How can I get better at replicating/remembering proofs? [closed]
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Whenever I read proofs, I make sure to understand every detail, and the steps in between those details. I am very diligent in this.
However, I notice that if I think back to a theorem some time later, say the next day or so, I cannot remember the details of the proof and if asked to replicate the proof, I don't believe I would be able to.
Are there techniques, or what are some of your techniques, to making sure you can replicate a proof?
proof-writing soft-question education
asked Aug 10 at 21:41
Al Jebr
3,95743070
closed as primarily opinion-based by José Carlos Santos, mfl, Xander Henderson, max_zorn, Taroccoesbrocco Aug 11 at 5:20
Many good questions generate some degree of opinion based on expert experience, but answers to this question will tend to be almost entirely based on opinions, rather than facts, references, or specific expertise. If this question can be reworded to fit the rules in the help center, please edit the question.
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up vote
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Whenever I read proofs, I make sure to understand every detail, and the steps in between those details. I am very diligent in this.
However, I notice that if I think back to a theorem some time later, say the next day or so, I cannot remember the details of the proof and if asked to replicate the proof, I don't believe I would be able to.
Are there techniques, or what are some of your techniques, to making sure you can replicate a proof?
proof-writing soft-question education
asked Aug 10 at 21:41
Al Jebr
3,95743070
closed as primarily opinion-based by José Carlos Santos, mfl, Xander Henderson, max_zorn, Taroccoesbrocco Aug 11 at 5:20
Many good questions generate some degree of opinion based on expert experience, but answers to this question will tend to be almost entirely based on opinions, rather than facts, references, or specific expertise. If this question can be reworded to fit the rules in the help center, please edit the question.
1
I think, an important concept would be not to hard-learn a proof, but to understand the result and prove it (partly) yourself. It's your own proof that stays in your head.
– zzuussee
Aug 10 at 21:42
1
@AlJebr: Maybe some of thoughts are helpful at: math.stackexchange.com/questions/1091908/…
– Moo
Aug 10 at 21:46
1
I don't think you should try to remember every detail. You should only try to remember the sketch of the proof, or the main idea, and be able to deduce the intermediate steps.
– Doug M
Aug 10 at 21:47
It depends upon the sub-discipline and the particular proof, but I always remember a proof better if I have a graphic or associated figure. Look up the great figure for the proof that $n choose 2$ based on triangular numbers.
– David G. Stork
Aug 10 at 22:16
I like to see students compute examples, in as concrete a manner as possible. Examples where the hypotheses of the theorem apply show how the thing works out. Examples where the hypotheses don't apply may reveal limitations of the result. For instance, when someone asks about Jordan Normal Form on this site, I often solve $P^-1 AP = J$ and type in all the matrices. I wish the students would do that much themselves. Practice makes firm memories.
– Will Jagy
Aug 10 at 22:20
add a comment |Â
up vote
1
down vote
favorite
up vote
1
down vote
favorite
Whenever I read proofs, I make sure to understand every detail, and the steps in between those details. I am very diligent in this.
However, I notice that if I think back to a theorem some time later, say the next day or so, I cannot remember the details of the proof and if asked to replicate the proof, I don't believe I would be able to.
Are there techniques, or what are some of your techniques, to making sure you can replicate a proof?
proof-writing soft-question education
asked Aug 10 at 21:41
Al Jebr
3,95743070
Whenever I read proofs, I make sure to understand every detail, and the steps in between those details. I am very diligent in this.
However, I notice that if I think back to a theorem some time later, say the next day or so, I cannot remember the details of the proof and if asked to replicate the proof, I don't believe I would be able to.
Are there techniques, or what are some of your techniques, to making sure you can replicate a proof?
proof-writing soft-question education
asked Aug 10 at 21:41
Al Jebr
3,95743070
asked Aug 10 at 21:41
Al Jebr
3,95743070
asked Aug 10 at 21:41
Al Jebr
3,95743070
asked Aug 10 at 21:41
Al Jebr
3,95743070
3,95743070
closed as primarily opinion-based by José Carlos Santos, mfl, Xander Henderson, max_zorn, Taroccoesbrocco Aug 11 at 5:20
Many good questions generate some degree of opinion based on expert experience, but answers to this question will tend to be almost entirely based on opinions, rather than facts, references, or specific expertise. If this question can be reworded to fit the rules in the help center, please edit the question.
closed as primarily opinion-based by José Carlos Santos, mfl, Xander Henderson, max_zorn, Taroccoesbrocco Aug 11 at 5:20
Many good questions generate some degree of opinion based on expert experience, but answers to this question will tend to be almost entirely based on opinions, rather than facts, references, or specific expertise. If this question can be reworded to fit the rules in the help center, please edit the question.
1
I think, an important concept would be not to hard-learn a proof, but to understand the result and prove it (partly) yourself. It's your own proof that stays in your head.
– zzuussee
Aug 10 at 21:42
1
@AlJebr: Maybe some of thoughts are helpful at: math.stackexchange.com/questions/1091908/…
– Moo
Aug 10 at 21:46
1
I don't think you should try to remember every detail. You should only try to remember the sketch of the proof, or the main idea, and be able to deduce the intermediate steps.
