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 Academic Guidance Academic Guidance - Academic guidance for those pursuing a college degree... what college? Grad school? PhD help?

 June 18th, 2014, 09:48 PM #2 Newbie   Joined: Jun 2014 From: USA Posts: 21 Thanks: 2 Better to share the problem here. Make a thread with question.
 June 19th, 2014, 05:16 AM #3 Math Team   Joined: Dec 2013 From: Colombia Posts: 6,940 Thanks: 2267 Math Focus: Mainly analysis and algebra Sharing individual problems is a good way to get help on individual questions. You could try asking for hints only, not complete solutions. That would perhaps help your problem solving. On the knowledge side the first thing to say is: don't worry. The University should not admit you if you don't have sufficient knowledge. You might have to work hard to fill some holes, but that shouldn't stop you from understanding the course. I too have big holes in my geometry knowledge. I use wikipedia, wikiproof and other web resources as references especially for geometric theorems. The key is to never look only at the result, but to read the proof and be suure that you understand it. My approach to learning is first to learn what tools are available (in terms of theorems and methods) and where I can find the detail. Learrning the detail myself comes later, but I never use a theorem that I can't understand. If I think a theorem is sufficiently useful, I try to learn the proof. This helps to fix the result in my mind and also allows me to derive it if I can't remember it clearly. Finally, at university and online, always work a problem as far as you can before asking for help, but ALWAYS ask for help if you need it. Sitting quietly staring at a problem won't solve it. Often leavinng it to turn over in the back of your mind while you do something else is good for getting solutions.
 June 19th, 2014, 08:09 AM #4 Newbie   Joined: Jun 2014 From: Canada Posts: 2 Thanks: 0 Okay sure, here are two problems. 4. Let there be a number x such that x is an integer and x is > or = to 8. Prove that x may be expressed in the form 3a + 5b for some integers a and b. So I know that x can be either odd or even and that is how far I got, and then I set forth some cases to show that they can be written in the form 3a + 5b, but I could not get to the general case as I would be assuming the very thing I am trying to prove. 4.9) Let b = a mod (n), prove that b^2 = a^2 (n). I got to the part that n divides a-b so a-b = nx for some integer x, now I am at a loss at how to manipulate the equation to yield a^-b^2. If anyone has good encyclopedia like websites for knowledge please let me know, I will try to work on learning the ideas, thanks!
 June 19th, 2014, 08:32 AM #5 Math Team   Joined: Dec 2013 From: Colombia Posts: 6,940 Thanks: 2267 Math Focus: Mainly analysis and algebra 4.8$$) This is a question about modular arithmetic. If you work in \mod{3} you need only to think about three cases: n = 3k, n=3k+1 and n=3k+2. b need only take the values 0, 1, 2 to be able to make any n. 4.9$$) What about $a+b$?

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