Mixing
Memorising lots of maths theorems/lemmas
$begingroup$
In a few weeks I'll have my summer exams in a Senior Freshman Mathematics course. Two of my modules have a huge number of theorems, lemmas and definitions - over 200 definitions and 250 proofs by my last count - and I'm struggling to find a way to memorise them all. I know the key to memorisation is to understand the topic (which I do) however I still need to be able to perfectly recall the exact proof/definition in question. (It doesn't help that a lot of the material is similar and can be confused with a different proof/definition.)
So my question is, how do I memorise all this information? Is there something similar to the memory palace/method of loci, but for maths stuff?
abstract-algebra definition learning
asked Mar 5 '15 at 21:07
user221330user221330
2815
$endgroup$
add a comment |
$begingroup$
In a few weeks I'll have my summer exams in a Senior Freshman Mathematics course. Two of my modules have a huge number of theorems, lemmas and definitions - over 200 definitions and 250 proofs by my last count - and I'm struggling to find a way to memorise them all. I know the key to memorisation is to understand the topic (which I do) however I still need to be able to perfectly recall the exact proof/definition in question. (It doesn't help that a lot of the material is similar and can be confused with a different proof/definition.)
So my question is, how do I memorise all this information? Is there something similar to the memory palace/method of loci, but for maths stuff?
abstract-algebra definition learning
asked Mar 5 '15 at 21:07
user221330user221330
2815
$endgroup$
1
$begingroup$
Well. You can figure out what the most important definitions are, figure out what the major theorems are. Many definitions in algebra are the only things that make sense. For instance, you should be able to 'figure out' the definition of a ring homomorphism. You should spend time actually proving the theorems that you think you can, rather than simply reading the supplied proofs. For harder theorems, you might not be able to prove them, but trying to will certainly help you remember. 'Mathematics is not a spectator sport.'
$endgroup$
– RougeSegwayUser
Mar 5 '15 at 21:16
2
$begingroup$
Rote memorization won't work unless you have a photographic memory. You have to understand the proof. Once you do, you should be able to remember it. I took general topology 10 years ago and I'm not a topologist but I'm pretty sure I can still prove the Urysohn metrization theorem, because I understood the proof.
$endgroup$
– Matt Samuel
Mar 5 '15 at 21:26
add a comment |
$begingroup$
In a few weeks I'll have my summer exams in a Senior Freshman Mathematics course. Two of my modules have a huge number of theorems, lemmas and definitions - over 200 definitions and 250 proofs by my last count - and I'm struggling to find a way to memorise them all. I know the key to memorisation is to understand the topic (which I do) however I still need to be able to perfectly recall the exact proof/definition in question. (It doesn't help that a lot of the material is similar and can be confused with a different proof/definition.)
So my question is, how do I memorise all this information? Is there something similar to the memory palace/method of loci, but for maths stuff?
abstract-algebra definition learning
asked Mar 5 '15 at 21:07
user221330user221330
2815
$endgroup$
In a few weeks I'll have my summer exams in a Senior Freshman Mathematics course. Two of my modules have a huge number of theorems, lemmas and definitions - over 200 definitions and 250 proofs by my last count - and I'm struggling to find a way to memorise them all. I know the key to memorisation is to understand the topic (which I do) however I still need to be able to perfectly recall the exact proof/definition in question. (It doesn't help that a lot of the material is similar and can be confused with a different proof/definition.)
So my question is, how do I memorise all this information? Is there something similar to the memory palace/method of loci, but for maths stuff?
abstract-algebra definition learning
abstract-algebra definition learning
asked Mar 5 '15 at 21:07
user221330user221330
2815
asked Mar 5 '15 at 21:07
user221330user221330
2815
asked Mar 5 '15 at 21:07
user221330user221330
2815
asked Mar 5 '15 at 21:07
user221330user221330
2815
asked Mar 5 '15 at 21:07
user221330user221330
2815
2815
1
$begingroup$
Well. You can figure out what the most important definitions are, figure out what the major theorems are. Many definitions in algebra are the only things that make sense. For instance, you should be able to 'figure out' the definition of a ring homomorphism. You should spend time actually proving the theorems that you think you can, rather than simply reading the supplied proofs. For harder theorems, you might not be able to prove them, but trying to will certainly help you remember. 'Mathematics is not a spectator sport.'
