1. Post #41
    Gold Member
    ThisIsTheOne's Avatar
    July 2011
    656 Posts
    I learnt absolute value as modulus. Oh. I understand now! Thanks!
    Well it's just another word for absolute value, but people generally use the term "absolute value" for real numbers, and modulus for complex numbers etc

    What they both have in common is that they are a measure of a number's distance to the origin, but since the line of real numbers is represented one dimensional, the distance just is the positive of the number, whereas with complex numbers the Argand diagram is 2 dimensional so you have to use pythag to find the distance from the origin.

    http://en.wikipedia.org/wiki/Absolut...and_properties
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  2. Post #42
    Krinkels's Avatar
    March 2011
    3,680 Posts
    What lies at the end of 1/i^(z-2)?

    Edited:

    Oh man I've been just fooling around with this complex function grapher and I just love the colours.
    I've just put in 1/i^((z^2)-2) and I think I might have broken it.
    sin(log(i^(z^2)))

    Edited:

    Wait, I think I found something even weirder:
    log(z^i)-i*log(z)
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  3. Post #43
    Pedophila's Avatar
    November 2009
    265 Posts
    Have been trying to prove these 2 identities the past 3 hours and I have simply come to a gridlock. I've tried practically everything I know of and yet no dice.

    Prove the following identities using factor formulae:

    a) sinx -sin3x + sin5x - sin7x = -1/2 * sin8x * secx
    b) (sin2x)^2 - (sinx)^2 = sinx * sin3x

    Solved it.
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  4. Post #44
    Functional derivatives are kind of neat.
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  5. Post #45
    I got zero points for the delta-fine tagged partition question. There was one correction on there about the inf, and the only other thing written was "Too simple."


    FFFFFFFFFFFFFFFFFFFFFFFFFF THAT IS THE POINT.

    Edited:

    Seriously, how can that possibly be worth no points if I showed you can always construct a delta-fine tagged partition fsifnfsjskdlgfjb;as
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  6. Post #46
    Gold Member
    ThisIsTheOne's Avatar
    July 2011
    656 Posts
    A really good tutor I had always said maths is about trying to solve something as simply as you can, and it's true. It's a shame with uni tests I seem to get, I find there's never much room to figure out a really quick, ingenious way to solve the problem.
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  7. Post #47
    A really good tutor I had always said maths is about trying to solve something as simply as you can, and it's true. It's a shame with uni tests I seem to get, I find there's never much room to figure out a really quick, ingenious way to solve the problem.
    There probably is, it's just insanely ingenious
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  8. Post #48
    There probably is, it's just insanely ingenious
    Yeah, there was a question on a mechanics test that involved showing that the three moments of inertia of a given body were equal and then calculating them by working out one of the three. It was a pretty nasty integral UNLESS, as the professor showed us afterward, you added all three integrals together in which case it simplified to an integral over r^2.
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  9. Post #49
    Krinkels's Avatar
    March 2011
    3,680 Posts
    Okay so why won't the complex function grapher process f(z)=z^z?
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  10. Post #50
    Gold Member
    ThisIsTheOne's Avatar
    July 2011
    656 Posts
    Could be fucking up at z=0 (indeterminate)??

    It should be okay because i^i (for example i^i equals e^-pi/2, which is a real number) and such don't require a new number system, they're all contained in the set of complex numbers (which contains the reals) so that shouldn't be a problem.

    It's strange, it lets me plot z^(z+2) and (z+2)^z and (z+0.000000000000000000000000001)^z but not z^z.

    Also might be to do with this: http://www.math.ksu.edu/~bennett/jomacg/identity.html
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  11. Post #51
    Chocolate.'s Avatar
    December 2011
    961 Posts
    High School Mathematics make me realize just how MAGICAL math really is.
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  12. Post #52
    How ironic. High school math is the worst.

