathaniel has the right of it. Sorry I didn't see that sooner.

NB for double post.
Cedric Dubbersare - Thu, 18 Jun 2015 12:28:42 EST ID:nyIjuDfA No.14802 Ignore Report Quick Reply
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It's a "restate the momentum equation" kind of problem. You're calculating the change in Momentum"dM" over a given time period "dt". Naturally, we all remember that momentum"M" is given by mass"m" times velocity aka: M=m*v. We're given both the velocity"v" and the change in mass"dm" over a period of time"dt" so the equation looks like "dMomentum/dt = dmass/dt * v" fortunately for us, the "dt"s on both sides of the equation have a value of 1 second and can be ignored because anything/1=anything. this problem is now a simple multiplication problem: "dM = -710kg * 7500m/s" which anyone may plug into a calculater at their leasure.

Good night, sweet prince. by Barnaby Drapperstat - Sun, 24 May 2015 14:29:23 EST ID:z/dIPyff No.14746 Ignore Report Reply Quick Reply
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John F. Nash Jr., a mathematician who shared a Nobel Prize in 1994 for work that greatly extended the reach and power of modern economic theory and whose decades-long descent into severe mental illness and eventual recovery were the subject of a book and a 2001 film, both titled “A Beautiful Mind,” was killed, along with his wife, in a car crash on Saturday in New Jersey. He was 86.
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Nakura !xMsGPnYjBI - Tue, 02 Jun 2015 20:07:20 EST ID:NAU1L+Of No.14770 Ignore Report Quick Reply
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stfu kid
Chaos strikes at the strangest of times. You really are disrespecting a great mathematician, and though I forgive you, just, idk, watch your mouth around the greats of mathematics. Their life force is a squared gamma function of an iteration of the trancendental # e anyway, so, he's probably chill.
Phineas Peblingshaw - Wed, 10 Jun 2015 23:42:43 EST ID:rp0UlP7W No.14788 Ignore Report Quick Reply
Was there even a thread for Grothendieck?
Nicholas Chingerperk - Thu, 11 Jun 2015 13:14:16 EST ID:QIXSgr8C No.14790 Ignore Report Quick Reply
media didnt make as much of an event of it
Basil Sasslehut - Fri, 12 Jun 2015 23:48:17 EST ID:rp0UlP7W No.14794 Ignore Report Quick Reply
It's just weird, even my friends who are mathematicians didn't say anything about it but posted something about John Nash. I guess it's amazing what a movie can do to public perception. No disrespect to Nash I'm just kinda bummed that Grothendieck wasn't appreciated when he was one of the greatest mathematicians of the 20th century.
Fanny Soddlestut - Sat, 13 Jun 2015 21:37:56 EST ID:QBhQLlLE No.14798 Ignore Report Quick Reply

No one can deny that Nash was more well known than Grothendieck. Not to disparage Grothendieck, but I think Nash focused on much more practical and "relevant" areas of mathematics such as game theory and computer science, which is interesting to everyone, while Grothendieck was more of a specialist in the field of Algebraic Geometry and Topos theory, which is niche. Nash also did excellent Algebraic Geometry.

Basically, Nash achieved more and had a more interesting story and received more attention as a result. They were both great mathematicians and their death is a huge loss, but Nash was a bigger deal for many reasons.

Drinking your wallet by Whitey Bomblefodge - Fri, 12 Jun 2015 02:09:00 EST ID:vX6Harxq No.14791 Ignore Report Reply Quick Reply
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I thought this was a question for hooch, but I have a second thought here.

Say you pour a $8.00 bottle of vodka into a glass. You suddenly envision coins dripping out of the bottle. My question for you, what coin were you seeing?
Whitey Criffingbanks - Fri, 12 Jun 2015 05:32:17 EST ID:i84x+n57 No.14792 Ignore Report Quick Reply
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$8 for a 750 ml bottle? I'd imagine diarrhea dripping out, not coins.

Assuming we're talking about US currency and 750 ml bottles, using the penny - the coin with the greatest volume to value - you'd only fill the bottle up close to 2/5 of the way. This is assuming that the pennies sorta melt like the watches in pic related, which is a fair assumption considerring your wording. This way we don't have to worry about space between the pennies.
Whitey Criffingbanks - Fri, 12 Jun 2015 05:50:14 EST ID:i84x+n57 No.14793 Ignore Report Quick Reply
Clara Wennerfock - Sat, 13 Jun 2015 06:22:58 EST ID:YsOAl7K9 No.14797 Ignore Report Quick Reply
I'm assuming it's half that size. That sounds about right. It's cheap but might not make you go blind.

Anyway it's 2.13(recurring) cents per ml at that quality/quantity. Vodka is about 37% alcohol and a smidge of glycerine if it's that cheap. Glycerol is about 1.2g/ml water is 1 and alcohol is .789. Vodka can be up to 40% but by assuming it's cheap shit. Glycerine is like 5% and the rest water so 1 ml is .05*1.2g + .37*.789g + .58g

a cent has a displacement of about .0433ml while the current rate is about .46ml per cent so US cents are probably pretty appropriate actually.

If ti's a 350ml bottle it's probably dead on.

