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Is there a flowchart with a DAG of the different branches of mathematics?
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I'd like to dip my toes into some specific areas of mathematics (like Category Theory) and my problem is that I did not find a flow chart which displays how different branches of mathematics depend on each other so I can narrow down the topics I need to look into.
I've found this question but the links in the answers are either broken or useless.
Having a flowchart like that would be immensely helpful for a lot of people. Is there such a thing? If yes, where?
self-learning learning
asked Jul 16 at 22:21
Adam Arold
153117
 |Â
show 2 more comments
up vote
5
down vote
favorite
I'd like to dip my toes into some specific areas of mathematics (like Category Theory) and my problem is that I did not find a flow chart which displays how different branches of mathematics depend on each other so I can narrow down the topics I need to look into.
I've found this question but the links in the answers are either broken or useless.
Having a flowchart like that would be immensely helpful for a lot of people. Is there such a thing? If yes, where?
self-learning learning
asked Jul 16 at 22:21
Adam Arold
153117
Almost any two areas of mathematics can be related, and abundant literature could be referenced to illustrate the unexpected connections that have been made. A flow chart will not help in the way you expect. You should pick a direction and go, IMHO.
– hardmath
Jul 16 at 22:35
3
Dividing mathematics into "branches" is a non-trivial problem in itself. The MSC classification system (the "useless" link) is about the best we have, really. My last paper had a classification I settled on, but brought in ideas and intuitions from certain other branches, which is totally normal in research mathematics. The boundaries are just not clearly defined, at all.
– Theo Bendit
Jul 16 at 22:37
Thanks for the insightful comments. I haven't studied math in 10 years so this pretty much explains how clueless I am currently.
– Adam Arold
Jul 16 at 22:42
1
In theory it’s a nice idea, but such a directed graph would be horribly complicated in order to be accurate. The best advice I have is state your goals and interests and ask for advice regarding pre requisites. For category theory, some general experience with abstract algebra and commutative algebra would probably help. The field will maybe seem more motivated if you happen to have done some things (homologous algebra, algebraic geometry) without category theory. Then when you switch to category theory you realize how great it is. But you could probably also
– Prince M
Jul 16 at 22:51
1
Become an expert in pure category theory without even knowing what homologous algebra or algebraic geometry are.
– Prince M
Jul 16 at 22:51
 |Â
show 2 more comments
up vote
5
down vote
favorite
up vote
5
down vote
favorite
I'd like to dip my toes into some specific areas of mathematics (like Category Theory) and my problem is that I did not find a flow chart which displays how different branches of mathematics depend on each other so I can narrow down the topics I need to look into.
I've found this question but the links in the answers are either broken or useless.
Having a flowchart like that would be immensely helpful for a lot of people. Is there such a thing? If yes, where?
self-learning learning
asked Jul 16 at 22:21
Adam Arold
153117
I'd like to dip my toes into some specific areas of mathematics (like Category Theory) and my problem is that I did not find a flow chart which displays how different branches of mathematics depend on each other so I can narrow down the topics I need to look into.
I've found this question but the links in the answers are either broken or useless.
Having a flowchart like that would be immensely helpful for a lot of people. Is there such a thing? If yes, where?
self-learning learning
asked Jul 16 at 22:21
Adam Arold
153117
asked Jul 16 at 22:21
Adam Arold
153117
asked Jul 16 at 22:21
Adam Arold
153117
asked Jul 16 at 22:21
Adam Arold
153117
153117
Almost any two areas of mathematics can be related, and abundant literature could be referenced to illustrate the unexpected connections that have been made. A flow chart will not help in the way you expect. You should pick a direction and go, IMHO.
– hardmath
Jul 16 at 22:35
3
Dividing mathematics into "branches" is a non-trivial problem in itself. The MSC classification system (the "useless" link) is about the best we have, really. My last paper had a classification I settled on, but brought in ideas and intuitions from certain other branches, which is totally normal in research mathematics. The boundaries are just not clearly defined, at all.
