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Thread: Introduction. (Math help required for the long term!)

  1. #1
    Oct 2012
    United Kingdom

    Introduction. (Math help required for the long term!)

    Hey everyone, wanted to introduce myself and explain why I am here and what I want to gain out of being here. Firstly, I'd like to meet new people who share a love for math like I do. I want to declare that I am not of a very high level of math and am only just now at the age of 24 trying to re-take my GCSE Math. In 2007 - I got a grade D on my math course and i've had jobs and stuff since then, but for the past 3 years...I haven't been very well with finding out that i have asperger-syndrome but I know that doesnt make me ILL as such, but the depression, anxiety, aspergers all together and I didnt know for all this time about why im very socially-awkward and find it hard to be around people..i find it hard to be out in crowds and have no confidence or self-esteem and everything, I am not looking for sympathy, ill be okay if i can get help which i am looking for. the doctors and psychologists say im not ready for work and to be honest I agree, I normally work in Admin. but at the same time I'm frustrated the doctors are being slow in diagnosing and helping me to be honest so I have been unemployed for the past 3 years and I figured I should do math to get my grade up. giving me something else to focus on as well. so I went to the council and im doing adult-education for level 2 Math trying to get my grade up. there are a lot of problem areas that I need help with in understand and so this is why I am here.

    Topics i'm finding hard at the moment...

    Trigonometry SIN,COS,TAN all of that stuff.
    Surds on decimal numbers ie. surd 0.04 is actually 0.2 multiplied by itself. ect, the other ones. i have noticed a pattern that for the first lot...the square root appears to look like Square-numbers.

    Data - the different types of charts and how to multiply and divide on them - for example a VECTOR 3-4 how id be able to multiply it

    Basically i dont know where to start what should i do first? im in my adult-education class but they are actually doing foundation and i want to do higher but i dont know what to start with. I tried looking at past-papers and I can do some of the questions but not all of them and most of it I can't do so i wondered if i could find help here.
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  2. #2
    MHF Contributor

    Mar 2011

    Re: Introduction. (Math help required for the long term!)

    some general observations: math is not like a movie, or a novel, where you take it in "as a whole, in its entirety, at once". it's more like a chain: forged one link at a time (or maybe a jigsaw puzzle).

    so you have to focus on "one step at a time", it takes some times before you can assemble the tinker-toys into "big structures".

    some thoughts on trigonometry: everything is pythagoras: A2 + B2 = C2. this should remind you of the equation for a circle:

    x2 + y2 = r2, because...well, it's the same underlying concept: the distance between a point on the circle, and the origin, IS the radius of the circle, which IS the length of the hypotenuse of the right triangle with vertical leg "y" and horizontal leg "x".

    cosine is just a fancy name for all the possible x's we get, and sine a fancy name for all the y's we get on a circle. cosine and sine of..."what"? well, if we have a point on the circle, we have two lines:

    the x-axis, and the line going through (0,0) and (x,y). so we can speak of the angle between these two lines. it turns out it's more convenient to consider the "half-lines" (rays) starting at (0,0), and considering the angle between the two rays (so we know which "V" of the "X" the two lines make we're talking about).

    of course, if you're struggling with algebra, trig is going to be hell...because there is lots of "algebraic rearrangement" always going on.

    here's the deal with algebra: it's just like arithmetic but "we don't know which numbers we have". what we DO have is the RULES of arithmetic to guide us. it's like this: if you owe me $10, how much do you have to pay me? $10. ok, let's just say you don't remember how much you owe me. what do you have to pay? "whatever you owe me".

    that is:

    X - X = 0 (where X = "whatever you owe me") <---one of the basic rules of arithmetic. also written as: X + (-X) = 0. this says something special about -X, and 0 (if you pay what you owe, you owe nothing).

    so even though we don't KNOW (or remember) what "X" is, that doesn't mean we're totally "lost". we still know that what you owe, and what you pay should MATCH. so just the "rules themselves" give us SOME information, which we can sometimes use like a detective, to narrow down the possibilities.

    of course, that's a "baby example"...but the rules are very powerful. for example, in grade school, one often learns "times tables":

    1 times 6 is 6
    2 times 6 is 12
    3 times 6 is 18
    and so on.

    hmm...if one has already learned the "3's", one already knows that 6*3 is 18: 3+3+3+3+3+3+3 = 3+(3+3+3+3+3) = 3+(3+(3+3+3+3))

    = 3+(3+(3+(3+3+3))) = 3+(3+(3+(3+(3+3)))) = 3+(3+(3+(3+6))) = 3+(3+(3+9)) = 3+(3+12) = 3+15 = 18

    (because in learning the "times 3" we "count up by 3 each time" you can use your's OK).

    now if we know the RULE a*b = b*a, then we don't need to store 3*6 in our heads, just 6*3. this saves wear and tear on the old brain. so we can do this:

    memorize a*1 for a = 0 through 9
    memorize a*2 for a = 2 though 9 (since we already know a*1 = 1*a, and we've already covered it "in the 1's")
    memorize a*9 for a = 9 (although the "lower numbers of a" have already been covered).

    all of the arithmetic we do "long-hand" is based on the SAME RULES we use to do algebra. here is another example:

    (x+y)(x+y) = x*x + x*y + y*x + y*y = x2 + 2xy + y2 (because...xy = x*y = y*x = so x*y + y*x = xy + xy = (1+1)(xy) = 2xy).

    now that seems "abstract", but look:

    (11)(11) = (10+1)(10+1) = 10*10 + 10 + 10 + 1 = 100 + 20 + 1 = 121. it's the same rules, it's just with "actual numbers" we're so used to "collecting the 100's, 10's and 1's" we forget that it's the RULES that let us actually DO that.


    unless you have some time-limit imposed upon you, feel free to take it as slow as you need until you UNDERSTAND. mathematics has a certain "organic" quality to it, the logic of it is designed for things 'to make sense". so if something is causing you trouble, don't "skip ahead" hoping it will "make sense later". untangle that knot, and lay the threads straight.
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