If you're that desperate to get drunk buy some cheap cider though. White lightning actually does taste like it's been through someone's kidneys already but it's got the same alcohol content in a 3 litre bottle as a quart of vodka and when I was young enough to be desperate it was about 1/3 of the price of the absolute worst vodka I could get that wasn't toxic and illegal.

fertilizer question by Isabella Blackforth - Fri, 22 May 2015 19:43:11 EST ID:YCs1tF7z No.14741 Ignore Report Reply Quick Reply
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Hello /MATH/ I have a quick question for you to help me out with if that's cool.
Basically I just need to know how much fertilizer 20-4-8 would be in a 100lb bag
Betsy Pongerlock - Fri, 22 May 2015 21:34:36 EST ID:rw1aY/ny No.14742 Ignore Report Quick Reply
about 100lb
Phineas Hepperdock - Wed, 27 May 2015 23:45:30 EST ID:Jz+dW0dw No.14755 Ignore Report Quick Reply
Those are percentages.

Surely you know what a percent is.

<3 <3 by Jack Benninghat - Wed, 18 Jun 2014 06:38:10 EST ID:Fj/YvlCk No.14096 Ignore Report Reply Quick Reply
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I love maths and I love you <3

Share whatever proof, trick, theorem, mathematical tool, number, or other maths-related stuff you like in this thread.

I like e. It's always felt a bit "blue" for me, you know 2.7182818284590452353... A nice deep blue.
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Emma Dibblelidge - Sun, 03 May 2015 01:57:34 EST ID:K8qJv5EF No.14717 Ignore Report Quick Reply
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I'm a bigger fan of the spectral theorem (orthogonality is the bee's knees), but functional analysis is ballin' no matter how you do it.

Integration by parts is sneakily one of the most powerful tools in calculus. Seemingly just a technique for calculating integrals in a second semester course, the IBP formula is actually the backbone of Sobolev Spaces, and thus the backbone of the theory of Partial Differential Equations.
Martin Dribberdark - Sat, 09 May 2015 02:05:15 EST ID:YlDX0MWs No.14728 Ignore Report Quick Reply
I have been meaning to learn what spectral theory is all about, but fuck wikipedia for learning, why do I ever bother with it. Got a free reading recommendation and/or care to write a bit about what it is, essentially? (audience: math BS)

That IBP bit is really interesting and I want to know more. I remember a similar feeling when learning Variation of Parameters in diff eq, like it was a specific case of something more fundamental but I can't recall the line of thought now. Seeing it again, but applied, in physics was neat.

I have looked at and hatefully closed the wiki for Sobolev spaces before, I think, and definitely Hilbert spaces (which came up in spectral theorem wiki). Fucking wikipedia, I just can't learn from it and need to accept that.
Caroline Brebbermag - Fri, 15 May 2015 20:25:48 EST ID:K8qJv5EF No.14733 Ignore Report Quick Reply
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Hmm, to really understand the gravity of the spectral theorem, you'd need to have a pretty firm understanding of functional analysis, which in turn requires a firm understanding of linear algebra *and* measure theory.

For measure theory, probably the best beginner's book would be Royden's "Real Analysis", 3rd edition. Very clear language, motivates the study, etc. Be ready for some abstraction, though: measurable sets and functions are ill-behaved to say the least.

Once you understand the Lebesgue Integral, you'll be ready for functional analysis. There are many fantastic texts on the topic, but if you're *only* interested in learning spectral theory, you might want to try "Theory of Linear Operators in Hilbert Space," by Akhiezer and Glazman. This is a Dover book, and therefore very cheap. It covers everything from the basics of functional analysis (on inner product spaces) to the full spectral theorem for self-adjoint operators.

If you want a basic rundown of the spectral theorem, it basically says that very symmetric operations of certain kinds (like multiplication by a real number [boring] or the second derivative operator [interesting]) can be used to decompose certain vector spaces via an orthonormal basis, i.e. into a coordinate system where each axis is at "a right angle" with each other axis. This allows one to decompose your symmetric operation into a sum of very simple transformations on individual components. Like any other "decomposition" theorem, this is *extremely* advantageous when solving tough problems where these operators play a big role.

As for IBP, when combined with Sobolev spaces, it allows you to transform a second order partial differential equation into an integral equation of sorts. If your original PDE was linear, your integral equation gets alllll sorts of special properties (bilinear forms are what they become). This allows for really interesting theorems from functional analysis, like the Lax-Milgram theorem or the spectral theorem, to become immediately applicable to solving, or at least guaranteeing a solution to, your PDE. You *must* have Sobolev spaces for this approach to be sou…
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Ian Noffingdock - Tue, 19 May 2015 15:35:08 EST ID:NCaB2rkH No.14738 Ignore Report Quick Reply
You've provided some great resources to look into here and a clear path forward Brebbermag, I thank you for it.
Caroline Murdbury - Wed, 27 May 2015 04:01:40 EST ID:96SVbDTc No.14753 Ignore Report Quick Reply
This is along the same lines as my little trick for squaring, will use the same number. I don't even remember where I got it from, I think my calc 3 teacher squared some big number with it and I thought it was really elegant.


As for my favorite thing, the bisection method of root finding is up there. Just a really really beautiful and simple way of looking at the problem. The idea of "just split an interval in half and figure out which half has the root in it, repeat" is just really neat to me.

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