Mixing
Number theory learning curve
$begingroup$
I am a software developer with a Bachelor's degree in IT. During my educational years I have never been even remotely interested in math and also believed that you have to be born with mathematical aptitude to understand it. In high school I was passing math by the skin of my teeth having studied exactly 0 hours.
This past year something clicked in my head and I decided that I would teach myself math from the ground up, i.e. following the school progression all the way to college math. I read somewhere that number theory basically has no prerequisites other than some elementary arithmetic so I tried to self study that. Almost every problem or proof I have encountered was a big roadblock. I am not seeing anything implicit when someone writes "and therefore this" or "thus this", hence my stupid questions on this website. It also makes me think that I just might not be cut out for this.
So I am seeking advice. Number theory in my country is taught in college so I think that there are prerequisites to number theory. I want to reach a certain above average level of mathematical proficiency(number theory being my main interest) and I am willing to put in the time.
My question is do I keep trying to understand number theory without any other knowledge that I could have received in school or do I go from the bottom, self study until I am capable to think like a college student(if that is even possible) and then dive into number theory?
elementary-number-theory advice
asked Jan 28 at 6:56
Michael MuntaMichael Munta
99111
$endgroup$
|
show 1 more comment
$begingroup$
I am a software developer with a Bachelor's degree in IT. During my educational years I have never been even remotely interested in math and also believed that you have to be born with mathematical aptitude to understand it. In high school I was passing math by the skin of my teeth having studied exactly 0 hours.
This past year something clicked in my head and I decided that I would teach myself math from the ground up, i.e. following the school progression all the way to college math. I read somewhere that number theory basically has no prerequisites other than some elementary arithmetic so I tried to self study that. Almost every problem or proof I have encountered was a big roadblock. I am not seeing anything implicit when someone writes "and therefore this" or "thus this", hence my stupid questions on this website. It also makes me think that I just might not be cut out for this.
So I am seeking advice. Number theory in my country is taught in college so I think that there are prerequisites to number theory. I want to reach a certain above average level of mathematical proficiency(number theory being my main interest) and I am willing to put in the time.
My question is do I keep trying to understand number theory without any other knowledge that I could have received in school or do I go from the bottom, self study until I am capable to think like a college student(if that is even possible) and then dive into number theory?
elementary-number-theory advice
asked Jan 28 at 6:56
Michael MuntaMichael Munta
99111
$endgroup$
$begingroup$
I'd just say that stick with what keeps you interested in mathematics. And don't try to do anything too hard, at least for too long, if it could lead into a burn out. If you just self study, you shouldn't take any pressure and feel obligated to study mathematics.
$endgroup$
– Miksu
Jan 28 at 7:10
$begingroup$
Almost every day I am at the point of burn out. :) I am trying to find out the experiences of others in this regard. I see you are also self studying. What is your background in math?
$endgroup$
– Michael Munta
Jan 28 at 7:16
$begingroup$
I started self-studying mathematics when I saw interesting YouTube videos about mathematics :D When I was in the seventh grade I bought myself high school level mathematics books and started studying high school mathematics. In the end of elementary school, I started studying university level mathematics. I've just followed basic curriculum. But I didn't study for example probability, and only the subjects that interested me...
$endgroup$
– Miksu
Jan 28 at 7:21
$begingroup$
That is what I am wondering. To do what you did before diving into number theory because it just might be too hard for my background right now. I am hoping that once I get more proficient with some other things I will be able to understand topics/problems in number theory that I can not understand now.
$endgroup$
– Michael Munta
Jan 28 at 7:26
$begingroup$
Perhaps you'd be better served studying "introduction to proofs and the mathematical vernacular", or some other introductory proof book. These are where i learned how proofs work, how to read them, and how to write my own.
$endgroup$
– Artimis Fowl
Jan 28 at 7:31
|
show 1 more comment
$begingroup$
I am a software developer with a Bachelor's degree in IT. During my educational years I have never been even remotely interested in math and also believed that you have to be born with mathematical aptitude to understand it. In high school I was passing math by the skin of my teeth having studied exactly 0 hours.
This past year something clicked in my head and I decided that I would teach myself math from the ground up, i.e. following the school progression all the way to college math. I read somewhere that number theory basically has no prerequisites other than some elementary arithmetic so I tried to self study that. Almost every problem or proof I have encountered was a big roadblock. I am not seeing anything implicit when someone writes "and therefore this" or "thus this", hence my stupid questions on this website. It also makes me think that I just might not be cut out for this.
