Mixing
Start understanding analysis [closed]
Currently, I have read and re-read the Stephen Abbott Understanding Analysis for about $3$ or $4$ times up to and including the chapter $6$. However, I can't say that now I am feeling more confident about understanding and completing problems in analysis, than when I hadn't read it. It is so frustrating to read the text, when you think that you get almost everything in the explanation parts, because it is so well written and clear, but after that struggling to complete even the easiest exercise in the problems section of the chapter, even when redoing it the $3$-rd time.
Therefore, I am willing to ask, can you suggest a way to start really understanding the analysis? How should I approach to solving the problems? Will it make a sense to switch to another book (I was thinking about Apostol/Pugh/Kolmogorov)?
$P.S.$ I am a self-learner. It is my second book in analysis, after Fichtengoltz's first volume, which was too theoretical for my test as there were no problem sets. My problem is not just in exercises. While reading the proof I understand it, however if I try to do the proof on my own, for example, after $3$ hours from reading I can not manage to recall how it was done.
real-analysis analysis soft-question book-recommendation
edited Nov 22 '18 at 13:03
Jean-Claude Arbaut
14.7k63464
asked Nov 22 '18 at 12:53
Sargis IskandaryanSargis Iskandaryan
560112
closed as primarily opinion-based by Sargis Iskandaryan, Cesareo, KReiser, max_zorn, user10354138 Nov 23 '18 at 8:00
Many good questions generate some degree of opinion based on expert experience, but answers to this question will tend to be almost entirely based on opinions, rather than facts, references, or specific expertise. If this question can be reworded to fit the rules in the help center, please edit the question.
add a comment |
Currently, I have read and re-read the Stephen Abbott Understanding Analysis for about $3$ or $4$ times up to and including the chapter $6$. However, I can't say that now I am feeling more confident about understanding and completing problems in analysis, than when I hadn't read it. It is so frustrating to read the text, when you think that you get almost everything in the explanation parts, because it is so well written and clear, but after that struggling to complete even the easiest exercise in the problems section of the chapter, even when redoing it the $3$-rd time.
Therefore, I am willing to ask, can you suggest a way to start really understanding the analysis? How should I approach to solving the problems? Will it make a sense to switch to another book (I was thinking about Apostol/Pugh/Kolmogorov)?
$P.S.$ I am a self-learner. It is my second book in analysis, after Fichtengoltz's first volume, which was too theoretical for my test as there were no problem sets. My problem is not just in exercises. While reading the proof I understand it, however if I try to do the proof on my own, for example, after $3$ hours from reading I can not manage to recall how it was done.
real-analysis analysis soft-question book-recommendation
edited Nov 22 '18 at 13:03
Jean-Claude Arbaut
14.7k63464
asked Nov 22 '18 at 12:53
Sargis IskandaryanSargis Iskandaryan
560112
closed as primarily opinion-based by Sargis Iskandaryan, Cesareo, KReiser, max_zorn, user10354138 Nov 23 '18 at 8:00
Many good questions generate some degree of opinion based on expert experience, but answers to this question will tend to be almost entirely based on opinions, rather than facts, references, or specific expertise. If this question can be reworded to fit the rules in the help center, please edit the question.
3
It's good that you attempt to reproduce the proofs yourself and attempt to solve the problems yourself. How long do you spend struggling with a particular problem before giving up? When you are sufficiently stuck, it can help to get just a hint instead of reading the full solution. For example if you are trying to reproduce a proof from the book and you get stuck (and you have struggled but you are still stuck), then you can read just enough of the proof to get unstuck, then try to finish the proof yourself without reading the full solution.
– littleO
Nov 22 '18 at 15:40
1
Some proofs aren't meant to be reproduced. Some are just too technical.
– Math_QED
Nov 22 '18 at 18:09
I think this question is specific enough for Mathematics Educators (it's about specific books and about the learning process), so I hope you'll ask it there. I'm interested in the answer.
