How should I go about reading mathematics papers and textbooks as a PhD
It shames me to admit it, but I feel like I still haven’t figured out the right way to efficiently read papers and textbooks. I am a second year PhD student in pure mathematics, and I struggle a lot to balance the need to learn a lot new mathematics with the fact that I have a finite amount of time in which to do it.
I should have asked this question years ago: what is best (i.e. most efficient) way to read papers and textbooks in order to have a working knowledge of the subject?
Maybe I should be more precise.
I am working in both algebraic geometry and homotopy theory (think simplicial presheaves and K-Theory), and I have recently found myself overwhelmed by the amount that I need to learn. In an ideal world I would read background material by doing every exercise in every textbook, and by working carefully through every proof in every paper, but I worry that I just don’t have enough time. On the flip side, I often find myself “reading” mathematics without actually absorbing any working knowledge, so I basically don’t make any direct research progress.
I understand that reading in great volume is still constructive, and I have certainly learnt a lot about how mathematics fits together, but when I actually need to do new mathematics I consistently find myself lost.
To rephrase my question: can anyone offer an advice on their workflow when it comes to learning new mathematics?
Perhaps the way I feel is more or less how everyone feels, and it is confidence and organisation which is the problem. If that is the case, then I ask: can anyone offer advice on how to organise oneself day to day in a PhD to be productive? Moreover, can anyone offer advice on how to break out of a lack of self confidence when it comes to doing research mathematics?
I apologise in advance if this question has been asked many times before, but I haven’t been able to find the right thread. I apologise also if my questions are too multi-pronged, I just feel that they are all to interconnected to be split up.
research-process
migrated from math.stackexchange.com 8 hours ago
This question came from our site for people studying math at any level and professionals in related fields.
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show 1 more comment
It shames me to admit it, but I feel like I still haven’t figured out the right way to efficiently read papers and textbooks. I am a second year PhD student in pure mathematics, and I struggle a lot to balance the need to learn a lot new mathematics with the fact that I have a finite amount of time in which to do it.
I should have asked this question years ago: what is best (i.e. most efficient) way to read papers and textbooks in order to have a working knowledge of the subject?
Maybe I should be more precise.
I am working in both algebraic geometry and homotopy theory (think simplicial presheaves and K-Theory), and I have recently found myself overwhelmed by the amount that I need to learn. In an ideal world I would read background material by doing every exercise in every textbook, and by working carefully through every proof in every paper, but I worry that I just don’t have enough time. On the flip side, I often find myself “reading” mathematics without actually absorbing any working knowledge, so I basically don’t make any direct research progress.
I understand that reading in great volume is still constructive, and I have certainly learnt a lot about how mathematics fits together, but when I actually need to do new mathematics I consistently find myself lost.
To rephrase my question: can anyone offer an advice on their workflow when it comes to learning new mathematics?
Perhaps the way I feel is more or less how everyone feels, and it is confidence and organisation which is the problem. If that is the case, then I ask: can anyone offer advice on how to organise oneself day to day in a PhD to be productive? Moreover, can anyone offer advice on how to break out of a lack of self confidence when it comes to doing research mathematics?
I apologise in advance if this question has been asked many times before, but I haven’t been able to find the right thread. I apologise also if my questions are too multi-pronged, I just feel that they are all to interconnected to be split up.
research-process
migrated from math.stackexchange.com 8 hours ago
This question came from our site for people studying math at any level and professionals in related fields.
With no fear, and with passion.
– Yossi Lonke
10 hours ago
2
This seems a bit too personal to answer, but surely there is good advise you can receive. I think this is a better fit for academia.SE however. Definitely your area (which only slightly overlaps with mine) has a tremendous amount of technical definitions to digest, I feel like at some point the 'learn as you work' method really works, but it seems to be the case too that, in such areas, you need the input of your advisor to keep you from drowning. I mostly feel like I learn things by myself, but my advisor is the one that convinces me that I understand them (before I actually do?!).
– Pedro Tamaroff
10 hours ago
Thanks @Pedro, I’ll post it on academia.SE too. I’m new to this site, so I didn’t quite know the right place. I will keep it here though too, since I feel mathematics carries unique challenges for research.
– Patrick Elliott
9 hours ago
@PatrickElliott If you want to, I can migrate this to that site. But please avoid cross-posting that there.
– Pedro Tamaroff
8 hours ago
Ah, thanks @Pedro, that’s probably better. I’ll didn’t know cross-posting was an issue.