– Theo Bendit
Jul 16 at 22:37
Thanks for the insightful comments. I haven't studied math in 10 years so this pretty much explains how clueless I am currently.
– Adam Arold
Jul 16 at 22:42
1
In theory it’s a nice idea, but such a directed graph would be horribly complicated in order to be accurate. The best advice I have is state your goals and interests and ask for advice regarding pre requisites. For category theory, some general experience with abstract algebra and commutative algebra would probably help. The field will maybe seem more motivated if you happen to have done some things (homologous algebra, algebraic geometry) without category theory. Then when you switch to category theory you realize how great it is. But you could probably also
– Prince M
Jul 16 at 22:51
1
Become an expert in pure category theory without even knowing what homologous algebra or algebraic geometry are.
– Prince M
Jul 16 at 22:51
 |Â
show 2 more comments
Almost any two areas of mathematics can be related, and abundant literature could be referenced to illustrate the unexpected connections that have been made. A flow chart will not help in the way you expect. You should pick a direction and go, IMHO.
– hardmath
Jul 16 at 22:35
3
Dividing mathematics into "branches" is a non-trivial problem in itself. The MSC classification system (the "useless" link) is about the best we have, really. My last paper had a classification I settled on, but brought in ideas and intuitions from certain other branches, which is totally normal in research mathematics. The boundaries are just not clearly defined, at all.
– Theo Bendit
Jul 16 at 22:37
Thanks for the insightful comments. I haven't studied math in 10 years so this pretty much explains how clueless I am currently.
– Adam Arold
Jul 16 at 22:42
1
In theory it’s a nice idea, but such a directed graph would be horribly complicated in order to be accurate. The best advice I have is state your goals and interests and ask for advice regarding pre requisites. For category theory, some general experience with abstract algebra and commutative algebra would probably help. The field will maybe seem more motivated if you happen to have done some things (homologous algebra, algebraic geometry) without category theory. Then when you switch to category theory you realize how great it is. But you could probably also
– Prince M
Jul 16 at 22:51
1
Become an expert in pure category theory without even knowing what homologous algebra or algebraic geometry are.
– Prince M
Jul 16 at 22:51
Almost any two areas of mathematics can be related, and abundant literature could be referenced to illustrate the unexpected connections that have been made. A flow chart will not help in the way you expect. You should pick a direction and go, IMHO.
– hardmath
Jul 16 at 22:35
Almost any two areas of mathematics can be related, and abundant literature could be referenced to illustrate the unexpected connections that have been made. A flow chart will not help in the way you expect. You should pick a direction and go, IMHO.
– hardmath
Jul 16 at 22:35
3
3
Dividing mathematics into "branches" is a non-trivial problem in itself. The MSC classification system (the "useless" link) is about the best we have, really. My last paper had a classification I settled on, but brought in ideas and intuitions from certain other branches, which is totally normal in research mathematics. The boundaries are just not clearly defined, at all.
– Theo Bendit
Jul 16 at 22:37
Dividing mathematics into "branches" is a non-trivial problem in itself. The MSC classification system (the "useless" link) is about the best we have, really. My last paper had a classification I settled on, but brought in ideas and intuitions from certain other branches, which is totally normal in research mathematics. The boundaries are just not clearly defined, at all.
– Theo Bendit
Jul 16 at 22:37
Thanks for the insightful comments. I haven't studied math in 10 years so this pretty much explains how clueless I am currently.
– Adam Arold
Jul 16 at 22:42
Thanks for the insightful comments. I haven't studied math in 10 years so this pretty much explains how clueless I am currently.