– timtfj
Dec 16 '18 at 23:40
add a comment |
Currently, I have read and re-read the Stephen Abbott Understanding Analysis for about $3$ or $4$ times up to and including the chapter $6$. However, I can't say that now I am feeling more confident about understanding and completing problems in analysis, than when I hadn't read it. It is so frustrating to read the text, when you think that you get almost everything in the explanation parts, because it is so well written and clear, but after that struggling to complete even the easiest exercise in the problems section of the chapter, even when redoing it the $3$-rd time.
Therefore, I am willing to ask, can you suggest a way to start really understanding the analysis? How should I approach to solving the problems? Will it make a sense to switch to another book (I was thinking about Apostol/Pugh/Kolmogorov)?
$P.S.$ I am a self-learner. It is my second book in analysis, after Fichtengoltz's first volume, which was too theoretical for my test as there were no problem sets. My problem is not just in exercises. While reading the proof I understand it, however if I try to do the proof on my own, for example, after $3$ hours from reading I can not manage to recall how it was done.
real-analysis analysis soft-question book-recommendation
edited Nov 22 '18 at 13:03
Jean-Claude Arbaut
14.7k63464
asked Nov 22 '18 at 12:53
Sargis IskandaryanSargis Iskandaryan
560112
Currently, I have read and re-read the Stephen Abbott Understanding Analysis for about $3$ or $4$ times up to and including the chapter $6$. However, I can't say that now I am feeling more confident about understanding and completing problems in analysis, than when I hadn't read it. It is so frustrating to read the text, when you think that you get almost everything in the explanation parts, because it is so well written and clear, but after that struggling to complete even the easiest exercise in the problems section of the chapter, even when redoing it the $3$-rd time.
Therefore, I am willing to ask, can you suggest a way to start really understanding the analysis? How should I approach to solving the problems? Will it make a sense to switch to another book (I was thinking about Apostol/Pugh/Kolmogorov)?
$P.S.$ I am a self-learner. It is my second book in analysis, after Fichtengoltz's first volume, which was too theoretical for my test as there were no problem sets. My problem is not just in exercises. While reading the proof I understand it, however if I try to do the proof on my own, for example, after $3$ hours from reading I can not manage to recall how it was done.
real-analysis analysis soft-question book-recommendation
real-analysis analysis soft-question book-recommendation
edited Nov 22 '18 at 13:03
Jean-Claude Arbaut
14.7k63464
asked Nov 22 '18 at 12:53
Sargis IskandaryanSargis Iskandaryan
560112
edited Nov 22 '18 at 13:03
Jean-Claude Arbaut
14.7k63464
asked Nov 22 '18 at 12:53
Sargis IskandaryanSargis Iskandaryan
560112
edited Nov 22 '18 at 13:03
Jean-Claude Arbaut
14.7k63464
edited Nov 22 '18 at 13:03
Jean-Claude Arbaut
14.7k63464
edited Nov 22 '18 at 13:03
Jean-Claude Arbaut
14.7k63464
14.7k63464
asked Nov 22 '18 at 12:53
Sargis IskandaryanSargis Iskandaryan
560112
asked Nov 22 '18 at 12:53
Sargis IskandaryanSargis Iskandaryan
560112
asked Nov 22 '18 at 12:53
Sargis IskandaryanSargis Iskandaryan
560112
560112
closed as primarily opinion-based by Sargis Iskandaryan, Cesareo, KReiser, max_zorn, user10354138 Nov 23 '18 at 8:00
Many good questions generate some degree of opinion based on expert experience, but answers to this question will tend to be almost entirely based on opinions, rather than facts, references, or specific expertise. If this question can be reworded to fit the rules in the help center, please edit the question.
closed as primarily opinion-based by Sargis Iskandaryan, Cesareo, KReiser, max_zorn, user10354138 Nov 23 '18 at 8:00
Many good questions generate some degree of opinion based on expert experience, but answers to this question will tend to be almost entirely based on opinions, rather than facts, references, or specific expertise. If this question can be reworded to fit the rules in the help center, please edit the question.