    Edited:

    Analysis is fucking magical. Riemann integrating a function that's discontinuous every rational? Waaat
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  13. Post #53
    Hi Jo
    Jo The Shmo's Avatar
    February 2009
    22,914 Posts
    my bc calculus has officially gone past the curriculum covered by khanacademy :(
    and a few of the kids in my class have a tutor outside of school and they said the tutors all said "I don't cover this material"
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  14. Post #54
    What are you doing now
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  15. Post #55
    Chocolate.'s Avatar
    December 2011
    961 Posts
    How ironic. High school math is the worst.

    Edited:

    Analysis is fucking magical. Riemann integrating a function that's discontinuous every rational? Waaat
    Yeah that was the joke
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  16. Post #56
    That was a stupid joke fyi, sorry
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  17. Post #57
    Gold Member
    ThisIsTheOne's Avatar
    July 2011
    656 Posts
    I think I got pretty lucky with my high school maths compared to other countries.
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  18. Post #58
    Chocolate.'s Avatar
    December 2011
    961 Posts
    That was a stupid joke fyi, sorry
    its okay, I know.
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  19. Post #59
    Hi Jo
    Jo The Shmo's Avatar
    February 2009
    22,914 Posts
    its whatever's after lagrange error in my textbook

    im on vacation now and the past week of school I wasn't paying attention to anything so I honestly don't know what we're doing

    Edited:

    I just know lagrange error is the last thing in the calculus section of his website, and I heard the stories about the tutors from my classmates
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  20. Post #60
    Question. You know complex numbers aren't an ordered field? I've seen the proof, because all OF obey a^2 > 0, but i doesn't. But which of the axioms for the definition of an OF does i break? Can't we just pick P as the set of all complex numbers with b > 0?
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  21. Post #61
    Landre899's Avatar
    July 2011
    139 Posts
    how would i solve this?
    find the 4th term of (2X+6Y)^8
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  22. Post #62
    With this, if I didn't fuck anything up:

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  23. Post #63
    Gold Member
    Mr. Bleak's Avatar
    March 2011
    4,991 Posts
    Aww yeeeee

    Was completely confused by formal significance testing earlier, but I've figured it out now.

    Now, I just have to decide if I'm going to take the AP Statistics exam or not. I don't know if I'll do well, as I completely bombed the sample questions I tried earlier, and it costs $90 to take.

    That, and the school I want to go to (Caltech) doesn't accept AP credits. What do, Johnny?

    Edited:

    I mean, I could study my butt off and not do anything else for a few weeks, but even then I don't see what passing it will help in the big picture.

    Plus my parents don't really have $90 just laying around right now.
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  24. Post #64
    Landre899's Avatar
    July 2011
    139 Posts
    With this, if I didn't fuck anything up:

    thank you very much
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  25. Post #65
    Gold Member
    POLOPOZOZO's Avatar
    May 2006
    14,997 Posts
    the school I want to go to (Caltech)
    I hope you have some contingency plans, if not then good luck with that.
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  26. Post #66
    Gold Member
    Mr. Bleak's Avatar
    March 2011
    4,991 Posts
    I hope you have some contingency plans, if not then good luck with that.
    Naturally. I don't have the highest of hopes of getting in, but it's basically my goal standard.

    Though more likely I'll end up going to some dumpy unknown college because my family has no money to help me with school.
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  27. Post #67
    Gold Member
    POLOPOZOZO's Avatar
    May 2006
    14,997 Posts
    I scoffed at the idea of community colleges when I was applying to places. Now that I'm going to a university I've realized how incredibly useless an overpriced ivory tower is for undergrad and seriously regretted not going to a junior or community college first.
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  28. Post #68
    Collin665's Avatar
    January 2008
    2,339 Posts
    Naturally. I don't have the highest of hopes of getting in, but it's basically my goal standard.

    Though more likely I'll end up going to some dumpy unknown college because my family has no money to help me with school.
    1. Take the AP because it'll help you get in. I've known quite a few people with 2200+ SAT scores and quite a few APs and decent extracurriculars who've gotten denied. Sometimes people underestimate how selective upper-tier universities can be.

