Mixing
Where to go from here (Warning: SOFT QUESTION)
It is now nearing summer time and as consequence, I will have a lot of time on my hands. As such I've been trying to figure out how to spend my time in a productive manner.
I need to practice to get better at math but what do I practice to do so?
soft-question advice
asked Jun 22 '18 at 1:22
oypus
518
|
show 2 more comments
It is now nearing summer time and as consequence, I will have a lot of time on my hands. As such I've been trying to figure out how to spend my time in a productive manner.
I need to practice to get better at math but what do I practice to do so?
soft-question advice
asked Jun 22 '18 at 1:22
oypus
518
What kind of mathematics do you know already? What interests you? My best suggestion is to find a problem that interests you and try to solve it on your own, or to try to follow an established solution. If you provide more details in your question, I'd elaborate more in an answer.
– Sambo
Jun 22 '18 at 2:38
If you want to do research mathematics, and you already know calculus, why don't you start teaching yourself the undergraduate curriculum for a typical math major? Intro to proofs, real analysis, abstract algebra, linear algebra, topology. Get some books like baby Rudin, Hungerford, Axler, and Munkres.
– D_S
Jun 22 '18 at 2:54
1
Interestingly, for me, just skulking around this website and at least READING good questions, at all levels, even if you don't fully grasp everything, can expose you to a great deal of possible directions. From there, you can pick and choose whatever you think sounds cool
– JuliusL33t
Jun 22 '18 at 4:42
1
And Linear Algebra. Lots and lots of Linear Algebra...
– JuliusL33t
Jun 22 '18 at 4:44
3
@MorganRodgers It seems a bit too bad that there isn't a place for questions like this. The MSE community is large and active, and seems like a good place for people interested in math. It would be great if there were a space for talking about things that aren't strictly right-or-wrong math problems.
– Sambo
Jun 22 '18 at 13:37
|
show 2 more comments
It is now nearing summer time and as consequence, I will have a lot of time on my hands. As such I've been trying to figure out how to spend my time in a productive manner.
I need to practice to get better at math but what do I practice to do so?
soft-question advice
asked Jun 22 '18 at 1:22
oypus
518
It is now nearing summer time and as consequence, I will have a lot of time on my hands. As such I've been trying to figure out how to spend my time in a productive manner.
I need to practice to get better at math but what do I practice to do so?
soft-question advice
soft-question advice
asked Jun 22 '18 at 1:22
oypus
518
asked Jun 22 '18 at 1:22
oypus
518
edited Nov 21 '18 at 10:27
asked Jun 22 '18 at 1:22
oypus
518
asked Jun 22 '18 at 1:22
oypus
518
asked Jun 22 '18 at 1:22
oypus
518
518
What kind of mathematics do you know already? What interests you? My best suggestion is to find a problem that interests you and try to solve it on your own, or to try to follow an established solution. If you provide more details in your question, I'd elaborate more in an answer.
– Sambo
Jun 22 '18 at 2:38
If you want to do research mathematics, and you already know calculus, why don't you start teaching yourself the undergraduate curriculum for a typical math major? Intro to proofs, real analysis, abstract algebra, linear algebra, topology. Get some books like baby Rudin, Hungerford, Axler, and Munkres.
– D_S
Jun 22 '18 at 2:54
1
Interestingly, for me, just skulking around this website and at least READING good questions, at all levels, even if you don't fully grasp everything, can expose you to a great deal of possible directions. From there, you can pick and choose whatever you think sounds cool
– JuliusL33t
Jun 22 '18 at 4:42
1
And Linear Algebra. Lots and lots of Linear Algebra...
– JuliusL33t
Jun 22 '18 at 4:44
3
@MorganRodgers It seems a bit too bad that there isn't a place for questions like this. The MSE community is large and active, and seems like a good place for people interested in math. It would be great if there were a space for talking about things that aren't strictly right-or-wrong math problems.
– Sambo
Jun 22 '18 at 13:37
|
show 2 more comments
What kind of mathematics do you know already? What interests you? My best suggestion is to find a problem that interests you and try to solve it on your own, or to try to follow an established solution. If you provide more details in your question, I'd elaborate more in an answer.
– Sambo
Jun 22 '18 at 2:38
If you want to do research mathematics, and you already know calculus, why don't you start teaching yourself the undergraduate curriculum for a typical math major? Intro to proofs, real analysis, abstract algebra, linear algebra, topology. Get some books like baby Rudin, Hungerford, Axler, and Munkres.
– D_S
Jun 22 '18 at 2:54
1
Interestingly, for me, just skulking around this website and at least READING good questions, at all levels, even if you don't fully grasp everything, can expose you to a great deal of possible directions. From there, you can pick and choose whatever you think sounds cool
– JuliusL33t
Jun 22 '18 at 4:42
1
And Linear Algebra. Lots and lots of Linear Algebra...