So I am seeking advice. Number theory in my country is taught in college so I think that there are prerequisites to number theory. I want to reach a certain above average level of mathematical proficiency(number theory being my main interest) and I am willing to put in the time.
My question is do I keep trying to understand number theory without any other knowledge that I could have received in school or do I go from the bottom, self study until I am capable to think like a college student(if that is even possible) and then dive into number theory?
elementary-number-theory advice
asked Jan 28 at 6:56
Michael MuntaMichael Munta
99111
$endgroup$
I am a software developer with a Bachelor's degree in IT. During my educational years I have never been even remotely interested in math and also believed that you have to be born with mathematical aptitude to understand it. In high school I was passing math by the skin of my teeth having studied exactly 0 hours.
This past year something clicked in my head and I decided that I would teach myself math from the ground up, i.e. following the school progression all the way to college math. I read somewhere that number theory basically has no prerequisites other than some elementary arithmetic so I tried to self study that. Almost every problem or proof I have encountered was a big roadblock. I am not seeing anything implicit when someone writes "and therefore this" or "thus this", hence my stupid questions on this website. It also makes me think that I just might not be cut out for this.
So I am seeking advice. Number theory in my country is taught in college so I think that there are prerequisites to number theory. I want to reach a certain above average level of mathematical proficiency(number theory being my main interest) and I am willing to put in the time.
My question is do I keep trying to understand number theory without any other knowledge that I could have received in school or do I go from the bottom, self study until I am capable to think like a college student(if that is even possible) and then dive into number theory?
elementary-number-theory advice
elementary-number-theory advice
asked Jan 28 at 6:56
Michael MuntaMichael Munta
99111
asked Jan 28 at 6:56
Michael MuntaMichael Munta
99111
asked Jan 28 at 6:56
Michael MuntaMichael Munta
99111
asked Jan 28 at 6:56
Michael MuntaMichael Munta
99111
asked Jan 28 at 6:56
Michael MuntaMichael Munta
99111
99111
$begingroup$
I'd just say that stick with what keeps you interested in mathematics. And don't try to do anything too hard, at least for too long, if it could lead into a burn out. If you just self study, you shouldn't take any pressure and feel obligated to study mathematics.
$endgroup$
– Miksu
Jan 28 at 7:10
$begingroup$
Almost every day I am at the point of burn out. :) I am trying to find out the experiences of others in this regard. I see you are also self studying. What is your background in math?
$endgroup$
– Michael Munta
Jan 28 at 7:16
$begingroup$
I started self-studying mathematics when I saw interesting YouTube videos about mathematics :D When I was in the seventh grade I bought myself high school level mathematics books and started studying high school mathematics. In the end of elementary school, I started studying university level mathematics. I've just followed basic curriculum. But I didn't study for example probability, and only the subjects that interested me...
$endgroup$
– Miksu
Jan 28 at 7:21
$begingroup$
That is what I am wondering. To do what you did before diving into number theory because it just might be too hard for my background right now. I am hoping that once I get more proficient with some other things I will be able to understand topics/problems in number theory that I can not understand now.
$endgroup$
– Michael Munta
Jan 28 at 7:26
$begingroup$
Perhaps you'd be better served studying "introduction to proofs and the mathematical vernacular", or some other introductory proof book. These are where i learned how proofs work, how to read them, and how to write my own.
$endgroup$
– Artimis Fowl
Jan 28 at 7:31
|
show 1 more comment
$begingroup$
I'd just say that stick with what keeps you interested in mathematics. And don't try to do anything too hard, at least for too long, if it could lead into a burn out. If you just self study, you shouldn't take any pressure and feel obligated to study mathematics.
$endgroup$
– Miksu
Jan 28 at 7:10
$begingroup$
Almost every day I am at the point of burn out. :) I am trying to find out the experiences of others in this regard. I see you are also self studying. What is your background in math?
$endgroup$
– Michael Munta
Jan 28 at 7:16
$begingroup$
I started self-studying mathematics when I saw interesting YouTube videos about mathematics :D When I was in the seventh grade I bought myself high school level mathematics books and started studying high school mathematics. In the end of elementary school, I started studying university level mathematics. I've just followed basic curriculum. But I didn't study for example probability, and only the subjects that interested me...
