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Math maturity 
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#1
Jan1513, 08:50 PM

P: 228

One of things I noticed when I self study is when I go check my answers against the solutions, some of my answers seem to be way off. For example there was a question that went "show that for any nxn non singular matrix it is row equivalent." I happened to show a proof by induction but in the solutions it just drew a arbirtrary nxn matrix with 1's running down the diagonal( these entries are obviously the pivot positions). I'm not sure if this normal or not?Will I just get better by practicing and struggling? But I fear I won't be able to get any better than I am now. The way I approach each section of a book is I first read very carefully and reread a few times before I feel I have a good understanding. Then I go to the problems and try to do all of them on my own. About 3/4 of them I can do and end up with the correct answer. Of course I recheck my solution. Then I check my solutions against the solution manual but at times like I said earlier my answers are way off than what is written in the solutions. This happens mostly on problems that say "show this...". I try my best to go back and fix my answer but I just end up leaving it since I feel its not worth it since I already know the solution. I'm trying hard to make sure that I can get up to the point where I can answer all the problems correctly but it seems quite hard.



#2
Jan1513, 09:28 PM

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P: 6,959

There are often several ways to prove the same math result. The fact that your proof is completely different from the book doesn't necessarily mean you are wrong.
If you want advice on whether your proof is correct, or help understanding a proof in the book, the math forums here are a good place to ask! 


#3
Jan1513, 09:38 PM

P: 228

Of course I ask for help on these forums but I don't want to ask for help on all the problems i'm stuck on here. I just feel that if can't do all the problems in each section that I don't understand the section well then. And once I know the solution I feel its useless going back since I already know the answer. And if I don't check my answers then ill never know if I did it correct or not. I do make an honest effort on each problem and at times like I said my answers are way off and I get discouraged easily. Hopefully you understand where I'm coming from.



#4
Jan1613, 04:00 AM

P: 828

Math maturity
And the same thing goes for the computational problems. 


#5
Jan1613, 11:25 AM

P: 228

Oh ok thanks. Now I'm encouraged to go on and struggle it out.



#6
Jan1613, 02:31 PM

P: 76

So if you turn to the solution and yours is wrong, I encourage you to retry your attempt. Often I find that seeing the solution makes me go, 'Oh ok!' and recognise where I went wrong. But if not, think of it this way: you now have one extra piece of data for making your solution. You still need to build the bridge from the data in the question to the solution provided. Plus, you can now work backwards from the solution to the question and maybe meet somewhere in the middle! Your confidence will grow when you go back and spot where you went wrong, I think. It is very disheartening to see you have got it wrong but not see why. 


#7
Jan1613, 04:13 PM

P: 1,197




#8
Jan1613, 04:31 PM

P: 228

Thanks guys and I agree with 3.141592's answer plus i'm trying to self study these things on my own in absence of a professor or friends. I guess that I should change the way I think. I shouldn't take it hard upon myself if I get some my answers wrong. Eventually i'll get better even though it will take me some time on my own. Most of us who are self studying I guess go through a similar process like i'm going through and eventually we all get better unless of course you are a genius.



#9
Jan1913, 10:24 PM

P: 1,042




#10
Jan2013, 09:05 AM

P: 76

When you get a solution wrong, try it with another easier method. When you get it right, try it with another harder method. A simple example: when converting units in a calculation let's say involving division, it is easy to cancel just by drawing a line through whatever like terms are written above and below the division line. It's a tiny bit harder to move units above or below the division line, and adjust the + or  sign of the exponents accordingly, and then add or subtract powers. Mostly because you have to do a tiny bit more thinking and there is more chance for arithmetical errors. But if you get it wrong, try it the easier way and see if you get it right. That might open up the door to where you went wrong the first time. And if you get it right, trying it the harder way might reveal some mechanism that was hidden with the easier method, or just generally help you get a different POV on the problem. 


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