– JuliusL33t
Jun 22 '18 at 4:44
3
@MorganRodgers It seems a bit too bad that there isn't a place for questions like this. The MSE community is large and active, and seems like a good place for people interested in math. It would be great if there were a space for talking about things that aren't strictly right-or-wrong math problems.
– Sambo
Jun 22 '18 at 13:37
What kind of mathematics do you know already? What interests you? My best suggestion is to find a problem that interests you and try to solve it on your own, or to try to follow an established solution. If you provide more details in your question, I'd elaborate more in an answer.
– Sambo
Jun 22 '18 at 2:38
What kind of mathematics do you know already? What interests you? My best suggestion is to find a problem that interests you and try to solve it on your own, or to try to follow an established solution. If you provide more details in your question, I'd elaborate more in an answer.
– Sambo
Jun 22 '18 at 2:38
If you want to do research mathematics, and you already know calculus, why don't you start teaching yourself the undergraduate curriculum for a typical math major? Intro to proofs, real analysis, abstract algebra, linear algebra, topology. Get some books like baby Rudin, Hungerford, Axler, and Munkres.
– D_S
Jun 22 '18 at 2:54
If you want to do research mathematics, and you already know calculus, why don't you start teaching yourself the undergraduate curriculum for a typical math major? Intro to proofs, real analysis, abstract algebra, linear algebra, topology. Get some books like baby Rudin, Hungerford, Axler, and Munkres.
– D_S
Jun 22 '18 at 2:54
1
1
Interestingly, for me, just skulking around this website and at least READING good questions, at all levels, even if you don't fully grasp everything, can expose you to a great deal of possible directions. From there, you can pick and choose whatever you think sounds cool
– JuliusL33t
Jun 22 '18 at 4:42
Interestingly, for me, just skulking around this website and at least READING good questions, at all levels, even if you don't fully grasp everything, can expose you to a great deal of possible directions. From there, you can pick and choose whatever you think sounds cool
– JuliusL33t
Jun 22 '18 at 4:42
1
1
And Linear Algebra. Lots and lots of Linear Algebra...
– JuliusL33t
Jun 22 '18 at 4:44
And Linear Algebra. Lots and lots of Linear Algebra...
– JuliusL33t
Jun 22 '18 at 4:44
3
3
@MorganRodgers It seems a bit too bad that there isn't a place for questions like this. The MSE community is large and active, and seems like a good place for people interested in math. It would be great if there were a space for talking about things that aren't strictly right-or-wrong math problems.
– Sambo
Jun 22 '18 at 13:37
@MorganRodgers It seems a bit too bad that there isn't a place for questions like this. The MSE community is large and active, and seems like a good place for people interested in math. It would be great if there were a space for talking about things that aren't strictly right-or-wrong math problems.
– Sambo
Jun 22 '18 at 13:37
|
show 2 more comments
2 Answers
2
active
oldest
votes
If you want to find a way to express your creativity through mathematics, the best thing to do is to find problems that interest you and then try to solve them.
Some of my favorite things to discover were:
- Real analysis: the $epsilon-delta$ definition of limits and trying to do some simple proofs with them. Given that you have taught yourself calculus, this should be your next step.
- The problem: how are limits defined precisely?
- The problem: how are limits defined precisely?
- Linear algebra: eigenvalue decomposition and its applications in the real world. These sorts of problems are intriguing because they seem inscrutable at first, but easy once you've learned the material. It requires you to learn quite a bit of linear algebra at first, but it's a motivating goal.
- Sample problem: what's the probability of arriving at a given node when moving ranodmly in a graph?
- Sample problem: what's the probability of arriving at a given node when moving ranodmly in a graph?
- Induction: this is a key concept for mathematics. There are lots of problems you can try that involve it!
- Sample problem: Prove that $2^n > n^2$ for $n geq 5$
- Sample problem: Prove that $2^n > n^2$ for $n geq 5$
Altogether, my first suggestion is: if you know a problem that intrigues you, try to learn the tools to solve it. If not, try to look at some beginner books of some undergrad-level math (basics of proof, real analysis, linear algebra... then group theory, measure theory, etc.), and see if there are some sample problems that interest you. Finally, I suggest going on Youtube and watching some math videos to get inspired. Some of my favorites are: ViHart, Mathologer, Numberphile, 3Blue1Brown. These are great for discovering new ideas and interesting problems!
Keep in mind that high school math is mostly computational, and not very representative of what higher-level math is like. Keep learning about stuff that interests you. Good luck!
answered Jun 22 '18 at 14:04
Sambo
2,1382532
add a comment |
I would recommend you have a look at some of the books on this list in a library, particularly some of nos. 1, 3, 15, 19, 20, 34 and the series by Yaglom.
answered Jun 22 '18 at 6:56
Dave
391
add a comment |
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2 Answers
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active
oldest
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2 Answers
2
active
oldest
votes
active
oldest
votes
active
oldest
votes
If you want to find a way to express your creativity through mathematics, the best thing to do is to find problems that interest you and then try to solve them.