3
It's good that you attempt to reproduce the proofs yourself and attempt to solve the problems yourself. How long do you spend struggling with a particular problem before giving up? When you are sufficiently stuck, it can help to get just a hint instead of reading the full solution. For example if you are trying to reproduce a proof from the book and you get stuck (and you have struggled but you are still stuck), then you can read just enough of the proof to get unstuck, then try to finish the proof yourself without reading the full solution.
– littleO
Nov 22 '18 at 15:40
1
Some proofs aren't meant to be reproduced. Some are just too technical.
– Math_QED
Nov 22 '18 at 18:09
I think this question is specific enough for Mathematics Educators (it's about specific books and about the learning process), so I hope you'll ask it there. I'm interested in the answer.
– timtfj
Dec 16 '18 at 23:40
add a comment |
3
It's good that you attempt to reproduce the proofs yourself and attempt to solve the problems yourself. How long do you spend struggling with a particular problem before giving up? When you are sufficiently stuck, it can help to get just a hint instead of reading the full solution. For example if you are trying to reproduce a proof from the book and you get stuck (and you have struggled but you are still stuck), then you can read just enough of the proof to get unstuck, then try to finish the proof yourself without reading the full solution.
– littleO
Nov 22 '18 at 15:40
1
Some proofs aren't meant to be reproduced. Some are just too technical.
– Math_QED
Nov 22 '18 at 18:09
I think this question is specific enough for Mathematics Educators (it's about specific books and about the learning process), so I hope you'll ask it there. I'm interested in the answer.
– timtfj
Dec 16 '18 at 23:40
3
3
It's good that you attempt to reproduce the proofs yourself and attempt to solve the problems yourself. How long do you spend struggling with a particular problem before giving up? When you are sufficiently stuck, it can help to get just a hint instead of reading the full solution. For example if you are trying to reproduce a proof from the book and you get stuck (and you have struggled but you are still stuck), then you can read just enough of the proof to get unstuck, then try to finish the proof yourself without reading the full solution.
– littleO
Nov 22 '18 at 15:40
It's good that you attempt to reproduce the proofs yourself and attempt to solve the problems yourself. How long do you spend struggling with a particular problem before giving up? When you are sufficiently stuck, it can help to get just a hint instead of reading the full solution. For example if you are trying to reproduce a proof from the book and you get stuck (and you have struggled but you are still stuck), then you can read just enough of the proof to get unstuck, then try to finish the proof yourself without reading the full solution.
– littleO
Nov 22 '18 at 15:40
1
1
Some proofs aren't meant to be reproduced. Some are just too technical.
– Math_QED
Nov 22 '18 at 18:09
Some proofs aren't meant to be reproduced. Some are just too technical.
– Math_QED
Nov 22 '18 at 18:09
I think this question is specific enough for Mathematics Educators (it's about specific books and about the learning process), so I hope you'll ask it there. I'm interested in the answer.
– timtfj
Dec 16 '18 at 23:40
I think this question is specific enough for Mathematics Educators (it's about specific books and about the learning process), so I hope you'll ask it there. I'm interested in the answer.
– timtfj
Dec 16 '18 at 23:40
add a comment |
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It's good that you attempt to reproduce the proofs yourself and attempt to solve the problems yourself. How long do you spend struggling with a particular problem before giving up? When you are sufficiently stuck, it can help to get just a hint instead of reading the full solution. For example if you are trying to reproduce a proof from the book and you get stuck (and you have struggled but you are still stuck), then you can read just enough of the proof to get unstuck, then try to finish the proof yourself without reading the full solution.
– littleO
Nov 22 '18 at 15:40
1
Some proofs aren't meant to be reproduced. Some are just too technical.
– Math_QED
Nov 22 '18 at 18:09
I think this question is specific enough for Mathematics Educators (it's about specific books and about the learning process), so I hope you'll ask it there. I'm interested in the answer.
– timtfj
Dec 16 '18 at 23:40