$endgroup$
– RougeSegwayUser
Mar 5 '15 at 21:16
2
$begingroup$
Rote memorization won't work unless you have a photographic memory. You have to understand the proof. Once you do, you should be able to remember it. I took general topology 10 years ago and I'm not a topologist but I'm pretty sure I can still prove the Urysohn metrization theorem, because I understood the proof.
$endgroup$
– Matt Samuel
Mar 5 '15 at 21:26
add a comment |
1
$begingroup$
Well. You can figure out what the most important definitions are, figure out what the major theorems are. Many definitions in algebra are the only things that make sense. For instance, you should be able to 'figure out' the definition of a ring homomorphism. You should spend time actually proving the theorems that you think you can, rather than simply reading the supplied proofs. For harder theorems, you might not be able to prove them, but trying to will certainly help you remember. 'Mathematics is not a spectator sport.'
$endgroup$
– RougeSegwayUser
Mar 5 '15 at 21:16
2
$begingroup$
Rote memorization won't work unless you have a photographic memory. You have to understand the proof. Once you do, you should be able to remember it. I took general topology 10 years ago and I'm not a topologist but I'm pretty sure I can still prove the Urysohn metrization theorem, because I understood the proof.
$endgroup$
– Matt Samuel
Mar 5 '15 at 21:26
1
1
$begingroup$
Well. You can figure out what the most important definitions are, figure out what the major theorems are. Many definitions in algebra are the only things that make sense. For instance, you should be able to 'figure out' the definition of a ring homomorphism. You should spend time actually proving the theorems that you think you can, rather than simply reading the supplied proofs. For harder theorems, you might not be able to prove them, but trying to will certainly help you remember. 'Mathematics is not a spectator sport.'
$endgroup$
– RougeSegwayUser
Mar 5 '15 at 21:16
$begingroup$
Well. You can figure out what the most important definitions are, figure out what the major theorems are. Many definitions in algebra are the only things that make sense. For instance, you should be able to 'figure out' the definition of a ring homomorphism. You should spend time actually proving the theorems that you think you can, rather than simply reading the supplied proofs. For harder theorems, you might not be able to prove them, but trying to will certainly help you remember. 'Mathematics is not a spectator sport.'
$endgroup$
– RougeSegwayUser
Mar 5 '15 at 21:16
2
2
$begingroup$
Rote memorization won't work unless you have a photographic memory. You have to understand the proof. Once you do, you should be able to remember it. I took general topology 10 years ago and I'm not a topologist but I'm pretty sure I can still prove the Urysohn metrization theorem, because I understood the proof.
$endgroup$
– Matt Samuel
Mar 5 '15 at 21:26
$begingroup$
Rote memorization won't work unless you have a photographic memory. You have to understand the proof. Once you do, you should be able to remember it. I took general topology 10 years ago and I'm not a topologist but I'm pretty sure I can still prove the Urysohn metrization theorem, because I understood the proof.
$endgroup$
– Matt Samuel
Mar 5 '15 at 21:26
add a comment |
2 Answers
2
active
oldest
votes
$begingroup$
Formal proof of theorems is a sequential process.
[0] Start by absolutely knowing the definitions used in the theorem. You need to know what you're talking about.
Try to understand the theorem. If you don't understand it all at the beginning, then identify the parts of it that you do understand.
[1] Begin by making a list of the hypotheses.
If you are making up your own theorem, to construct a proof you can keep adding to the list of your hypotheses. Keep it up until there are enough hypotheses to imply the desired conclusion that you want to arrive at (the QED - look it up).
If you want to understand someone else's proof, you need to take ownership of the theorem as if you were creating it yourself. It pays to own the theorem and your proof of it.
[2] Then you start adding a list of intermediate conclusions.
Each intermediate conclusion should follow from
the hypotheses. together with
the previous intermediate conclusions.