    2. Take the AP because if you don't get in, it will transfer somewhere else.

    3. Just because you don't get into caltech, if you don't, doesn't mean you're going to some 'dumpy unknown college' and even if you did, you'd probably be fine either way. The university you go to isn't as big of a deal as you think.
    Also I don't know where you live, but considering you're thinking about caltech I'm assuming you live in California. California has some awesome universities, even their public universities are known across the country. So shush, you're lucky.

    By the way, are you a senior or junior or?
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  29. Post #69
    Gold Member
    Octave's Avatar
    January 2009
    2,530 Posts
    Naturally. I don't have the highest of hopes of getting in, but it's basically my goal standard.

    Though more likely I'll end up going to some dumpy unknown college because my family has no money to help me with school.
    If you believe you can get in, Princeton has a shitton of financial aid -- I visited it this week and for incomes < $100,000 they pay like 100% of your tuition or so.
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  30. Post #70
    Collin665's Avatar
    January 2008
    2,339 Posts
    MIT has full financial aid, too.
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  31. Post #71
    Gold Member
    Mr. Bleak's Avatar
    March 2011
    4,991 Posts
    I suppose I did overreact. I think I'll take it, after all it won't hurt anything.

    Now that I think of it, I just want to go to a college with a nice CS program, and Caltech might be overkill for what I want to do (application design).

    Edited:

    Thanks guys.
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  32. Post #72
    Hi Jo
    Jo The Shmo's Avatar
    February 2009
    22,914 Posts
    i had an awful dream where I got rejected from every school I applied to

    Edited:

    oh i thought this was the school chat thread
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  33. Post #73
    Guys, I can express every number as a sum of fractions, right? 9.87365 = 9 + 8/10 + 7/100, etc., and every sum of fractions is a fraction itself. So, how can there be irrational numbers? I mean, just because there are infinite fractions doesn't mean the sum of all of them isn't one, we can keep adding them one-by-one infinitely.
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  34. Post #74
    NitronikALT's Avatar
    September 2010
    7,118 Posts
    err, excuse me,

    since you guys seem to know a LOT more than I do, if I were to have issues with math could I pop a few questions here?
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  35. Post #75
    and every sum of fractions is a fraction itself.
    That's the flaw. Not true. It's true of every finite sum of fractions but as the number of terms necessary becomes infinite, to add up the terms and express an irrational as a ratio would require an infinitely large integer in the numerator or denominator.

    It seems strange but there are plenty of instances like this in analysis where a property which holds for all finite sums does not hold for an infinite sum.

    This is how it can be seen that the rational numbers are not complete: That is, we can construct a Cauchy series of rational numbers which does not converge to a rational number.

    Edited:

    err, excuse me,

    since you guys seem to know a LOT more than I do, if I were to have issues with math could I pop a few questions here?
    Sure.
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  36. Post #76
    That's the flaw. Not true. It's true of every finite sum of fractions but as the number of terms necessary becomes infinite, to add up the terms and express an irrational as a ratio would require an infinitely large integer in the numerator or denominator.
    Wait, why? We can add rational numbers that follow that same infinite string structure but with repeated digits like 1/3, why would randomizing those digits cause a problem?
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  37. Post #77
    There's no "problem." Just because a Cauchy sequence of rational numbers doesn't have to converge in the rationals doesn't mean it can't converge in them.

    Also, irrational numbers don't have to have "random" digits. Take 0.1001000100001... for example.
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  38. Post #78
    I am a moderator.
    Swebonny's Avatar
    August 2006
    13,248 Posts
    Linear Algebra finals coming up 15th March.
    So far it has been fun, not really a hard subject to be honest. Just a bunch of number crunching.
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  39. Post #79
    Krinkels's Avatar
    March 2011
    3,680 Posts
    Another neat one:
    exp(i^mod(z)) with the domains set to -4<x<4
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  40. Post #80
    Question, in a segment of line, how do we define the extremities? I mean, does the line exist at its end? I mean, the separation can't belong to either the line or the space around it, right? if it belongs to the line or the space, I can find another separation point to the right or to the left. But it can't be both space and line.
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