– Patrick Elliott
8 hours ago
|
show 1 more comment
It shames me to admit it, but I feel like I still haven’t figured out the right way to efficiently read papers and textbooks. I am a second year PhD student in pure mathematics, and I struggle a lot to balance the need to learn a lot new mathematics with the fact that I have a finite amount of time in which to do it.
I should have asked this question years ago: what is best (i.e. most efficient) way to read papers and textbooks in order to have a working knowledge of the subject?
Maybe I should be more precise.
I am working in both algebraic geometry and homotopy theory (think simplicial presheaves and K-Theory), and I have recently found myself overwhelmed by the amount that I need to learn. In an ideal world I would read background material by doing every exercise in every textbook, and by working carefully through every proof in every paper, but I worry that I just don’t have enough time. On the flip side, I often find myself “reading” mathematics without actually absorbing any working knowledge, so I basically don’t make any direct research progress.
I understand that reading in great volume is still constructive, and I have certainly learnt a lot about how mathematics fits together, but when I actually need to do new mathematics I consistently find myself lost.
To rephrase my question: can anyone offer an advice on their workflow when it comes to learning new mathematics?
Perhaps the way I feel is more or less how everyone feels, and it is confidence and organisation which is the problem. If that is the case, then I ask: can anyone offer advice on how to organise oneself day to day in a PhD to be productive? Moreover, can anyone offer advice on how to break out of a lack of self confidence when it comes to doing research mathematics?
I apologise in advance if this question has been asked many times before, but I haven’t been able to find the right thread. I apologise also if my questions are too multi-pronged, I just feel that they are all to interconnected to be split up.
research-process
It shames me to admit it, but I feel like I still haven’t figured out the right way to efficiently read papers and textbooks. I am a second year PhD student in pure mathematics, and I struggle a lot to balance the need to learn a lot new mathematics with the fact that I have a finite amount of time in which to do it.
I should have asked this question years ago: what is best (i.e. most efficient) way to read papers and textbooks in order to have a working knowledge of the subject?
Maybe I should be more precise.
I am working in both algebraic geometry and homotopy theory (think simplicial presheaves and K-Theory), and I have recently found myself overwhelmed by the amount that I need to learn. In an ideal world I would read background material by doing every exercise in every textbook, and by working carefully through every proof in every paper, but I worry that I just don’t have enough time. On the flip side, I often find myself “reading” mathematics without actually absorbing any working knowledge, so I basically don’t make any direct research progress.
I understand that reading in great volume is still constructive, and I have certainly learnt a lot about how mathematics fits together, but when I actually need to do new mathematics I consistently find myself lost.
To rephrase my question: can anyone offer an advice on their workflow when it comes to learning new mathematics?
Perhaps the way I feel is more or less how everyone feels, and it is confidence and organisation which is the problem. If that is the case, then I ask: can anyone offer advice on how to organise oneself day to day in a PhD to be productive? Moreover, can anyone offer advice on how to break out of a lack of self confidence when it comes to doing research mathematics?
I apologise in advance if this question has been asked many times before, but I haven’t been able to find the right thread. I apologise also if my questions are too multi-pronged, I just feel that they are all to interconnected to be split up.
research-process
research-process
asked 10 hours ago
Patrick Elliott
migrated from math.stackexchange.com 8 hours ago
This question came from our site for people studying math at any level and professionals in related fields.
migrated from math.stackexchange.com 8 hours ago
This question came from our site for people studying math at any level and professionals in related fields.
With no fear, and with passion.
– Yossi Lonke
10 hours ago
2
This seems a bit too personal to answer, but surely there is good advise you can receive. I think this is a better fit for academia.SE however. Definitely your area (which only slightly overlaps with mine) has a tremendous amount of technical definitions to digest, I feel like at some point the 'learn as you work' method really works, but it seems to be the case too that, in such areas, you need the input of your advisor to keep you from drowning. I mostly feel like I learn things by myself, but my advisor is the one that convinces me that I understand them (before I actually do?!).
– Pedro Tamaroff
10 hours ago
Thanks @Pedro, I’ll post it on academia.SE too. I’m new to this site, so I didn’t quite know the right place. I will keep it here though too, since I feel mathematics carries unique challenges for research.
– Patrick Elliott
9 hours ago
@PatrickElliott If you want to, I can migrate this to that site. But please avoid cross-posting that there.
– Pedro Tamaroff
8 hours ago
Ah, thanks @Pedro, that’s probably better. I’ll didn’t know cross-posting was an issue.