Keep adding to the list of intermediates until you finally are ready to conclude.
[3] the conclusion is the statement of what needed to be proved.
I have to memorize by repeated engagement with the process of writing the steps down. Generally I can do it by memory somewhere around the fourth run through the steps.
In a less formal setting, say where you want to explain something to someone unfamiliar with the topic, you paint a background picture of what's going on in the context of the theorem.
Then you keep building the picture, making it more and more detailed, until there is no escaping the conclusion. Repeat four times.
Memorization follows from the engaged repetition, but NOT from rote repetition. See if you can generate a sort of emotional involvement. You have an intention, and you are emotionally committed to fulfilling that intention. Then I get the (emotional) payoff that goes with accomplishing the goal.
You might as well. It's kind of like solving a puzzle or winning a game. Ideally you'll be having a lot of fun and having a heck of a good time. That makes the repetition struggle-free.
Ideally, since the definitions are declared hypotheses, they will be absorbed by your memory as you repeat the proof, engaging committedly with the accomplishment of your goal.
answered Mar 5 '15 at 22:43
user37278user37278
112
$endgroup$
add a comment |
$begingroup$
Then you keep building the picture, making it more and more detailed, until there is no escaping the conclusion. Repeat four times.
Memorization follows from the engaged repetition, but NOT from rote repetition. See if you can generate a sort of emotional involvement. You have an intention, and you are emotionally committed to fulfilling that intention. Then I get the (emotional) payoff that goes with accomplishing the goal. You may as well. It's kind of like solving a puzzle or winning a game.
Ideally, since the definitions are declared hypotheses, they will be drawn into your memory as you repeat the proof, engaging committedly with accomplishing your goal.
answered Mar 5 '15 at 22:56
user37278user37278
112
$endgroup$
$begingroup$
Did you mean to post two answers?
$endgroup$
– Barry Cipra
Mar 5 '15 at 23:25
$begingroup$
I meant the two answers to be merged into one. Right now I don't know how to do that.
$endgroup$
– user37278
Jun 15 '18 at 3:38
$begingroup$
You should be able to edit your first answer with a copy of the second, and then delete the second answer. Look for options labeled "edit" and "delete" beneath the answers.
$endgroup$
– Barry Cipra
Jun 15 '18 at 12:08
$begingroup$
Thanks for the coaching, Barry. I've gone back and polished the original answer. Hopefully the result will be better than first.
$endgroup$
– user37278
Jan 18 at 1:35
$begingroup$
Glad to be of help.
$endgroup$
– Barry Cipra
Jan 18 at 1:37
add a comment |
Your Answer
StackExchange.ifUsing("editor", function () {
return StackExchange.using("mathjaxEditing", function () {
StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix) {
StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
});
});
}, "mathjax-editing");
StackExchange.ready(function() {
var channelOptions = {
tags: "".split(" "),
id: "69"
};
initTagRenderer("".split(" "), "".split(" "), channelOptions);
StackExchange.using("externalEditor", function() {
// Have to fire editor after snippets, if snippets enabled
if (StackExchange.settings.snippets.snippetsEnabled) {
StackExchange.using("snippets", function() {
createEditor();
});
}
else {
createEditor();
}
});
function createEditor() {
StackExchange.prepareEditor({
heartbeatType: 'answer',
autoActivateHeartbeat: false,
convertImagesToLinks: true,
noModals: true,
showLowRepImageUploadWarning: true,
reputationToPostImages: 10,
bindNavPrevention: true,
postfix: "",
imageUploader: {
brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
allowUrls: true
},
noCode: true, onDemand: true,
discardSelector: ".discard-answer"
,immediatelyShowMarkdownHelp:true
});
}
});
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f1177245%2fmemorising-lots-of-maths-theorems-lemmas%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
2 Answers
2
active
oldest
votes
2 Answers
2
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
Formal proof of theorems is a sequential process.
[0] Start by absolutely knowing the definitions used in the theorem. You need to know what you're talking about.
Try to understand the theorem. If you don't understand it all at the beginning, then identify the parts of it that you do understand.
