Linear algebra

AbdelRahmanShady said:
I know what you both mean but when you are reading a proof for 2 days straight. Yoi start to convince yourself subconsiouly without knowing that you are beginning to understand while your understatement didnt change you are just nore familiar with proof. How to avoid that
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I wouldn't recommend reading a proof for 2 days straight -- at the very least take a break :) Switch to something else, maybe even move on to see what else is the book; then come back later and see if it gets any easier. Students attending lectures rarely understand everything during the lecture, but things get clearer when they get back to the subject later.

Unfortunately, there is no single magic advice to make things painless. You just keep trying, see what works for you, and try getting help where you can. But also, and also unfortunately, you might discover, as I have on many occasions, that some subjects are too difficult for self-studies. I used to work with a very bright engineer who just graduated from an engineering school. He too tried to study linear algebra on his own and eventually gave up even though there were several colleagues who could help him. I don't want to discourage you, but nor do I want you to start hating all math just because some subjects turned out too tough for self-study.
 
I am currently grade 10 so coollugues who know linear algebra is out of the picture. 2 days was just an example but sometimes it takes me a month. It is not that I dont understand the proof I feel something is missing. proof not rigorous or depend on intution which is good to learn but intution isnt always right and if I learn things by intution i will make wrong proofs with intuition
 
AbdelRahmanShady said:
I know what you both mean but when you are reading a proof for 2 days straight. Yoi start to convince yourself subconsiouly without knowing that you are beginning to understand while your understatement didnt change you are just nore familiar with proof. How to avoid that
Click to expand...
This was what I used to do in my "school/college" days:

After studying the proof,

In a fresh sheet of paper I would write the proposition - looking at the book and making sure that I wrote it exactly.

Then I will shut the book and try to write the proof. I would open the book and get a nudge till and until I had completed the proof.

Now I'll read my writing and compare carefully with book's writing. If there were no mistakes, I would take another fresh piece of paper and try the above steps again. I would repeat it again about a week later - till and until I could re-write the proof without referring back to the book.
 
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something like this
When he say We recigniz ethis or we notice that. I feel something is missing not rigorous or something i feel this itching feel i dont recignize that i am juust believing
 
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or when he operate on list length n and start manippulating it I tememberr if i wanted to do something terms in pair there are catches like odd or even so why when he do it there is not.
 
Subhotosh Khan said:
This was what I used to do in my "school/college" days:

After studying the proof,

In a fresh sheet of paper I would write the proposition - looking at the book and making sure that I wrote it exactly.

Then I will shut the book and try to write the proof. I would open the book and get a nudge till and until I had completed the proof.

Now I'll read my writing and compare carefully with book's writing. If there were no mistakes, I would take another fresh piece of paper and try the above steps again. I would repeat it again about a week later - till and until I could re-write the proof without referring back to the book.
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You need to see this twice.

After studying the proof,

In a fresh sheet of paper I would write the proposition - looking at the book and making sure that I wrote it exactly.

Then I will shut the book and try to write the proof. I would open the book and get a nudge till and until I had completed the proof.

Now I'll read my writing and compare carefully with book's writing. If there were no mistakes, I would take another fresh piece of paper and try the above steps again. I would repeat it again about a week later - till and until I could re-write the proof without referring back to the book.
 
AbdelRahmanShady said:
When he say We recigniz ethis or we notice that. I feel something is missing not rigorous or something i feel this itching feel i dont recignize that i am juust believing
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As a student when I read in my textbook as easily seen I knew that it was going to be a long night. I almost never easily saw what they were saying. It was very depressing but I knew that I would eventually see what the author was saying. Sometime it took 10-15 minutes other times I had to think about it for days until I understood it to my satisfaction. Studying math is not always easy but if you have some talent then you can do it. Never worry about the rate that you learn at.
I remember leaving my Abstract Algebra class one day thinking that I understood everything in that class and could actually teach that same lecture later that day. Then I spoke with this classmate of mine and I thought that he attended a different class that I had. His understanding was so much deeper than mine, but before the next test came around I was at his level. Just stick with the material, don't leave anything unsettled for too long and you'll do fine.
 
I understand most of math to the point of making my own sometimes but the problem if my proof relied on obvious facts not intuition like in his book when the say something is row reduced or when in pother proof I add terms with pattern in columns. I remember infinite math and other loop holes so I want my proof or the proof in this book to be more algebraic and rigorous but don't know how. My problem is not mostly understanding proof to intuition my problem is formalizing intuition thrown in textbooks
 
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AbdelRahmanShady said:
I understand most of math to the point of making my own sometimes but the problem if my proof relied on obvious facts not intuition like in his book when the say something is row reduced or when in pother proof I add terms with pattern in columns. I remember infinite math and other loop holes so I want my proof or the proof in this book to be more algebraic and rigorous but don't know how. My problem is not mostly understanding proof to intuition my problem is formalizing intuition thrown in textbooks
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Please review your post before posting. You had ~10 typos in the post above (# 28). Those can be easily located and corrected because those will be red-lined.
 
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