[QUOTE=Fourier;48315713]But that doesn't make sense, unless we split set for example {2} into {1} and {1}?
Also that Banach-Tarski paradox, professor told us about it many times.[/QUOTE]
Well, it's not quite that simple. Evidently it relies on all sets of real numbers being Lebesgue measurable and ordinals and shit.
I know there must be some underlying mechanism, but it can't be so hard I guess. You break numbers into smaller parts with some rule, and then you can add them together into original set.
But this means set must be ordered correct?
[editline]29th July 2015[/editline]
Maybe if Set = Vector (ordered set of same type numbers), but I can't imagine something else yet.
The other day I realized that you can use the geometric series sum formula to express any repeating decimal as a fraction. I was excited, I never realized this before. I was going to write a program to automate it for a little bit of Python practice. Then I realized it's trivially easy. Divide the repeating digits by as many nines.
I think I don't know any real math. I just know a series of trivially simple facts.
[QUOTE=JohnnyMo1;48342349]The other day I realized that you can use the geometric series sum formula to express any repeating decimal as a fraction. I was excited, I never realized this before. I was going to write a program to automate it for a little bit of Python practice. Then I realized it's trivially easy. Divide the repeating digits by as many nines.
I think I don't know any real math. I just know a series of trivially simple facts.[/QUOTE]
How about writing a program that converts x^(1/2) into its continued fraction form?
Square roots always have a periodic continued fraction.
Info:
[url]https://en.wikipedia.org/wiki/Continued_fraction[/url]
[QUOTE=Drakehawke;48214652]Are there any major math specific forums any of you frequent?[/QUOTE]
I tried posting on the xkcd 'Mathematics' subforum when someone else posted a new thread about a discovery made by my collaborators and myself.
The moderator removed my post because it was 'Off-topic'.
Hey so I'm alright at maths but I need an equation that's above my level: Lets assume I find the intersection point of a ray trace and a plane at an angle (lets assume that pitch and roll are constant). How would I find the 2D coordinates on the place, if I had the 3D intersection point, the 3D vector for the (0,0) point on the plane, and the 3D angle of the plane?
[QUOTE=James xX;48371274]Hey so I'm alright at maths but I need an equation that's above my level: Lets assume I find the intersection point of a ray trace and a plane at an angle (lets assume that pitch and roll are constant). How would I find the 2D coordinates on the place, if I had the 3D intersection point, the 3D vector for the (0,0) point on the plane, and the 3D angle of the plane?[/QUOTE]
It should just be the vector directed at the origin of the plane subtracted from the vector directed at the intersection point.
[URL="http://www.theguardian.com/science/alexs-adventures-in-numberland/2015/aug/10/attack-on-the-pentagon-results-in-discovery-of-new-mathematical-tile"]http://www.theguardian.com/science/alexs-adventures-in-numberland/2015/aug/10/attack-on-the-pentagon-results-in-discovery-of-new-mathematical-tile[/URL]
[URL="http://www.forbes.com/sites/kevinknudson/2015/08/06/a-new-way-to-tile-your-floor-if-you-like-pentagons"]http://www.forbes.com/sites/kevinknudson/2015/08/06/a-new-way-to-tile-your-floor-if-you-like-pentagons
[/URL]
[THUMB]http://i.imgur.com/c4zd4S4.png[/THUMB]
Rarely do new discoveries in pure mathematics get noticed outside of academia.
College has gave me some starter A2 work sheet . It was fractions which are fine but I cant do functions.
Okay so I suck at fucking math. I'm trying to get my GED and my grades are amazing in reading/writing and social studies etcera but I fail totally in math.
Like, I passed the social studies and reading/writing practice test already with a prescore of 10 or higher. Math besides decimal points and fractions, I have a score of like...4 or less. I have discalculia and it's hard.
Is there any sites or videos I should know about to make math easier?
[QUOTE=HandsomeFrog;48522727]Okay so I suck at fucking math. I'm trying to get my GED and my grades are amazing in reading/writing and social studies etcera but I fail totally in math.
Like, I passed the social studies and reading/writing practice test already with a prescore of 10 or higher. Math besides decimal points and fractions, I have a score of like...4 or less. I have discalculia and it's hard.
Is there any sites or videos I should know about to make math easier?[/QUOTE]
I like exam solutions
Guys, how do I make myself not suck at trigonometry?
So my friend needed a 10.5 to pass a course but he actually got 10.499...
Notes can't be rounded.
Did he pass?
With the nines repeating indefinitely? Yes.
[editline]24th August 2015[/editline]
But his teacher has a very odd grading system.
[editline]24th August 2015[/editline]
[QUOTE=Maddog's Here;48522702]College has gave me some starter A2 work sheet . It was fractions which are fine but I cant do functions.[/QUOTE]
What problems do you have with functions? They're basically central to all math.
[QUOTE=mikester112;48522793]Guys, how do I make myself not suck at trigonometry?[/QUOTE]
By studying trigonometry
[QUOTE=PopLot;48533394]By studying trigonometry[/QUOTE]
I figured that my main problem was that a lot of times I just treated it like algebra and geometry, both of which I found really easy so I sort of neglected the fundamentals. Oops. I'm doing much better now though.