– Doug M
Aug 10 at 21:47
It depends upon the sub-discipline and the particular proof, but I always remember a proof better if I have a graphic or associated figure. Look up the great figure for the proof that $n choose 2$ based on triangular numbers.
– David G. Stork
Aug 10 at 22:16
I like to see students compute examples, in as concrete a manner as possible. Examples where the hypotheses of the theorem apply show how the thing works out. Examples where the hypotheses don't apply may reveal limitations of the result. For instance, when someone asks about Jordan Normal Form on this site, I often solve $P^-1 AP = J$ and type in all the matrices. I wish the students would do that much themselves. Practice makes firm memories.
– Will Jagy
Aug 10 at 22:20
add a comment |Â
1
I think, an important concept would be not to hard-learn a proof, but to understand the result and prove it (partly) yourself. It's your own proof that stays in your head.
– zzuussee
Aug 10 at 21:42
1
@AlJebr: Maybe some of thoughts are helpful at: math.stackexchange.com/questions/1091908/…
– Moo
Aug 10 at 21:46
1
I don't think you should try to remember every detail. You should only try to remember the sketch of the proof, or the main idea, and be able to deduce the intermediate steps.
– Doug M
Aug 10 at 21:47
It depends upon the sub-discipline and the particular proof, but I always remember a proof better if I have a graphic or associated figure. Look up the great figure for the proof that $n choose 2$ based on triangular numbers.
– David G. Stork
Aug 10 at 22:16
I like to see students compute examples, in as concrete a manner as possible. Examples where the hypotheses of the theorem apply show how the thing works out. Examples where the hypotheses don't apply may reveal limitations of the result. For instance, when someone asks about Jordan Normal Form on this site, I often solve $P^-1 AP = J$ and type in all the matrices. I wish the students would do that much themselves. Practice makes firm memories.
– Will Jagy
Aug 10 at 22:20
1
1
I think, an important concept would be not to hard-learn a proof, but to understand the result and prove it (partly) yourself. It's your own proof that stays in your head.
– zzuussee
Aug 10 at 21:42
I think, an important concept would be not to hard-learn a proof, but to understand the result and prove it (partly) yourself. It's your own proof that stays in your head.
– zzuussee
Aug 10 at 21:42
1
1
@AlJebr: Maybe some of thoughts are helpful at: math.stackexchange.com/questions/1091908/…
– Moo
Aug 10 at 21:46
@AlJebr: Maybe some of thoughts are helpful at: math.stackexchange.com/questions/1091908/…
– Moo
Aug 10 at 21:46
1
1
I don't think you should try to remember every detail. You should only try to remember the sketch of the proof, or the main idea, and be able to deduce the intermediate steps.
– Doug M
Aug 10 at 21:47
I don't think you should try to remember every detail. You should only try to remember the sketch of the proof, or the main idea, and be able to deduce the intermediate steps.
– Doug M
Aug 10 at 21:47
It depends upon the sub-discipline and the particular proof, but I always remember a proof better if I have a graphic or associated figure. Look up the great figure for the proof that $n choose 2$ based on triangular numbers.
– David G. Stork
Aug 10 at 22:16
It depends upon the sub-discipline and the particular proof, but I always remember a proof better if I have a graphic or associated figure. Look up the great figure for the proof that $n choose 2$ based on triangular numbers.
– David G. Stork
Aug 10 at 22:16
I like to see students compute examples, in as concrete a manner as possible. Examples where the hypotheses of the theorem apply show how the thing works out. Examples where the hypotheses don't apply may reveal limitations of the result. For instance, when someone asks about Jordan Normal Form on this site, I often solve $P^-1 AP = J$ and type in all the matrices. I wish the students would do that much themselves. Practice makes firm memories.
– Will Jagy
Aug 10 at 22:20
I like to see students compute examples, in as concrete a manner as possible. Examples where the hypotheses of the theorem apply show how the thing works out. Examples where the hypotheses don't apply may reveal limitations of the result. For instance, when someone asks about Jordan Normal Form on this site, I often solve $P^-1 AP = J$ and type in all the matrices. I wish the students would do that much themselves. Practice makes firm memories.
– Will Jagy
Aug 10 at 22:20
add a comment |Â
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I think, an important concept would be not to hard-learn a proof, but to understand the result and prove it (partly) yourself. It's your own proof that stays in your head.
– zzuussee
Aug 10 at 21:42
1
@AlJebr: Maybe some of thoughts are helpful at: math.stackexchange.com/questions/1091908/…
– Moo
Aug 10 at 21:46
1
I don't think you should try to remember every detail. You should only try to remember the sketch of the proof, or the main idea, and be able to deduce the intermediate steps.
– Doug M
Aug 10 at 21:47
It depends upon the sub-discipline and the particular proof, but I always remember a proof better if I have a graphic or associated figure. Look up the great figure for the proof that $n choose 2$ based on triangular numbers.
– David G. Stork
Aug 10 at 22:16
I like to see students compute examples, in as concrete a manner as possible. Examples where the hypotheses of the theorem apply show how the thing works out. Examples where the hypotheses don't apply may reveal limitations of the result. For instance, when someone asks about Jordan Normal Form on this site, I often solve $P^-1 AP = J$ and type in all the matrices. I wish the students would do that much themselves. Practice makes firm memories.
– Will Jagy
Aug 10 at 22:20