$endgroup$
– Miksu
Jan 28 at 7:21
$begingroup$
That is what I am wondering. To do what you did before diving into number theory because it just might be too hard for my background right now. I am hoping that once I get more proficient with some other things I will be able to understand topics/problems in number theory that I can not understand now.
$endgroup$
– Michael Munta
Jan 28 at 7:26
$begingroup$
Perhaps you'd be better served studying "introduction to proofs and the mathematical vernacular", or some other introductory proof book. These are where i learned how proofs work, how to read them, and how to write my own.
$endgroup$
– Artimis Fowl
Jan 28 at 7:31
$begingroup$
I'd just say that stick with what keeps you interested in mathematics. And don't try to do anything too hard, at least for too long, if it could lead into a burn out. If you just self study, you shouldn't take any pressure and feel obligated to study mathematics.
$endgroup$
– Miksu
Jan 28 at 7:10
$begingroup$
I'd just say that stick with what keeps you interested in mathematics. And don't try to do anything too hard, at least for too long, if it could lead into a burn out. If you just self study, you shouldn't take any pressure and feel obligated to study mathematics.
$endgroup$
– Miksu
Jan 28 at 7:10
$begingroup$
Almost every day I am at the point of burn out. :) I am trying to find out the experiences of others in this regard. I see you are also self studying. What is your background in math?
$endgroup$
– Michael Munta
Jan 28 at 7:16
$begingroup$
Almost every day I am at the point of burn out. :) I am trying to find out the experiences of others in this regard. I see you are also self studying. What is your background in math?
$endgroup$
– Michael Munta
Jan 28 at 7:16
$begingroup$
I started self-studying mathematics when I saw interesting YouTube videos about mathematics :D When I was in the seventh grade I bought myself high school level mathematics books and started studying high school mathematics. In the end of elementary school, I started studying university level mathematics. I've just followed basic curriculum. But I didn't study for example probability, and only the subjects that interested me...
$endgroup$
– Miksu
Jan 28 at 7:21
$begingroup$
I started self-studying mathematics when I saw interesting YouTube videos about mathematics :D When I was in the seventh grade I bought myself high school level mathematics books and started studying high school mathematics. In the end of elementary school, I started studying university level mathematics. I've just followed basic curriculum. But I didn't study for example probability, and only the subjects that interested me...
$endgroup$
– Miksu
Jan 28 at 7:21
$begingroup$
That is what I am wondering. To do what you did before diving into number theory because it just might be too hard for my background right now. I am hoping that once I get more proficient with some other things I will be able to understand topics/problems in number theory that I can not understand now.
$endgroup$
– Michael Munta
Jan 28 at 7:26
$begingroup$
That is what I am wondering. To do what you did before diving into number theory because it just might be too hard for my background right now. I am hoping that once I get more proficient with some other things I will be able to understand topics/problems in number theory that I can not understand now.
$endgroup$
– Michael Munta
Jan 28 at 7:26
$begingroup$
Perhaps you'd be better served studying "introduction to proofs and the mathematical vernacular", or some other introductory proof book. These are where i learned how proofs work, how to read them, and how to write my own.
$endgroup$
– Artimis Fowl
Jan 28 at 7:31
$begingroup$
Perhaps you'd be better served studying "introduction to proofs and the mathematical vernacular", or some other introductory proof book. These are where i learned how proofs work, how to read them, and how to write my own.
$endgroup$
– Artimis Fowl
Jan 28 at 7:31
|
show 1 more comment
1 Answer
1
active
oldest
votes
$begingroup$
I think terms "number theory" or even "elementary number theory" can be deceptive understatements, to the novice especially, of just how difficult some of the problems in these fields can be. There are many topics and questions which can be stated in terms of basic arithmetic and algebra which are notoriously difficult!!! (Ever hear of Fermat's Last Theorem? 😀) So I would suggest the beginner on this path pay careful heed to just what he or she encounters and adjust their steps accordingly. There are in fact plenty of facts in beginning number theory which are both delightful and accessible. I mean, it's OK to work on proving the product of two odds is odd for awhile. Just take it as it comes, and work at a simple enough level that you enjoy and enrich yourself.