– Adam Arold
Jul 16 at 22:42
1
1
In theory it’s a nice idea, but such a directed graph would be horribly complicated in order to be accurate. The best advice I have is state your goals and interests and ask for advice regarding pre requisites. For category theory, some general experience with abstract algebra and commutative algebra would probably help. The field will maybe seem more motivated if you happen to have done some things (homologous algebra, algebraic geometry) without category theory. Then when you switch to category theory you realize how great it is. But you could probably also
– Prince M
Jul 16 at 22:51
In theory it’s a nice idea, but such a directed graph would be horribly complicated in order to be accurate. The best advice I have is state your goals and interests and ask for advice regarding pre requisites. For category theory, some general experience with abstract algebra and commutative algebra would probably help. The field will maybe seem more motivated if you happen to have done some things (homologous algebra, algebraic geometry) without category theory. Then when you switch to category theory you realize how great it is. But you could probably also
– Prince M
Jul 16 at 22:51
1
1
Become an expert in pure category theory without even knowing what homologous algebra or algebraic geometry are.
– Prince M
Jul 16 at 22:51
Become an expert in pure category theory without even knowing what homologous algebra or algebraic geometry are.
– Prince M
Jul 16 at 22:51
 |Â
show 2 more comments
5 Answers
5
active
oldest
votes
up vote
3
down vote
If you coarse grain your areas of mathematics like as broad as "category theory" then there will be parts were you need a certain prerequisite and parts where you don't. This means you will not really get a DAG anymore.
Say you have A is a prerequisite for B for C for D. Simple example. But A and C are both treated as parts of the subject 1 and B and D as parts of subject 2. You now have a loop where both subjects require each other.
Because these broad subjects have lots of parts that are interconnected with each other like this, you won't be able to have a directed system if you want such broad branch titles. If you go with the very specific parts, then you might be able to build a flowchart, but it will be too big to be useful.
answered Jul 16 at 22:38
AHusain
1,849714
I got it. I just have no idea where to start. I dropped out of college 10+ years ago and I don't know where to pick up.
– Adam Arold
Jul 16 at 22:43
Why do you think that big flowcharts are not useful? We have computers to analyze them. There is no need to actually draw them on paper.
– beroal
Jul 20 at 18:05
add a comment |Â
up vote
2
down vote
If you're looking for a subject that is taught in Math Bachelor/Master, you can backtrack the dependencies of the subject by looking up the requirements in the module hand book of a university that's teaching this course.
Otherwise, maybe this link helps you:
Dependencies of various of areas of mathematics
answered Jul 16 at 23:45
Sudix
7911316
add a comment |Â
up vote
1
down vote
It is my opinion that no such flow chart can exist. Plausibly, one could produce a directed graph of math subjects, but there is no chance it could be accurate and acyclic. The reality is that subjects build off each other.
Further, the main obstacle to learning math is not so much "not knowing the prerequisites" as that learning math takes a lot of effort. Learning math is a trainable skill, which you gain by... working hard to learn lots of math. If you haven't learned to learn math to a sufficient degree, you can technically know the prerequisites for, say, measure theory and still get nowhere trying to work through a book on it. This is in part (but not entirely) what people refer to when they speak of "mathematical maturity."
So if you want to learn about a specific area, what you should really do is find out what topics are somewhat connected to it that have textbooks at a level you currently find readable, learn from those, and every once in a while come back and try to learn your target subject.
Category theory, which you expressed interest in, provides a sharp example of this. There is a very, very good book "Category Theory in Context" by Emily Riehl. The technical prerequisites for C.T.C. are essentially zero, but the book is full of ideas and arguments that a mathematician might be able to pick up on with their first scan but which would cause fits in somebody without any math background. By far the best way to prepare to learn from this book is just to learn a bunch of vaguely algebraic and topological math until you can learn from it.
Summary: Figure out what is connected to your subject (which will be a lot) and learn whatever is interesting and accessible within those broad limits. Come back to the subject in question and see whether things are making more sense.
answered Jul 16 at 23:14
Cory Griffith
729411
PS: I don't mean to imply proceeding with this level of self direction is easy. If you need more structure than this, but can't take courses, one thing you could try is following course notes, which are all over the place online and often amount to lean textbooks.