[1] Begin by making a list of the hypotheses.
If you are making up your own theorem, to construct a proof you can keep adding to the list of your hypotheses. Keep it up until there are enough hypotheses to imply the desired conclusion that you want to arrive at (the QED - look it up).
If you want to understand someone else's proof, you need to take ownership of the theorem as if you were creating it yourself. It pays to own the theorem and your proof of it.
[2] Then you start adding a list of intermediate conclusions.
Each intermediate conclusion should follow from
the hypotheses. together with
the previous intermediate conclusions.
Keep adding to the list of intermediates until you finally are ready to conclude.
[3] the conclusion is the statement of what needed to be proved.
I have to memorize by repeated engagement with the process of writing the steps down. Generally I can do it by memory somewhere around the fourth run through the steps.
In a less formal setting, say where you want to explain something to someone unfamiliar with the topic, you paint a background picture of what's going on in the context of the theorem.
Then you keep building the picture, making it more and more detailed, until there is no escaping the conclusion. Repeat four times.
Memorization follows from the engaged repetition, but NOT from rote repetition. See if you can generate a sort of emotional involvement. You have an intention, and you are emotionally committed to fulfilling that intention. Then I get the (emotional) payoff that goes with accomplishing the goal.
You might as well. It's kind of like solving a puzzle or winning a game. Ideally you'll be having a lot of fun and having a heck of a good time. That makes the repetition struggle-free.
Ideally, since the definitions are declared hypotheses, they will be absorbed by your memory as you repeat the proof, engaging committedly with the accomplishment of your goal.
answered Mar 5 '15 at 22:43
user37278user37278
112
$endgroup$
add a comment |
$begingroup$
Formal proof of theorems is a sequential process.
[0] Start by absolutely knowing the definitions used in the theorem. You need to know what you're talking about.
Try to understand the theorem. If you don't understand it all at the beginning, then identify the parts of it that you do understand.
[1] Begin by making a list of the hypotheses.
If you are making up your own theorem, to construct a proof you can keep adding to the list of your hypotheses. Keep it up until there are enough hypotheses to imply the desired conclusion that you want to arrive at (the QED - look it up).
If you want to understand someone else's proof, you need to take ownership of the theorem as if you were creating it yourself. It pays to own the theorem and your proof of it.
[2] Then you start adding a list of intermediate conclusions.
Each intermediate conclusion should follow from
the hypotheses. together with
the previous intermediate conclusions.
Keep adding to the list of intermediates until you finally are ready to conclude.
[3] the conclusion is the statement of what needed to be proved.
I have to memorize by repeated engagement with the process of writing the steps down. Generally I can do it by memory somewhere around the fourth run through the steps.
In a less formal setting, say where you want to explain something to someone unfamiliar with the topic, you paint a background picture of what's going on in the context of the theorem.
Then you keep building the picture, making it more and more detailed, until there is no escaping the conclusion. Repeat four times.
Memorization follows from the engaged repetition, but NOT from rote repetition. See if you can generate a sort of emotional involvement. You have an intention, and you are emotionally committed to fulfilling that intention. Then I get the (emotional) payoff that goes with accomplishing the goal.
You might as well. It's kind of like solving a puzzle or winning a game. Ideally you'll be having a lot of fun and having a heck of a good time. That makes the repetition struggle-free.
Ideally, since the definitions are declared hypotheses, they will be absorbed by your memory as you repeat the proof, engaging committedly with the accomplishment of your goal.
answered Mar 5 '15 at 22:43
user37278user37278
112
$endgroup$
add a comment |
$begingroup$
Formal proof of theorems is a sequential process.
[0] Start by absolutely knowing the definitions used in the theorem. You need to know what you're talking about.
Try to understand the theorem. If you don't understand it all at the beginning, then identify the parts of it that you do understand.
[1] Begin by making a list of the hypotheses.
If you are making up your own theorem, to construct a proof you can keep adding to the list of your hypotheses. Keep it up until there are enough hypotheses to imply the desired conclusion that you want to arrive at (the QED - look it up).
