View source for 15-344/Homework Assignment 8

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This assignment is due <span style="color: blue;">at the tutorials on Thursday November 26</span>. Here and everywhere, '''neatness counts!!''' You may be brilliant and you may mean just the right things, but if the teaching assistants will be having hard time deciphering your work they will give up and assume it is wrong.

'''Reread''' sections 5.1-5.5 of our textbook. Remember that reading math isn't like reading a novel! If you read a novel and miss a few details most likely you'll still understand the novel. But if you miss a few details in a math text, often you'll miss everything that follows. So reading math takes reading and rereading and rerereading and a lot of thought about what you've read. Also, '''preread''' sections 6.1-6.3, just to get a feel for the future.

'''Solve and submit''' problems 7, 9a, 11, and 15 in section 5.5. (9b was originally also assigned, but it is too difficult).

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Homework Assignment 8 Solution

'''9a) Show by combinatorial argument that <math>\binom{2n}{2} = 2 \binom{n}{2} + n^2 </math>'''

'''A)'''Split <math> 2n </math> into two groups of n. Then choosing 2 out of <math> 2n </math> can be seen as either choosing 2 from group 1 only
, which is <math>\binom{n}{2} </math> or 2 from group 2 only, which is also <math>\binom{n}{2} </math>, or one from each group, which is
<math> n^2 </math>. Their sum gives the total number of possibilities, which is exactly the right hand side of the equality.

== Scanned Solution to Homework8 P7,11,15 == 
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