– Patrick Elliott
8 hours ago
|
show 1 more comment
With no fear, and with passion.
– Yossi Lonke
10 hours ago
2
This seems a bit too personal to answer, but surely there is good advise you can receive. I think this is a better fit for academia.SE however. Definitely your area (which only slightly overlaps with mine) has a tremendous amount of technical definitions to digest, I feel like at some point the 'learn as you work' method really works, but it seems to be the case too that, in such areas, you need the input of your advisor to keep you from drowning. I mostly feel like I learn things by myself, but my advisor is the one that convinces me that I understand them (before I actually do?!).
– Pedro Tamaroff
10 hours ago
Thanks @Pedro, I’ll post it on academia.SE too. I’m new to this site, so I didn’t quite know the right place. I will keep it here though too, since I feel mathematics carries unique challenges for research.
– Patrick Elliott
9 hours ago
@PatrickElliott If you want to, I can migrate this to that site. But please avoid cross-posting that there.
– Pedro Tamaroff
8 hours ago
Ah, thanks @Pedro, that’s probably better. I’ll didn’t know cross-posting was an issue.
– Patrick Elliott
8 hours ago
With no fear, and with passion.
– Yossi Lonke
10 hours ago
With no fear, and with passion.
– Yossi Lonke
10 hours ago
2
2
This seems a bit too personal to answer, but surely there is good advise you can receive. I think this is a better fit for academia.SE however. Definitely your area (which only slightly overlaps with mine) has a tremendous amount of technical definitions to digest, I feel like at some point the 'learn as you work' method really works, but it seems to be the case too that, in such areas, you need the input of your advisor to keep you from drowning. I mostly feel like I learn things by myself, but my advisor is the one that convinces me that I understand them (before I actually do?!).
– Pedro Tamaroff
10 hours ago
This seems a bit too personal to answer, but surely there is good advise you can receive. I think this is a better fit for academia.SE however. Definitely your area (which only slightly overlaps with mine) has a tremendous amount of technical definitions to digest, I feel like at some point the 'learn as you work' method really works, but it seems to be the case too that, in such areas, you need the input of your advisor to keep you from drowning. I mostly feel like I learn things by myself, but my advisor is the one that convinces me that I understand them (before I actually do?!).
– Pedro Tamaroff
10 hours ago
Thanks @Pedro, I’ll post it on academia.SE too. I’m new to this site, so I didn’t quite know the right place. I will keep it here though too, since I feel mathematics carries unique challenges for research.
– Patrick Elliott
9 hours ago
Thanks @Pedro, I’ll post it on academia.SE too. I’m new to this site, so I didn’t quite know the right place. I will keep it here though too, since I feel mathematics carries unique challenges for research.
– Patrick Elliott
9 hours ago
@PatrickElliott If you want to, I can migrate this to that site. But please avoid cross-posting that there.
– Pedro Tamaroff
8 hours ago
@PatrickElliott If you want to, I can migrate this to that site. But please avoid cross-posting that there.
– Pedro Tamaroff
8 hours ago
Ah, thanks @Pedro, that’s probably better. I’ll didn’t know cross-posting was an issue.
– Patrick Elliott
8 hours ago
Ah, thanks @Pedro, that’s probably better. I’ll didn’t know cross-posting was an issue.
– Patrick Elliott
8 hours ago
|
show 1 more comment
2 Answers
2
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I'm a second year student too.
I think that one have to study what really needs to know, for instance, if I need the Feit-Thompson Theorem (for some reason) I cite and use, if you need to use the tools and ideas that were used in that long proof, then you read the paper. Now, how to read it, in first instance, keep the central ideas and go deeper if you really need it for your work. There is a lot of mathematics, and nobody can learn everything, even if you only study algebraic geometry (it is a broad field). My tutor says that one will have a lot of years to study and go deep in topics that are of our interest, and in the moment, work hard fort getting the PhD (it is not easy, we know it), and publish
add a comment |
If you already have a good sense of how the relevant fields fit together, and you know your way around the standard references, I personally find that the best approach is to just jump into a good paper. Really studying a paper related to your research is a much better way to learn specific techniques than grinding through textbook exercises. I think there's generally too much emphasis on "background" at the expense of working on new mathematics.
add a comment |
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2 Answers
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2 Answers
2
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I'm a second year student too.