If you want to understand someone else's proof, you need to take ownership of the theorem as if you were creating it yourself. It pays to own the theorem and your proof of it.
[2] Then you start adding a list of intermediate conclusions.
Each intermediate conclusion should follow from
the hypotheses. together with
the previous intermediate conclusions.
Keep adding to the list of intermediates until you finally are ready to conclude.
[3] the conclusion is the statement of what needed to be proved.
I have to memorize by repeated engagement with the process of writing the steps down. Generally I can do it by memory somewhere around the fourth run through the steps.
In a less formal setting, say where you want to explain something to someone unfamiliar with the topic, you paint a background picture of what's going on in the context of the theorem.
Then you keep building the picture, making it more and more detailed, until there is no escaping the conclusion. Repeat four times.
Memorization follows from the engaged repetition, but NOT from rote repetition. See if you can generate a sort of emotional involvement. You have an intention, and you are emotionally committed to fulfilling that intention. Then I get the (emotional) payoff that goes with accomplishing the goal.
You might as well. It's kind of like solving a puzzle or winning a game. Ideally you'll be having a lot of fun and having a heck of a good time. That makes the repetition struggle-free.
Ideally, since the definitions are declared hypotheses, they will be absorbed by your memory as you repeat the proof, engaging committedly with the accomplishment of your goal.
answered Mar 5 '15 at 22:43
user37278user37278
112
$endgroup$
Formal proof of theorems is a sequential process.
[0] Start by absolutely knowing the definitions used in the theorem. You need to know what you're talking about.
Try to understand the theorem. If you don't understand it all at the beginning, then identify the parts of it that you do understand.
[1] Begin by making a list of the hypotheses.
If you are making up your own theorem, to construct a proof you can keep adding to the list of your hypotheses. Keep it up until there are enough hypotheses to imply the desired conclusion that you want to arrive at (the QED - look it up).
If you want to understand someone else's proof, you need to take ownership of the theorem as if you were creating it yourself. It pays to own the theorem and your proof of it.
[2] Then you start adding a list of intermediate conclusions.
Each intermediate conclusion should follow from
the hypotheses. together with
the previous intermediate conclusions.
Keep adding to the list of intermediates until you finally are ready to conclude.
[3] the conclusion is the statement of what needed to be proved.
I have to memorize by repeated engagement with the process of writing the steps down. Generally I can do it by memory somewhere around the fourth run through the steps.
In a less formal setting, say where you want to explain something to someone unfamiliar with the topic, you paint a background picture of what's going on in the context of the theorem.
Then you keep building the picture, making it more and more detailed, until there is no escaping the conclusion. Repeat four times.
Memorization follows from the engaged repetition, but NOT from rote repetition. See if you can generate a sort of emotional involvement. You have an intention, and you are emotionally committed to fulfilling that intention. Then I get the (emotional) payoff that goes with accomplishing the goal.
You might as well. It's kind of like solving a puzzle or winning a game. Ideally you'll be having a lot of fun and having a heck of a good time. That makes the repetition struggle-free.
Ideally, since the definitions are declared hypotheses, they will be absorbed by your memory as you repeat the proof, engaging committedly with the accomplishment of your goal.
answered Mar 5 '15 at 22:43
user37278user37278
112
edited Jan 18 at 1:32
answered Mar 5 '15 at 22:43
user37278user37278
112
answered Mar 5 '15 at 22:43
user37278user37278
112
answered Mar 5 '15 at 22:43
user37278user37278
112
112
add a comment |
add a comment |
$begingroup$
Then you keep building the picture, making it more and more detailed, until there is no escaping the conclusion. Repeat four times.
Memorization follows from the engaged repetition, but NOT from rote repetition. See if you can generate a sort of emotional involvement. You have an intention, and you are emotionally committed to fulfilling that intention. Then I get the (emotional) payoff that goes with accomplishing the goal. You may as well. It's kind of like solving a puzzle or winning a game.
Ideally, since the definitions are declared hypotheses, they will be drawn into your memory as you repeat the proof, engaging committedly with accomplishing your goal.
answered Mar 5 '15 at 22:56
user37278user37278
112
$endgroup$
$begingroup$
Did you mean to post two answers?