– Cory Griffith
Jul 16 at 23:22
add a comment |Â
up vote
1
down vote
Here's an article with a diagram that can be interpreted as a DAG with implicit arrows going in the up direction towards more advanced areas with annotations:
http://www.brainmaker.net/blog/you-mean-theres-math-after-calculus
It's a pragmatic breakdown starting with Algebra I. As others have stated here, there is no definitive topology for a canonical mathematical curriculum.
answered Jul 17 at 4:53
Paul Wolf
1112
add a comment |Â
up vote
1
down vote
If you want to enter some area of mathematics, it would be better to say what you already know and ask what are the prerequisites (wrt to what you know) of such area.
That being said, you should take a look at the diagrams on Mac Lane's "Mathematics, Form and Function". I guess the diagrams with the rest of the material in the book are going to be the helpful and useful to you.
answered Jul 17 at 6:14
Billy Rubina
10.1k1254128
Thanks, I'll look into it!
– Adam Arold
Jul 17 at 14:30
add a comment |Â
5 Answers
5
active
oldest
votes
5 Answers
5
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
3
down vote
If you coarse grain your areas of mathematics like as broad as "category theory" then there will be parts were you need a certain prerequisite and parts where you don't. This means you will not really get a DAG anymore.
Say you have A is a prerequisite for B for C for D. Simple example. But A and C are both treated as parts of the subject 1 and B and D as parts of subject 2. You now have a loop where both subjects require each other.
Because these broad subjects have lots of parts that are interconnected with each other like this, you won't be able to have a directed system if you want such broad branch titles. If you go with the very specific parts, then you might be able to build a flowchart, but it will be too big to be useful.
answered Jul 16 at 22:38
AHusain
1,849714
I got it. I just have no idea where to start. I dropped out of college 10+ years ago and I don't know where to pick up.
– Adam Arold
Jul 16 at 22:43
Why do you think that big flowcharts are not useful? We have computers to analyze them. There is no need to actually draw them on paper.
– beroal
Jul 20 at 18:05
add a comment |Â
up vote
3
down vote
If you coarse grain your areas of mathematics like as broad as "category theory" then there will be parts were you need a certain prerequisite and parts where you don't. This means you will not really get a DAG anymore.
Say you have A is a prerequisite for B for C for D. Simple example. But A and C are both treated as parts of the subject 1 and B and D as parts of subject 2. You now have a loop where both subjects require each other.
Because these broad subjects have lots of parts that are interconnected with each other like this, you won't be able to have a directed system if you want such broad branch titles. If you go with the very specific parts, then you might be able to build a flowchart, but it will be too big to be useful.
answered Jul 16 at 22:38
AHusain
1,849714
I got it. I just have no idea where to start. I dropped out of college 10+ years ago and I don't know where to pick up.
– Adam Arold
Jul 16 at 22:43
Why do you think that big flowcharts are not useful? We have computers to analyze them. There is no need to actually draw them on paper.
– beroal
Jul 20 at 18:05
add a comment |Â
up vote
3
down vote
up vote
3
down vote
If you coarse grain your areas of mathematics like as broad as "category theory" then there will be parts were you need a certain prerequisite and parts where you don't. This means you will not really get a DAG anymore.
Say you have A is a prerequisite for B for C for D. Simple example. But A and C are both treated as parts of the subject 1 and B and D as parts of subject 2. You now have a loop where both subjects require each other.
Because these broad subjects have lots of parts that are interconnected with each other like this, you won't be able to have a directed system if you want such broad branch titles. If you go with the very specific parts, then you might be able to build a flowchart, but it will be too big to be useful.
answered Jul 16 at 22:38
AHusain
1,849714
If you coarse grain your areas of mathematics like as broad as "category theory" then there will be parts were you need a certain prerequisite and parts where you don't. This means you will not really get a DAG anymore.
Say you have A is a prerequisite for B for C for D. Simple example. But A and C are both treated as parts of the subject 1 and B and D as parts of subject 2. You now have a loop where both subjects require each other.
Because these broad subjects have lots of parts that are interconnected with each other like this, you won't be able to have a directed system if you want such broad branch titles. If you go with the very specific parts, then you might be able to build a flowchart, but it will be too big to be useful.
answered Jul 16 at 22:38
AHusain
1,849714
answered Jul 16 at 22:38
AHusain
1,849714
answered Jul 16 at 22:38
AHusain
1,849714
answered Jul 16 at 22:38
AHusain
1,849714
1,849714
I got it. I just have no idea where to start. I dropped out of college 10+ years ago and I don't know where to pick up.