[QUOTE=JohnnyMo1;48529605]What problems do you have with functions? They're basically central to all math.[/QUOTE]
Well ive just studied them again, got it back into my head. So it turns out the only thing I hate about functions so far is the Domain and Range. Combining them and inverse functions are fine
Hey all, sorry if this has been asked before, but can you recommend some calculus books that will give me a more in depth understanding of the concepts and theories? I am not a complete stranger to calculus, having finished Calculus III, which goes up to Stokes and Divergence theorem. I was able to pass the class fairly well, but my understanding of the concepts isn't as in depth as I wish it to be. I am currently looking at the book "Calculus" by Michael Spivak, and am open to any other suggestions.
[QUOTE=lyna;48577752]Hey all, sorry if this has been asked before, but can you recommend some calculus books that will give me a more in depth understanding of the concepts and theories? I am not a complete stranger to calculus, having finished Calculus III, which goes up to Stokes and Divergence theorem. I was able to pass the class fairly well, but my understanding of the concepts isn't as in depth as I wish it to be. I am currently looking at the book "Calculus" by Michael Spivak, and am open to any other suggestions.[/QUOTE]
There are a few good choices. The book you're looking at is what I used for my introductory analysis class and I thought it was pretty good. Rudin is another one. Spivak's [I]Calculus on Manifolds[/I] begins with the inner product on Rn and ends with Green's Theorem and the Divergence Theorem if you were more interested in those concepts.
[QUOTE=lyna;48577752]Hey all, sorry if this has been asked before, but can you recommend some calculus books that will give me a more in depth understanding of the concepts and theories? I am not a complete stranger to calculus, having finished Calculus III, which goes up to Stokes and Divergence theorem. I was able to pass the class fairly well, but my understanding of the concepts isn't as in depth as I wish it to be. I am currently looking at the book "Calculus" by Michael Spivak, and am open to any other suggestions.[/QUOTE]
Spivak is good. I like Abbott's [I]Understanding Analysis[/I] and I feel it's very clear. Best would be Rudin. Usually that will wait for after one at the level of the other books I mentioned, but hey, I did Rudin first! It's not impossible.
alright, thanks for your suggestions, I'm probably going to do Calculus > Calculus on Manifolds > Understanding Analysis > Principles of Mathematical Analysis by Rudin
Does that seem right?
Another semi-related question. When it comes to learning to read and write proofs, with proper notation, does that come simply through study of the books listed above, or are there any separate resources you would recommend?
That's probably like 2 books too many. Rudin covers analysis on manifolds, so if you're going to do Rudin I would at least skip [I]Calculus on Manifolds[/I]. Maybe someone here has a different opinion on it but I don't think you'd gain much by doing both.
[QUOTE=lyna;48578399]alright, thanks for your suggestions, I'm probably going to do Calculus > Calculus on Manifolds > Understanding Analysis > Principles of Mathematical Analysis by Rudin
Does that seem right?
Another semi-related question. When it comes to learning to read and write proofs, with proper notation, does that come simply through study of the books listed above, or are there any separate resources you would recommend?[/QUOTE]
If you're interested in an accessible text on general proof writing and constructing mathematical arguments in a [I]ton[/I] of different areas, I'd recommend Velleman's [I]How to Prove It[/I].
[QUOTE=JohnnyMo1;48580791]That's probably like 2 books too many. Rudin covers analysis on manifolds, so if you're going to do Rudin I would at least skip [I]Calculus on Manifolds[/I]. Maybe someone here has a different opinion on it but I don't think you'd gain much by doing both.[/QUOTE]
Alright, so then I'll do Calculus > Rudin, guess I don't need to read as many books then
[QUOTE=PopLot;48581520]If you're interested in an accessible text on general proof writing and constructing mathematical arguments in a [I]ton[/I] of different areas, I'd recommend Velleman's [I]How to Prove It[/I].[/QUOTE]
Will check it out, thanks
Can someone explain to me why in Bohr's model of an atom centrifugal force is used in the force diagram of the electron. I understand that it's supposed to allow for the forces to equal out, but I was always under the impression that centrifugal force was not an actual force.
[QUOTE=gangstadiddle;48587574]Can someone explain to me why in Bohr's model of an atom centrifugal force is used in the force diagram of the electron. I understand that it's supposed to allow for the forces to equal out, but I was always under the impression that centrifugal force was not an actual force.[/QUOTE]
This looks like it is a physics question rather than a maths one, so you'll probably want to post it in the physics thread:
[URL]http://facepunch.com/showthread.php?t=1245020[/URL]
Learning Linear Algebra is quite straightforward :)
[QUOTE=gangstadiddle;48587574]Can someone explain to me why in Bohr's model of an atom centrifugal force is used in the force diagram of the electron. I understand that it's supposed to allow for the forces to equal out, but I was always under the impression that centrifugal force was not an actual force.[/QUOTE]
Its been a while but I don't think the centrifugal force has a play in it. Are you sure you are not mixing it up with the centripetal force? You are correct that it is not an actual force, but it still does get called one, along with the Coriolis force and the Euler force which arise as inertial forces in a rotating reference frame.
differential equations so far is going pretty well, i really like how the problems make you think, and how you can even see how useful they would be (even though I know most real world applications are PDEs, this is still cool). it's quite challenging to actually derive a DE from a word problem, but I guess that will just come with practice. would've loved to major instead of minor in math if i had the time for a double major
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