One parting shot: you might seek out books to start that are written for those with a more casual interest, semi-popular treatments; local libraries are full of such. And they are often easier to understand. Best of luck with it.
answered Jan 28 at 7:30
Robert LewisRobert Lewis
48.4k23167
$endgroup$
1
$begingroup$
"Work at a simple enough level", but also keep it challenging? So the most important thing is I attack the things I can chew and eventually I will be able to go for things that I could not comprehend before?
$endgroup$
– Michael Munta
Jan 28 at 8:03
1
$begingroup$
@MichaelMunta: that sounds about right. Remember to enjoy yourself! Cheers!
$endgroup$
– Robert Lewis
Jan 28 at 8:06
add a comment |
Your Answer
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1 Answer
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$begingroup$
I think terms "number theory" or even "elementary number theory" can be deceptive understatements, to the novice especially, of just how difficult some of the problems in these fields can be. There are many topics and questions which can be stated in terms of basic arithmetic and algebra which are notoriously difficult!!! (Ever hear of Fermat's Last Theorem? 😀) So I would suggest the beginner on this path pay careful heed to just what he or she encounters and adjust their steps accordingly. There are in fact plenty of facts in beginning number theory which are both delightful and accessible. I mean, it's OK to work on proving the product of two odds is odd for awhile. Just take it as it comes, and work at a simple enough level that you enjoy and enrich yourself.
One parting shot: you might seek out books to start that are written for those with a more casual interest, semi-popular treatments; local libraries are full of such. And they are often easier to understand. Best of luck with it.
answered Jan 28 at 7:30
Robert LewisRobert Lewis
48.4k23167
$endgroup$
1
$begingroup$
"Work at a simple enough level", but also keep it challenging? So the most important thing is I attack the things I can chew and eventually I will be able to go for things that I could not comprehend before?
$endgroup$
– Michael Munta
Jan 28 at 8:03
1
$begingroup$
@MichaelMunta: that sounds about right. Remember to enjoy yourself! Cheers!
$endgroup$
– Robert Lewis
Jan 28 at 8:06
add a comment |
$begingroup$
I think terms "number theory" or even "elementary number theory" can be deceptive understatements, to the novice especially, of just how difficult some of the problems in these fields can be. There are many topics and questions which can be stated in terms of basic arithmetic and algebra which are notoriously difficult!!! (Ever hear of Fermat's Last Theorem? 😀) So I would suggest the beginner on this path pay careful heed to just what he or she encounters and adjust their steps accordingly. There are in fact plenty of facts in beginning number theory which are both delightful and accessible. I mean, it's OK to work on proving the product of two odds is odd for awhile. Just take it as it comes, and work at a simple enough level that you enjoy and enrich yourself.
One parting shot: you might seek out books to start that are written for those with a more casual interest, semi-popular treatments; local libraries are full of such. And they are often easier to understand. Best of luck with it.
answered Jan 28 at 7:30
Robert LewisRobert Lewis
48.4k23167
$endgroup$
1
$begingroup$
"Work at a simple enough level", but also keep it challenging? So the most important thing is I attack the things I can chew and eventually I will be able to go for things that I could not comprehend before?
$endgroup$
– Michael Munta
Jan 28 at 8:03
1
$begingroup$
@MichaelMunta: that sounds about right. Remember to enjoy yourself! Cheers!
$endgroup$
– Robert Lewis
Jan 28 at 8:06
add a comment |
$begingroup$
I think terms "number theory" or even "elementary number theory" can be deceptive understatements, to the novice especially, of just how difficult some of the problems in these fields can be. There are many topics and questions which can be stated in terms of basic arithmetic and algebra which are notoriously difficult!!! (Ever hear of Fermat's Last Theorem? 😀) So I would suggest the beginner on this path pay careful heed to just what he or she encounters and adjust their steps accordingly. There are in fact plenty of facts in beginning number theory which are both delightful and accessible. I mean, it's OK to work on proving the product of two odds is odd for awhile. Just take it as it comes, and work at a simple enough level that you enjoy and enrich yourself.