– Adam Arold
Jul 16 at 22:43
Why do you think that big flowcharts are not useful? We have computers to analyze them. There is no need to actually draw them on paper.
– beroal
Jul 20 at 18:05
add a comment |Â
I got it. I just have no idea where to start. I dropped out of college 10+ years ago and I don't know where to pick up.
– Adam Arold
Jul 16 at 22:43
Why do you think that big flowcharts are not useful? We have computers to analyze them. There is no need to actually draw them on paper.
– beroal
Jul 20 at 18:05
I got it. I just have no idea where to start. I dropped out of college 10+ years ago and I don't know where to pick up.
– Adam Arold
Jul 16 at 22:43
I got it. I just have no idea where to start. I dropped out of college 10+ years ago and I don't know where to pick up.
– Adam Arold
Jul 16 at 22:43
Why do you think that big flowcharts are not useful? We have computers to analyze them. There is no need to actually draw them on paper.
– beroal
Jul 20 at 18:05
Why do you think that big flowcharts are not useful? We have computers to analyze them. There is no need to actually draw them on paper.
– beroal
Jul 20 at 18:05
add a comment |Â
up vote
2
down vote
If you're looking for a subject that is taught in Math Bachelor/Master, you can backtrack the dependencies of the subject by looking up the requirements in the module hand book of a university that's teaching this course.
Otherwise, maybe this link helps you:
Dependencies of various of areas of mathematics
answered Jul 16 at 23:45
Sudix
7911316
add a comment |Â
up vote
2
down vote
If you're looking for a subject that is taught in Math Bachelor/Master, you can backtrack the dependencies of the subject by looking up the requirements in the module hand book of a university that's teaching this course.
Otherwise, maybe this link helps you:
Dependencies of various of areas of mathematics
answered Jul 16 at 23:45
Sudix
7911316
add a comment |Â
up vote
2
down vote
up vote
2
down vote
If you're looking for a subject that is taught in Math Bachelor/Master, you can backtrack the dependencies of the subject by looking up the requirements in the module hand book of a university that's teaching this course.
Otherwise, maybe this link helps you:
Dependencies of various of areas of mathematics
answered Jul 16 at 23:45
Sudix
7911316
If you're looking for a subject that is taught in Math Bachelor/Master, you can backtrack the dependencies of the subject by looking up the requirements in the module hand book of a university that's teaching this course.
Otherwise, maybe this link helps you:
Dependencies of various of areas of mathematics
answered Jul 16 at 23:45
Sudix
7911316
answered Jul 16 at 23:45
Sudix
7911316
answered Jul 16 at 23:45
Sudix
7911316
answered Jul 16 at 23:45
Sudix
7911316
7911316
add a comment |Â
add a comment |Â
up vote
1
down vote
It is my opinion that no such flow chart can exist. Plausibly, one could produce a directed graph of math subjects, but there is no chance it could be accurate and acyclic. The reality is that subjects build off each other.
Further, the main obstacle to learning math is not so much "not knowing the prerequisites" as that learning math takes a lot of effort. Learning math is a trainable skill, which you gain by... working hard to learn lots of math. If you haven't learned to learn math to a sufficient degree, you can technically know the prerequisites for, say, measure theory and still get nowhere trying to work through a book on it. This is in part (but not entirely) what people refer to when they speak of "mathematical maturity."
So if you want to learn about a specific area, what you should really do is find out what topics are somewhat connected to it that have textbooks at a level you currently find readable, learn from those, and every once in a while come back and try to learn your target subject.
Category theory, which you expressed interest in, provides a sharp example of this. There is a very, very good book "Category Theory in Context" by Emily Riehl. The technical prerequisites for C.T.C. are essentially zero, but the book is full of ideas and arguments that a mathematician might be able to pick up on with their first scan but which would cause fits in somebody without any math background. By far the best way to prepare to learn from this book is just to learn a bunch of vaguely algebraic and topological math until you can learn from it.