Some of my favorite things to discover were:
- Real analysis: the $epsilon-delta$ definition of limits and trying to do some simple proofs with them. Given that you have taught yourself calculus, this should be your next step.
- The problem: how are limits defined precisely?
- The problem: how are limits defined precisely?
- Linear algebra: eigenvalue decomposition and its applications in the real world. These sorts of problems are intriguing because they seem inscrutable at first, but easy once you've learned the material. It requires you to learn quite a bit of linear algebra at first, but it's a motivating goal.
- Sample problem: what's the probability of arriving at a given node when moving ranodmly in a graph?
- Sample problem: what's the probability of arriving at a given node when moving ranodmly in a graph?
- Induction: this is a key concept for mathematics. There are lots of problems you can try that involve it!
- Sample problem: Prove that $2^n > n^2$ for $n geq 5$
- Sample problem: Prove that $2^n > n^2$ for $n geq 5$
Altogether, my first suggestion is: if you know a problem that intrigues you, try to learn the tools to solve it. If not, try to look at some beginner books of some undergrad-level math (basics of proof, real analysis, linear algebra... then group theory, measure theory, etc.), and see if there are some sample problems that interest you. Finally, I suggest going on Youtube and watching some math videos to get inspired. Some of my favorites are: ViHart, Mathologer, Numberphile, 3Blue1Brown. These are great for discovering new ideas and interesting problems!
Keep in mind that high school math is mostly computational, and not very representative of what higher-level math is like. Keep learning about stuff that interests you. Good luck!
answered Jun 22 '18 at 14:04
Sambo
2,1382532
add a comment |
If you want to find a way to express your creativity through mathematics, the best thing to do is to find problems that interest you and then try to solve them.
Some of my favorite things to discover were:
- Real analysis: the $epsilon-delta$ definition of limits and trying to do some simple proofs with them. Given that you have taught yourself calculus, this should be your next step.
- The problem: how are limits defined precisely?
- The problem: how are limits defined precisely?
- Linear algebra: eigenvalue decomposition and its applications in the real world. These sorts of problems are intriguing because they seem inscrutable at first, but easy once you've learned the material. It requires you to learn quite a bit of linear algebra at first, but it's a motivating goal.
- Sample problem: what's the probability of arriving at a given node when moving ranodmly in a graph?
- Sample problem: what's the probability of arriving at a given node when moving ranodmly in a graph?
- Induction: this is a key concept for mathematics. There are lots of problems you can try that involve it!
- Sample problem: Prove that $2^n > n^2$ for $n geq 5$
- Sample problem: Prove that $2^n > n^2$ for $n geq 5$
Altogether, my first suggestion is: if you know a problem that intrigues you, try to learn the tools to solve it. If not, try to look at some beginner books of some undergrad-level math (basics of proof, real analysis, linear algebra... then group theory, measure theory, etc.), and see if there are some sample problems that interest you. Finally, I suggest going on Youtube and watching some math videos to get inspired. Some of my favorites are: ViHart, Mathologer, Numberphile, 3Blue1Brown. These are great for discovering new ideas and interesting problems!
Keep in mind that high school math is mostly computational, and not very representative of what higher-level math is like. Keep learning about stuff that interests you. Good luck!
answered Jun 22 '18 at 14:04
Sambo
2,1382532
add a comment |
If you want to find a way to express your creativity through mathematics, the best thing to do is to find problems that interest you and then try to solve them.
Some of my favorite things to discover were:
- Real analysis: the $epsilon-delta$ definition of limits and trying to do some simple proofs with them. Given that you have taught yourself calculus, this should be your next step.
- The problem: how are limits defined precisely?
- The problem: how are limits defined precisely?
- Linear algebra: eigenvalue decomposition and its applications in the real world. These sorts of problems are intriguing because they seem inscrutable at first, but easy once you've learned the material. It requires you to learn quite a bit of linear algebra at first, but it's a motivating goal.
- Sample problem: what's the probability of arriving at a given node when moving ranodmly in a graph?
- Sample problem: what's the probability of arriving at a given node when moving ranodmly in a graph?
- Induction: this is a key concept for mathematics. There are lots of problems you can try that involve it!
