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drewva
 Post subject: GRA Help
PostPosted: Mon, 2 Jan 2012 15:01:28 UTC 
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I am studying for my GRA exam for college entrance. I was never great at math during high school.
Please help if you can direct me to some basic math and calculus study resources. Thanks for your help! :(

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outermeasure
 Post subject: Re: GRA Help
PostPosted: Mon, 2 Jan 2012 15:57:08 UTC 
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\begin{aligned} Spin(1)&=O(1)=\mathbb{Z}/2&\quad&\text{and}\\ Spin(2)&=U(1)=SO(2)&&\text{are obvious}\\ Spin(3)&=Sp(1)=SU(2)&&\text{by }q\mapsto(\mathop{\mathrm{Im}}\mathbb{H}\ni p\mapsto qp\bar{q})\\ Spin(4)&=Sp(1)\times Sp(1)&&\text{by }(q_1,q_2)\mapsto(\mathbb{H}\ni p\mapsto q_1p\bar{q_2})\\ Spin(5)&=Sp(2)&&\text{by }\mathbb{HP}^1\cong S^4_{round}\hookrightarrow\mathbb{R}^5\\ Spin(6)&=SU(4)&&\text{by the irrep }\Lambda_+\mathbb{C}^4 \end{aligned}
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Shadow
 Post subject: Re: GRA Help
PostPosted: Mon, 2 Jan 2012 20:12:34 UTC 
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drewva wrote:
I am studying for my GRA exam for college entrance. I was never great at math during high school.
Please help if you can direct me to some basic math and calculus study resources. Thanks for your help! :(


1. I have no idea what a GRA is, and google thinks you mean GRE, but that's for graduate school not basic college, so you're on your own there.
2. Have you tried googling "calculus help" or "practice calculus" there are like a jillion resources for that. Our own main site http://www.sosmath.com/ has a lot of great calculus review things. Google is your friend.

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