Summary: Figure out what is connected to your subject (which will be a lot) and learn whatever is interesting and accessible within those broad limits. Come back to the subject in question and see whether things are making more sense.
answered Jul 16 at 23:14
Cory Griffith
729411
PS: I don't mean to imply proceeding with this level of self direction is easy. If you need more structure than this, but can't take courses, one thing you could try is following course notes, which are all over the place online and often amount to lean textbooks.
– Cory Griffith
Jul 16 at 23:22
add a comment |Â
up vote
1
down vote
It is my opinion that no such flow chart can exist. Plausibly, one could produce a directed graph of math subjects, but there is no chance it could be accurate and acyclic. The reality is that subjects build off each other.
Further, the main obstacle to learning math is not so much "not knowing the prerequisites" as that learning math takes a lot of effort. Learning math is a trainable skill, which you gain by... working hard to learn lots of math. If you haven't learned to learn math to a sufficient degree, you can technically know the prerequisites for, say, measure theory and still get nowhere trying to work through a book on it. This is in part (but not entirely) what people refer to when they speak of "mathematical maturity."
So if you want to learn about a specific area, what you should really do is find out what topics are somewhat connected to it that have textbooks at a level you currently find readable, learn from those, and every once in a while come back and try to learn your target subject.
Category theory, which you expressed interest in, provides a sharp example of this. There is a very, very good book "Category Theory in Context" by Emily Riehl. The technical prerequisites for C.T.C. are essentially zero, but the book is full of ideas and arguments that a mathematician might be able to pick up on with their first scan but which would cause fits in somebody without any math background. By far the best way to prepare to learn from this book is just to learn a bunch of vaguely algebraic and topological math until you can learn from it.
Summary: Figure out what is connected to your subject (which will be a lot) and learn whatever is interesting and accessible within those broad limits. Come back to the subject in question and see whether things are making more sense.
answered Jul 16 at 23:14
Cory Griffith
729411
PS: I don't mean to imply proceeding with this level of self direction is easy. If you need more structure than this, but can't take courses, one thing you could try is following course notes, which are all over the place online and often amount to lean textbooks.
– Cory Griffith
Jul 16 at 23:22
add a comment |Â
up vote
1
down vote
up vote
1
down vote
It is my opinion that no such flow chart can exist. Plausibly, one could produce a directed graph of math subjects, but there is no chance it could be accurate and acyclic. The reality is that subjects build off each other.
Further, the main obstacle to learning math is not so much "not knowing the prerequisites" as that learning math takes a lot of effort. Learning math is a trainable skill, which you gain by... working hard to learn lots of math. If you haven't learned to learn math to a sufficient degree, you can technically know the prerequisites for, say, measure theory and still get nowhere trying to work through a book on it. This is in part (but not entirely) what people refer to when they speak of "mathematical maturity."
So if you want to learn about a specific area, what you should really do is find out what topics are somewhat connected to it that have textbooks at a level you currently find readable, learn from those, and every once in a while come back and try to learn your target subject.
Category theory, which you expressed interest in, provides a sharp example of this. There is a very, very good book "Category Theory in Context" by Emily Riehl. The technical prerequisites for C.T.C. are essentially zero, but the book is full of ideas and arguments that a mathematician might be able to pick up on with their first scan but which would cause fits in somebody without any math background. By far the best way to prepare to learn from this book is just to learn a bunch of vaguely algebraic and topological math until you can learn from it.
Summary: Figure out what is connected to your subject (which will be a lot) and learn whatever is interesting and accessible within those broad limits. Come back to the subject in question and see whether things are making more sense.
answered Jul 16 at 23:14
Cory Griffith
729411
It is my opinion that no such flow chart can exist. Plausibly, one could produce a directed graph of math subjects, but there is no chance it could be accurate and acyclic. The reality is that subjects build off each other.