- Sample problem: Prove that $2^n > n^2$ for $n geq 5$
- Sample problem: Prove that $2^n > n^2$ for $n geq 5$
Altogether, my first suggestion is: if you know a problem that intrigues you, try to learn the tools to solve it. If not, try to look at some beginner books of some undergrad-level math (basics of proof, real analysis, linear algebra... then group theory, measure theory, etc.), and see if there are some sample problems that interest you. Finally, I suggest going on Youtube and watching some math videos to get inspired. Some of my favorites are: ViHart, Mathologer, Numberphile, 3Blue1Brown. These are great for discovering new ideas and interesting problems!
Keep in mind that high school math is mostly computational, and not very representative of what higher-level math is like. Keep learning about stuff that interests you. Good luck!
answered Jun 22 '18 at 14:04
Sambo
2,1382532
If you want to find a way to express your creativity through mathematics, the best thing to do is to find problems that interest you and then try to solve them.
Some of my favorite things to discover were:
- Real analysis: the $epsilon-delta$ definition of limits and trying to do some simple proofs with them. Given that you have taught yourself calculus, this should be your next step.
- The problem: how are limits defined precisely?
- The problem: how are limits defined precisely?
- Linear algebra: eigenvalue decomposition and its applications in the real world. These sorts of problems are intriguing because they seem inscrutable at first, but easy once you've learned the material. It requires you to learn quite a bit of linear algebra at first, but it's a motivating goal.
- Sample problem: what's the probability of arriving at a given node when moving ranodmly in a graph?
- Sample problem: what's the probability of arriving at a given node when moving ranodmly in a graph?
- Induction: this is a key concept for mathematics. There are lots of problems you can try that involve it!
- Sample problem: Prove that $2^n > n^2$ for $n geq 5$
- Sample problem: Prove that $2^n > n^2$ for $n geq 5$
Altogether, my first suggestion is: if you know a problem that intrigues you, try to learn the tools to solve it. If not, try to look at some beginner books of some undergrad-level math (basics of proof, real analysis, linear algebra... then group theory, measure theory, etc.), and see if there are some sample problems that interest you. Finally, I suggest going on Youtube and watching some math videos to get inspired. Some of my favorites are: ViHart, Mathologer, Numberphile, 3Blue1Brown. These are great for discovering new ideas and interesting problems!
Keep in mind that high school math is mostly computational, and not very representative of what higher-level math is like. Keep learning about stuff that interests you. Good luck!
answered Jun 22 '18 at 14:04
Sambo
2,1382532
answered Jun 22 '18 at 14:04
Sambo
2,1382532
answered Jun 22 '18 at 14:04
Sambo
2,1382532
answered Jun 22 '18 at 14:04
Sambo
2,1382532
2,1382532
add a comment |
add a comment |
I would recommend you have a look at some of the books on this list in a library, particularly some of nos. 1, 3, 15, 19, 20, 34 and the series by Yaglom.
answered Jun 22 '18 at 6:56
Dave
391
add a comment |
I would recommend you have a look at some of the books on this list in a library, particularly some of nos. 1, 3, 15, 19, 20, 34 and the series by Yaglom.
answered Jun 22 '18 at 6:56
Dave
391
add a comment |
I would recommend you have a look at some of the books on this list in a library, particularly some of nos. 1, 3, 15, 19, 20, 34 and the series by Yaglom.
answered Jun 22 '18 at 6:56
Dave
391
I would recommend you have a look at some of the books on this list in a library, particularly some of nos. 1, 3, 15, 19, 20, 34 and the series by Yaglom.
answered Jun 22 '18 at 6:56
Dave
391
answered Jun 22 '18 at 6:56
Dave
391
answered Jun 22 '18 at 6:56
Dave
391
answered Jun 22 '18 at 6:56
Dave
391
391
add a comment |
add a comment |
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What kind of mathematics do you know already? What interests you? My best suggestion is to find a problem that interests you and try to solve it on your own, or to try to follow an established solution. If you provide more details in your question, I'd elaborate more in an answer.
– Sambo
Jun 22 '18 at 2:38
If you want to do research mathematics, and you already know calculus, why don't you start teaching yourself the undergraduate curriculum for a typical math major? Intro to proofs, real analysis, abstract algebra, linear algebra, topology. Get some books like baby Rudin, Hungerford, Axler, and Munkres.
– D_S
Jun 22 '18 at 2:54
1
Interestingly, for me, just skulking around this website and at least READING good questions, at all levels, even if you don't fully grasp everything, can expose you to a great deal of possible directions. From there, you can pick and choose whatever you think sounds cool
– JuliusL33t
Jun 22 '18 at 4:42
1
And Linear Algebra. Lots and lots of Linear Algebra...
– JuliusL33t
Jun 22 '18 at 4:44
3
@MorganRodgers It seems a bit too bad that there isn't a place for questions like this. The MSE community is large and active, and seems like a good place for people interested in math. It would be great if there were a space for talking about things that aren't strictly right-or-wrong math problems.
– Sambo
Jun 22 '18 at 13:37