$endgroup$
– Barry Cipra
Mar 5 '15 at 23:25
$begingroup$
I meant the two answers to be merged into one. Right now I don't know how to do that.
$endgroup$
– user37278
Jun 15 '18 at 3:38
$begingroup$
You should be able to edit your first answer with a copy of the second, and then delete the second answer. Look for options labeled "edit" and "delete" beneath the answers.
$endgroup$
– Barry Cipra
Jun 15 '18 at 12:08
$begingroup$
Thanks for the coaching, Barry. I've gone back and polished the original answer. Hopefully the result will be better than first.
$endgroup$
– user37278
Jan 18 at 1:35
$begingroup$
Glad to be of help.
$endgroup$
– Barry Cipra
Jan 18 at 1:37
add a comment |
$begingroup$
Then you keep building the picture, making it more and more detailed, until there is no escaping the conclusion. Repeat four times.
Memorization follows from the engaged repetition, but NOT from rote repetition. See if you can generate a sort of emotional involvement. You have an intention, and you are emotionally committed to fulfilling that intention. Then I get the (emotional) payoff that goes with accomplishing the goal. You may as well. It's kind of like solving a puzzle or winning a game.
Ideally, since the definitions are declared hypotheses, they will be drawn into your memory as you repeat the proof, engaging committedly with accomplishing your goal.
answered Mar 5 '15 at 22:56
user37278user37278
112
$endgroup$
$begingroup$
Did you mean to post two answers?
$endgroup$
– Barry Cipra
Mar 5 '15 at 23:25
$begingroup$
I meant the two answers to be merged into one. Right now I don't know how to do that.
$endgroup$
– user37278
Jun 15 '18 at 3:38
$begingroup$
You should be able to edit your first answer with a copy of the second, and then delete the second answer. Look for options labeled "edit" and "delete" beneath the answers.
$endgroup$
– Barry Cipra
Jun 15 '18 at 12:08
$begingroup$
Thanks for the coaching, Barry. I've gone back and polished the original answer. Hopefully the result will be better than first.
$endgroup$
– user37278
Jan 18 at 1:35
$begingroup$
Glad to be of help.
$endgroup$
– Barry Cipra
Jan 18 at 1:37
add a comment |
$begingroup$
Then you keep building the picture, making it more and more detailed, until there is no escaping the conclusion. Repeat four times.
Memorization follows from the engaged repetition, but NOT from rote repetition. See if you can generate a sort of emotional involvement. You have an intention, and you are emotionally committed to fulfilling that intention. Then I get the (emotional) payoff that goes with accomplishing the goal. You may as well. It's kind of like solving a puzzle or winning a game.
Ideally, since the definitions are declared hypotheses, they will be drawn into your memory as you repeat the proof, engaging committedly with accomplishing your goal.
answered Mar 5 '15 at 22:56
user37278user37278
112
$endgroup$
Then you keep building the picture, making it more and more detailed, until there is no escaping the conclusion. Repeat four times.
Memorization follows from the engaged repetition, but NOT from rote repetition. See if you can generate a sort of emotional involvement. You have an intention, and you are emotionally committed to fulfilling that intention. Then I get the (emotional) payoff that goes with accomplishing the goal. You may as well. It's kind of like solving a puzzle or winning a game.
Ideally, since the definitions are declared hypotheses, they will be drawn into your memory as you repeat the proof, engaging committedly with accomplishing your goal.
answered Mar 5 '15 at 22:56
user37278user37278
112
edited Mar 5 '15 at 23:02
answered Mar 5 '15 at 22:56
user37278user37278
112
answered Mar 5 '15 at 22:56
user37278user37278
112
answered Mar 5 '15 at 22:56
user37278user37278
112
112
$begingroup$
Did you mean to post two answers?
$endgroup$
– Barry Cipra
Mar 5 '15 at 23:25
$begingroup$
I meant the two answers to be merged into one. Right now I don't know how to do that.