One parting shot: you might seek out books to start that are written for those with a more casual interest, semi-popular treatments; local libraries are full of such. And they are often easier to understand. Best of luck with it.
answered Jan 28 at 7:30
Robert LewisRobert Lewis
48.4k23167
$endgroup$
I think terms "number theory" or even "elementary number theory" can be deceptive understatements, to the novice especially, of just how difficult some of the problems in these fields can be. There are many topics and questions which can be stated in terms of basic arithmetic and algebra which are notoriously difficult!!! (Ever hear of Fermat's Last Theorem? 😀) So I would suggest the beginner on this path pay careful heed to just what he or she encounters and adjust their steps accordingly. There are in fact plenty of facts in beginning number theory which are both delightful and accessible. I mean, it's OK to work on proving the product of two odds is odd for awhile. Just take it as it comes, and work at a simple enough level that you enjoy and enrich yourself.
One parting shot: you might seek out books to start that are written for those with a more casual interest, semi-popular treatments; local libraries are full of such. And they are often easier to understand. Best of luck with it.
answered Jan 28 at 7:30
Robert LewisRobert Lewis
48.4k23167
answered Jan 28 at 7:30
Robert LewisRobert Lewis
48.4k23167
answered Jan 28 at 7:30
Robert LewisRobert Lewis
48.4k23167
answered Jan 28 at 7:30
Robert LewisRobert Lewis
48.4k23167
48.4k23167
1
$begingroup$
"Work at a simple enough level", but also keep it challenging? So the most important thing is I attack the things I can chew and eventually I will be able to go for things that I could not comprehend before?
$endgroup$
– Michael Munta
Jan 28 at 8:03
1
$begingroup$
@MichaelMunta: that sounds about right. Remember to enjoy yourself! Cheers!
$endgroup$
– Robert Lewis
Jan 28 at 8:06
add a comment |
1
$begingroup$
"Work at a simple enough level", but also keep it challenging? So the most important thing is I attack the things I can chew and eventually I will be able to go for things that I could not comprehend before?
$endgroup$
– Michael Munta
Jan 28 at 8:03
1
$begingroup$
@MichaelMunta: that sounds about right. Remember to enjoy yourself! Cheers!
$endgroup$
– Robert Lewis
Jan 28 at 8:06
1
1
$begingroup$
"Work at a simple enough level", but also keep it challenging? So the most important thing is I attack the things I can chew and eventually I will be able to go for things that I could not comprehend before?
$endgroup$
– Michael Munta
Jan 28 at 8:03
$begingroup$
"Work at a simple enough level", but also keep it challenging? So the most important thing is I attack the things I can chew and eventually I will be able to go for things that I could not comprehend before?
$endgroup$
– Michael Munta
Jan 28 at 8:03
1
1
$begingroup$
@MichaelMunta: that sounds about right. Remember to enjoy yourself! Cheers!
$endgroup$
– Robert Lewis
Jan 28 at 8:06
$begingroup$
@MichaelMunta: that sounds about right. Remember to enjoy yourself! Cheers!
$endgroup$
– Robert Lewis
Jan 28 at 8:06
add a comment |
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$begingroup$
I'd just say that stick with what keeps you interested in mathematics. And don't try to do anything too hard, at least for too long, if it could lead into a burn out. If you just self study, you shouldn't take any pressure and feel obligated to study mathematics.
$endgroup$
– Miksu
Jan 28 at 7:10
$begingroup$
Almost every day I am at the point of burn out. :) I am trying to find out the experiences of others in this regard. I see you are also self studying. What is your background in math?
$endgroup$
– Michael Munta
Jan 28 at 7:16
$begingroup$
I started self-studying mathematics when I saw interesting YouTube videos about mathematics :D When I was in the seventh grade I bought myself high school level mathematics books and started studying high school mathematics. In the end of elementary school, I started studying university level mathematics. I've just followed basic curriculum. But I didn't study for example probability, and only the subjects that interested me...
$endgroup$
– Miksu
Jan 28 at 7:21
$begingroup$
That is what I am wondering. To do what you did before diving into number theory because it just might be too hard for my background right now. I am hoping that once I get more proficient with some other things I will be able to understand topics/problems in number theory that I can not understand now.
$endgroup$
– Michael Munta
Jan 28 at 7:26
$begingroup$
Perhaps you'd be better served studying "introduction to proofs and the mathematical vernacular", or some other introductory proof book. These are where i learned how proofs work, how to read them, and how to write my own.
$endgroup$
– Artimis Fowl
Jan 28 at 7:31