Further, the main obstacle to learning math is not so much "not knowing the prerequisites" as that learning math takes a lot of effort. Learning math is a trainable skill, which you gain by... working hard to learn lots of math. If you haven't learned to learn math to a sufficient degree, you can technically know the prerequisites for, say, measure theory and still get nowhere trying to work through a book on it. This is in part (but not entirely) what people refer to when they speak of "mathematical maturity."
So if you want to learn about a specific area, what you should really do is find out what topics are somewhat connected to it that have textbooks at a level you currently find readable, learn from those, and every once in a while come back and try to learn your target subject.
Category theory, which you expressed interest in, provides a sharp example of this. There is a very, very good book "Category Theory in Context" by Emily Riehl. The technical prerequisites for C.T.C. are essentially zero, but the book is full of ideas and arguments that a mathematician might be able to pick up on with their first scan but which would cause fits in somebody without any math background. By far the best way to prepare to learn from this book is just to learn a bunch of vaguely algebraic and topological math until you can learn from it.
Summary: Figure out what is connected to your subject (which will be a lot) and learn whatever is interesting and accessible within those broad limits. Come back to the subject in question and see whether things are making more sense.
answered Jul 16 at 23:14
Cory Griffith
729411
answered Jul 16 at 23:14
Cory Griffith
729411
answered Jul 16 at 23:14
Cory Griffith
729411
answered Jul 16 at 23:14
Cory Griffith
729411
729411
PS: I don't mean to imply proceeding with this level of self direction is easy. If you need more structure than this, but can't take courses, one thing you could try is following course notes, which are all over the place online and often amount to lean textbooks.
– Cory Griffith
Jul 16 at 23:22
add a comment |Â
PS: I don't mean to imply proceeding with this level of self direction is easy. If you need more structure than this, but can't take courses, one thing you could try is following course notes, which are all over the place online and often amount to lean textbooks.
– Cory Griffith
Jul 16 at 23:22
PS: I don't mean to imply proceeding with this level of self direction is easy. If you need more structure than this, but can't take courses, one thing you could try is following course notes, which are all over the place online and often amount to lean textbooks.
– Cory Griffith
Jul 16 at 23:22
PS: I don't mean to imply proceeding with this level of self direction is easy. If you need more structure than this, but can't take courses, one thing you could try is following course notes, which are all over the place online and often amount to lean textbooks.
– Cory Griffith
Jul 16 at 23:22
add a comment |Â
up vote
1
down vote
Here's an article with a diagram that can be interpreted as a DAG with implicit arrows going in the up direction towards more advanced areas with annotations:
http://www.brainmaker.net/blog/you-mean-theres-math-after-calculus
It's a pragmatic breakdown starting with Algebra I. As others have stated here, there is no definitive topology for a canonical mathematical curriculum.
answered Jul 17 at 4:53
Paul Wolf
1112
add a comment |Â
up vote
1
down vote
Here's an article with a diagram that can be interpreted as a DAG with implicit arrows going in the up direction towards more advanced areas with annotations:
http://www.brainmaker.net/blog/you-mean-theres-math-after-calculus
It's a pragmatic breakdown starting with Algebra I. As others have stated here, there is no definitive topology for a canonical mathematical curriculum.
answered Jul 17 at 4:53
Paul Wolf
1112
add a comment |Â
up vote
1
down vote
up vote
1
down vote
Here's an article with a diagram that can be interpreted as a DAG with implicit arrows going in the up direction towards more advanced areas with annotations:
http://www.brainmaker.net/blog/you-mean-theres-math-after-calculus
It's a pragmatic breakdown starting with Algebra I. As others have stated here, there is no definitive topology for a canonical mathematical curriculum.
answered Jul 17 at 4:53
Paul Wolf
1112
Here's an article with a diagram that can be interpreted as a DAG with implicit arrows going in the up direction towards more advanced areas with annotations:
http://www.brainmaker.net/blog/you-mean-theres-math-after-calculus
It's a pragmatic breakdown starting with Algebra I. As others have stated here, there is no definitive topology for a canonical mathematical curriculum.
answered Jul 17 at 4:53
Paul Wolf
1112
answered Jul 17 at 4:53
Paul Wolf
1112
answered Jul 17 at 4:53
Paul Wolf
1112
answered Jul 17 at 4:53
Paul Wolf
1112
1112
add a comment |Â
add a comment |Â
up vote
1
down vote
If you want to enter some area of mathematics, it would be better to say what you already know and ask what are the prerequisites (wrt to what you know) of such area.