$endgroup$
– user37278
Jun 15 '18 at 3:38
$begingroup$
You should be able to edit your first answer with a copy of the second, and then delete the second answer. Look for options labeled "edit" and "delete" beneath the answers.
$endgroup$
– Barry Cipra
Jun 15 '18 at 12:08
$begingroup$
Thanks for the coaching, Barry. I've gone back and polished the original answer. Hopefully the result will be better than first.
$endgroup$
– user37278
Jan 18 at 1:35
$begingroup$
Glad to be of help.
$endgroup$
– Barry Cipra
Jan 18 at 1:37
add a comment |
$begingroup$
Did you mean to post two answers?
$endgroup$
– Barry Cipra
Mar 5 '15 at 23:25
$begingroup$
I meant the two answers to be merged into one. Right now I don't know how to do that.
$endgroup$
– user37278
Jun 15 '18 at 3:38
$begingroup$
You should be able to edit your first answer with a copy of the second, and then delete the second answer. Look for options labeled "edit" and "delete" beneath the answers.
$endgroup$
– Barry Cipra
Jun 15 '18 at 12:08
$begingroup$
Thanks for the coaching, Barry. I've gone back and polished the original answer. Hopefully the result will be better than first.
$endgroup$
– user37278
Jan 18 at 1:35
$begingroup$
Glad to be of help.
$endgroup$
– Barry Cipra
Jan 18 at 1:37
$begingroup$
Did you mean to post two answers?
$endgroup$
– Barry Cipra
Mar 5 '15 at 23:25
$begingroup$
Did you mean to post two answers?
$endgroup$
– Barry Cipra
Mar 5 '15 at 23:25
$begingroup$
I meant the two answers to be merged into one. Right now I don't know how to do that.
$endgroup$
– user37278
Jun 15 '18 at 3:38
$begingroup$
I meant the two answers to be merged into one. Right now I don't know how to do that.
$endgroup$
– user37278
Jun 15 '18 at 3:38
$begingroup$
You should be able to edit your first answer with a copy of the second, and then delete the second answer. Look for options labeled "edit" and "delete" beneath the answers.
$endgroup$
– Barry Cipra
Jun 15 '18 at 12:08
$begingroup$
You should be able to edit your first answer with a copy of the second, and then delete the second answer. Look for options labeled "edit" and "delete" beneath the answers.
$endgroup$
– Barry Cipra
Jun 15 '18 at 12:08
$begingroup$
Thanks for the coaching, Barry. I've gone back and polished the original answer. Hopefully the result will be better than first.
$endgroup$
– user37278
Jan 18 at 1:35
$begingroup$
Thanks for the coaching, Barry. I've gone back and polished the original answer. Hopefully the result will be better than first.
$endgroup$
– user37278
Jan 18 at 1:35
$begingroup$
Glad to be of help.
$endgroup$
– Barry Cipra
Jan 18 at 1:37
$begingroup$
Glad to be of help.
$endgroup$
– Barry Cipra
Jan 18 at 1:37
add a comment |
Thanks for contributing an answer to Mathematics Stack Exchange!
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
Use MathJax to format equations. MathJax reference.
To learn more, see our tips on writing great answers.
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f1177245%2fmemorising-lots-of-maths-theorems-lemmas%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
1
$begingroup$
Well. You can figure out what the most important definitions are, figure out what the major theorems are. Many definitions in algebra are the only things that make sense. For instance, you should be able to 'figure out' the definition of a ring homomorphism. You should spend time actually proving the theorems that you think you can, rather than simply reading the supplied proofs. For harder theorems, you might not be able to prove them, but trying to will certainly help you remember. 'Mathematics is not a spectator sport.'
$endgroup$
– RougeSegwayUser
Mar 5 '15 at 21:16
2
$begingroup$
Rote memorization won't work unless you have a photographic memory. You have to understand the proof. Once you do, you should be able to remember it. I took general topology 10 years ago and I'm not a topologist but I'm pretty sure I can still prove the Urysohn metrization theorem, because I understood the proof.
$endgroup$
– Matt Samuel
Mar 5 '15 at 21:26