Linear algebra

A

AbdelRahmanShady

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Sorry dont know where to post this.
But i am planning on self learning linear algebra. I watched 3blue1brown series and want tp go deep, but i dont know which book to pick. I need it to begin from zero and build on that yet be completely rigrous. I dont mind if book doesnt cover advanced concepts if it can give me the right foundation to come up with my own proofs.any videos recommended will also be helpful
 
Kolman has good intro to Linear Algebra books. The classic book is by Hoffman and Kunze, but you might find it a bit advanced even though some colleges use it for their intro to Linear Algebra course.
 
The thinner books are not necessarily the easier ones. I studied commutative algebra from a thin book and it was the hardest book I ever studied from. In fact, it was a war between me and the problem sets in that book and I am sad to say that I lost that battle in my of the sections in that book. Commutative Algebra by far was the hardest course I have ever taken.
 
You should now what you understand. I am not sure what you are asking?
 
Sometimes just because proof in a book you falsely convince yourself that it works without actually fully understanding so how to defferrenciate between true understanding or just memorizkng or falsly cinbinving
 
Steven G said:
The thinner books are not necessarily the easier ones. I studied commutative algebra from a thin book and it was the hardest book I ever studied from. In fact, it was a war between me and the problem sets in that book and I am sad to say that I lost that battle in my of the sections in that book. Commutative Algebra by far was the hardest course I have ever taken.
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Coincidentally, I remember studying commutative algebra from a thin book too, but a very long time ago. Don't remember the author, but remember liking the book even if I haven't learned that much in the end.

I'd agree that thinness alone is not enough, but, personally, I find myself feeling lost and bored with thick books. They can be good for reference, but they rarely worked for me when I needed an introduction to a new subject.
 
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AbdelRahmanShady said:
Sometimes just because proof in a book you falsely convince yourself that it works without actually fully understanding so how to defferrenciate between true understanding or just memorizkng or falsly cinbinving
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I am quite familiar myself with those false convictions :( Some recommendations I can think of:
  • Trying to describe the proof to someone familiar with the subject, like other students. It helps if they challenge your statements as much as possible. Personally, I've often found holes in my understanding when trying to explain it to others.
  • Doing exercises which involve similar proofs.
  • Doing any exercises on the topic.
 
AbdelRahmanShady said:
Sometimes just because proof in a book you falsely convince yourself that it works without actually fully understanding so how to defferrenciate between true understanding or just memorizkng or falsly cinbinving
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And another one: do not be afraid to make mistakes and/or ask silly questions. One might feel slightly embarrassed when corrected, but, in my experience, realizing one's mistakes has been the most efficient way to learn.
 
blamocur said:
I am quite familiar myself with those false convictions :( Some recommendations I can think of:
  • Trying to describe the proof to someone familiar with the subject, like other students. It helps if they challenge your statements as much as possible. Personally, I've often found holes in my understanding when trying to explain it to others.
  • Doing exercises which involve similar proofs.
  • Doing any exercises on the topic.
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I know no students i am self learning
 
AbdelRahmanShady said:
Last question when to know tou understand a solution or just convinving yourself you understood
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Use the proof to work out examples. Usually this not only exposes any problems you made while deriving your proof but it also gives you practical experience in using it. You get a better feel for things.

-Dan
 
Sounds like freeMATHhelp is your only choice for now :) I wonder if there are other forums specifically for discussing math as opposed to having questions answered.
 
topsquark said:
Use the proof to work out examples. Usually this not only exposes any problems you made while deriving your proof but it also gives you practical experience in using it. You get a better feel for things.

-Dan
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I mostly prove previous theoems in my own way so even if my proof is wrong the theorm will hold. Most pf my proofs are logical but i am always afraid i messed an eedge case or a loop hole like what happens in programming
 
AbdelRahmanShady said:
I mostly prove previous theoems in my own way so even if my proof is wrong the theorm will hold. Most pf my proofs are logical but i am always afraid i messed an eedge case or a loop hole like what happens in programming
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If your proofs aren't too long and nicely typeset I am sure someone will try to check them.
 
Ok what about how to know if I understand a Proof. I can sure apply the theorm but fully understanding the proof. How to know if I fully understand each steps and constrains that will make proof fail if not present.
 
AbdelRahmanShady said:
Sometimes just because proof in a book you falsely convince yourself that it works without actually fully understanding so how to defferrenciate between true understanding or just memorizkng or falsly cinbinving
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You need to understand every line in the proof. Don't memorize anything. You should know if you are understanding something, are memorizing something or are falsely convincing yourself that you understand the lines in the proof.
 
AbdelRahmanShady said:
Ok what about how to know if I understand a Proof. I can sure apply the theorm but fully understanding the proof. How to know if I fully understand each steps and constrains that will make proof fail if not present.
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I don't have any advice for that. I remember that in my self-studies I often felt stuck on those. I also remember that I was held back by my inability to move on before I thought I understood the current material completely. In hindsight I should have been sloppier, in the sense that I should try moving on, work on exercises, then come back and try re-digesting the places where I was stuck. But I am not sure my experience is applicable to everybody.
 
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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