I think that one have to study what really needs to know, for instance, if I need the Feit-Thompson Theorem (for some reason) I cite and use, if you need to use the tools and ideas that were used in that long proof, then you read the paper. Now, how to read it, in first instance, keep the central ideas and go deeper if you really need it for your work. There is a lot of mathematics, and nobody can learn everything, even if you only study algebraic geometry (it is a broad field). My tutor says that one will have a lot of years to study and go deep in topics that are of our interest, and in the moment, work hard fort getting the PhD (it is not easy, we know it), and publish
add a comment |
I'm a second year student too.
I think that one have to study what really needs to know, for instance, if I need the Feit-Thompson Theorem (for some reason) I cite and use, if you need to use the tools and ideas that were used in that long proof, then you read the paper. Now, how to read it, in first instance, keep the central ideas and go deeper if you really need it for your work. There is a lot of mathematics, and nobody can learn everything, even if you only study algebraic geometry (it is a broad field). My tutor says that one will have a lot of years to study and go deep in topics that are of our interest, and in the moment, work hard fort getting the PhD (it is not easy, we know it), and publish
add a comment |
I'm a second year student too.
I think that one have to study what really needs to know, for instance, if I need the Feit-Thompson Theorem (for some reason) I cite and use, if you need to use the tools and ideas that were used in that long proof, then you read the paper. Now, how to read it, in first instance, keep the central ideas and go deeper if you really need it for your work. There is a lot of mathematics, and nobody can learn everything, even if you only study algebraic geometry (it is a broad field). My tutor says that one will have a lot of years to study and go deep in topics that are of our interest, and in the moment, work hard fort getting the PhD (it is not easy, we know it), and publish
I'm a second year student too.
I think that one have to study what really needs to know, for instance, if I need the Feit-Thompson Theorem (for some reason) I cite and use, if you need to use the tools and ideas that were used in that long proof, then you read the paper. Now, how to read it, in first instance, keep the central ideas and go deeper if you really need it for your work. There is a lot of mathematics, and nobody can learn everything, even if you only study algebraic geometry (it is a broad field). My tutor says that one will have a lot of years to study and go deep in topics that are of our interest, and in the moment, work hard fort getting the PhD (it is not easy, we know it), and publish
answered 10 hours ago
José Alejandro Aburto Araneda
1112
1112
add a comment |
add a comment |
If you already have a good sense of how the relevant fields fit together, and you know your way around the standard references, I personally find that the best approach is to just jump into a good paper. Really studying a paper related to your research is a much better way to learn specific techniques than grinding through textbook exercises. I think there's generally too much emphasis on "background" at the expense of working on new mathematics.
add a comment |
If you already have a good sense of how the relevant fields fit together, and you know your way around the standard references, I personally find that the best approach is to just jump into a good paper. Really studying a paper related to your research is a much better way to learn specific techniques than grinding through textbook exercises. I think there's generally too much emphasis on "background" at the expense of working on new mathematics.
add a comment |
If you already have a good sense of how the relevant fields fit together, and you know your way around the standard references, I personally find that the best approach is to just jump into a good paper. Really studying a paper related to your research is a much better way to learn specific techniques than grinding through textbook exercises. I think there's generally too much emphasis on "background" at the expense of working on new mathematics.
If you already have a good sense of how the relevant fields fit together, and you know your way around the standard references, I personally find that the best approach is to just jump into a good paper. Really studying a paper related to your research is a much better way to learn specific techniques than grinding through textbook exercises. I think there's generally too much emphasis on "background" at the expense of working on new mathematics.
answered 2 hours ago
Elizabeth Henning
5,38411032
5,38411032
add a comment |
add a comment |
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With no fear, and with passion.
– Yossi Lonke
10 hours ago
2
This seems a bit too personal to answer, but surely there is good advise you can receive. I think this is a better fit for academia.SE however. Definitely your area (which only slightly overlaps with mine) has a tremendous amount of technical definitions to digest, I feel like at some point the 'learn as you work' method really works, but it seems to be the case too that, in such areas, you need the input of your advisor to keep you from drowning. I mostly feel like I learn things by myself, but my advisor is the one that convinces me that I understand them (before I actually do?!).
– Pedro Tamaroff
10 hours ago
Thanks @Pedro, I’ll post it on academia.SE too. I’m new to this site, so I didn’t quite know the right place. I will keep it here though too, since I feel mathematics carries unique challenges for research.
– Patrick Elliott
9 hours ago
@PatrickElliott If you want to, I can migrate this to that site. But please avoid cross-posting that there.
– Pedro Tamaroff
8 hours ago
Ah, thanks @Pedro, that’s probably better. I’ll didn’t know cross-posting was an issue.
– Patrick Elliott
8 hours ago