That being said, you should take a look at the diagrams on Mac Lane's "Mathematics, Form and Function". I guess the diagrams with the rest of the material in the book are going to be the helpful and useful to you.
answered Jul 17 at 6:14
Billy Rubina
10.1k1254128
Thanks, I'll look into it!
– Adam Arold
Jul 17 at 14:30
add a comment |Â
up vote
1
down vote
If you want to enter some area of mathematics, it would be better to say what you already know and ask what are the prerequisites (wrt to what you know) of such area.
That being said, you should take a look at the diagrams on Mac Lane's "Mathematics, Form and Function". I guess the diagrams with the rest of the material in the book are going to be the helpful and useful to you.
answered Jul 17 at 6:14
Billy Rubina
10.1k1254128
Thanks, I'll look into it!
– Adam Arold
Jul 17 at 14:30
add a comment |Â
up vote
1
down vote
up vote
1
down vote
If you want to enter some area of mathematics, it would be better to say what you already know and ask what are the prerequisites (wrt to what you know) of such area.
That being said, you should take a look at the diagrams on Mac Lane's "Mathematics, Form and Function". I guess the diagrams with the rest of the material in the book are going to be the helpful and useful to you.
answered Jul 17 at 6:14
Billy Rubina
10.1k1254128
If you want to enter some area of mathematics, it would be better to say what you already know and ask what are the prerequisites (wrt to what you know) of such area.
That being said, you should take a look at the diagrams on Mac Lane's "Mathematics, Form and Function". I guess the diagrams with the rest of the material in the book are going to be the helpful and useful to you.
answered Jul 17 at 6:14
Billy Rubina
10.1k1254128
answered Jul 17 at 6:14
Billy Rubina
10.1k1254128
answered Jul 17 at 6:14
Billy Rubina
10.1k1254128
answered Jul 17 at 6:14
Billy Rubina
10.1k1254128
10.1k1254128
Thanks, I'll look into it!
– Adam Arold
Jul 17 at 14:30
add a comment |Â
Thanks, I'll look into it!
– Adam Arold
Jul 17 at 14:30
Thanks, I'll look into it!
– Adam Arold
Jul 17 at 14:30
Thanks, I'll look into it!
– Adam Arold
Jul 17 at 14:30
add a comment |Â
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Almost any two areas of mathematics can be related, and abundant literature could be referenced to illustrate the unexpected connections that have been made. A flow chart will not help in the way you expect. You should pick a direction and go, IMHO.
– hardmath
Jul 16 at 22:35
3
Dividing mathematics into "branches" is a non-trivial problem in itself. The MSC classification system (the "useless" link) is about the best we have, really. My last paper had a classification I settled on, but brought in ideas and intuitions from certain other branches, which is totally normal in research mathematics. The boundaries are just not clearly defined, at all.
– Theo Bendit
Jul 16 at 22:37
Thanks for the insightful comments. I haven't studied math in 10 years so this pretty much explains how clueless I am currently.
– Adam Arold
Jul 16 at 22:42
1
In theory it’s a nice idea, but such a directed graph would be horribly complicated in order to be accurate. The best advice I have is state your goals and interests and ask for advice regarding pre requisites. For category theory, some general experience with abstract algebra and commutative algebra would probably help. The field will maybe seem more motivated if you happen to have done some things (homologous algebra, algebraic geometry) without category theory. Then when you switch to category theory you realize how great it is. But you could probably also
– Prince M
Jul 16 at 22:51
1
Become an expert in pure category theory without even knowing what homologous algebra or algebraic geometry are.
– Prince M
Jul 16 at 22:51