Good undergraduate texts in analysis for self studying [duplicate]Good First Course in real analysis book for self studyReal analysis TextbookAny textbook on elementary real analysis that has many and good exercises?Textbook on Intro to Real AnalysisCalabi-Yau ManifoldsAdvice about taking mathematical analysis classLooking for texts in representation theorySelf-study Real analysis Tao or Rudin?recommendation on studying real-analysisAdvice for self-studying Inequalities and CalculusLooking for good intro book on differential equationsHow important is the choice of books in studying Analysis?The Readability of Rudin's “Real and Complex Analysis.”Self-studying multivariable real analysis (integration)?
Purchased new computer from DELL with pre-installed Ubuntu. Won't boot. Should assume its an error from DELL?
Why is Chromosome 1 called Chromosome 1?
Based on what criteria do you add/not add icons to labels within a toolbar?
Probably terminated or laid off soon; confront or not?
Does a humanoid possessed by a ghost register as undead to a paladin's Divine Sense?
If I build a custom theme, will it update?
Best way to explain to my boss that I cannot attend a team summit because it is on Rosh Hashana or any other Jewish Holiday
Why does putting a dot after the URL remove login information?
Identify Batman without getting caught
I was contacted by a private bank overseas to get my inheritance
Is the first page of a novel really that important?
Is a switch from R to Python worth it?
Is there a way to prevent the production team from messing up my paper?
If someone else uploads my GPL'd code to Github without my permission, is that a copyright violation?
How to check a file was encrypted (really & correctly)
How can I perform a deterministic physics simulation?
Not been paid even after reminding the Treasurer; what should I do?
Will a research paper be retracted if the code (which was made publically available ) is shown have a flaw in the logic?
Only charge capacitor when button pushed then turn on LED momentarily with capacitor when button released
split large formula in align
Ancients don't give a full level?
Pronouns when writing from the point of view of a robot
What was the role of Commodore-West Germany?
What is an air conditioner compressor hard start kit and how does it work?
Good undergraduate texts in analysis for self studying [duplicate]
Good First Course in real analysis book for self studyReal analysis TextbookAny textbook on elementary real analysis that has many and good exercises?Textbook on Intro to Real AnalysisCalabi-Yau ManifoldsAdvice about taking mathematical analysis classLooking for texts in representation theorySelf-study Real analysis Tao or Rudin?recommendation on studying real-analysisAdvice for self-studying Inequalities and CalculusLooking for good intro book on differential equationsHow important is the choice of books in studying Analysis?The Readability of Rudin's “Real and Complex Analysis.”Self-studying multivariable real analysis (integration)?
.everyoneloves__top-leaderboard:empty,.everyoneloves__mid-leaderboard:empty,.everyoneloves__bot-mid-leaderboard:empty margin-bottom:0;
$begingroup$
This question already has an answer here:
Good First Course in real analysis book for self study
7 answers
I know this question was asked many times but I have some specific questions. I know the usual recommendations but I am afraid of going for Rudin because I've read many reviews that said it wasn't good for self studying. I remember in one review I read the guy said " As you go through the book you get excited about some cool theorems and results only to find that Rudin gives a proof that only does the job and leaves out much of the intuition for you to either find on your own or look for elsewhere".
I don't like this type of texts because when the proof is too directed it becomes unsatisfactory. By directed I mean that the result is already established and we're just trying to make it formal by looking for arguments that just verify the fact without , for example , mentioning how one would first consider these arguments and how they would come up while trying to prove the result.
That said , There are other suggestions such as Barry Simon's comprehensive course in analysis. This is a new text which isn't reviewed a lot. The description says it may be suitable for a graduate level course but others say it gives a good introduction to the prerequisites but I'm not sure.
Any other suggestions ?
Edit : thanks for your answers
analysis reference-request soft-question
$endgroup$
marked as duplicate by Greek - Area 51 Proposal, cmk, YuiTo Cheng, The Count, Leucippus Jul 27 at 0:51
This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.
add a comment |
$begingroup$
This question already has an answer here:
Good First Course in real analysis book for self study
7 answers
I know this question was asked many times but I have some specific questions. I know the usual recommendations but I am afraid of going for Rudin because I've read many reviews that said it wasn't good for self studying. I remember in one review I read the guy said " As you go through the book you get excited about some cool theorems and results only to find that Rudin gives a proof that only does the job and leaves out much of the intuition for you to either find on your own or look for elsewhere".
I don't like this type of texts because when the proof is too directed it becomes unsatisfactory. By directed I mean that the result is already established and we're just trying to make it formal by looking for arguments that just verify the fact without , for example , mentioning how one would first consider these arguments and how they would come up while trying to prove the result.
That said , There are other suggestions such as Barry Simon's comprehensive course in analysis. This is a new text which isn't reviewed a lot. The description says it may be suitable for a graduate level course but others say it gives a good introduction to the prerequisites but I'm not sure.
Any other suggestions ?
Edit : thanks for your answers
analysis reference-request soft-question
$endgroup$
marked as duplicate by Greek - Area 51 Proposal, cmk, YuiTo Cheng, The Count, Leucippus Jul 27 at 0:51
This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.
2
$begingroup$
Robert Burn's "Numbers and Functions" is amazing.
$endgroup$
– dfnu
Jul 26 at 11:40
1
$begingroup$
royden is the standard text for real analysis at the graduate level.
$endgroup$
– Tony S.F.
Jul 26 at 11:44
1
$begingroup$
Tao, Zorich, Bartle (Elements), Bartle (Introduction), Pugh, Hubbard & Hubbard, Abbott, Apostol (Calculus), Apostol (Analysis), Spivak (Calculus), Spivak (Calculus on Manifolds), Munkres, Royden, Rudin, Kolmogorov/Fomin, Stein/Shakarchi... the list goes on. There are many, many choices and they are all heavily recommended in various threads. Use several sources if you find yourself having trouble with a particular section, or ask here.
$endgroup$
– graeme
Jul 26 at 12:26
1
$begingroup$
I will add that the benefit of going through a well-worn text like Rudin's PMA is that there are generally bountiful solutions and hints to be found online, including Professor Bergman's nearly 100 pages of notes, explanations, and supplementary exercises to accompany Rudin.
$endgroup$
– graeme
Jul 26 at 14:19
$begingroup$
math.stackexchange.com/questions/2725690/…, math.stackexchange.com/q/594640/53259, math.stackexchange.com/q/2096062/53259,
$endgroup$
– Greek - Area 51 Proposal
Jul 26 at 20:19
add a comment |
$begingroup$
This question already has an answer here:
Good First Course in real analysis book for self study
7 answers
I know this question was asked many times but I have some specific questions. I know the usual recommendations but I am afraid of going for Rudin because I've read many reviews that said it wasn't good for self studying. I remember in one review I read the guy said " As you go through the book you get excited about some cool theorems and results only to find that Rudin gives a proof that only does the job and leaves out much of the intuition for you to either find on your own or look for elsewhere".
I don't like this type of texts because when the proof is too directed it becomes unsatisfactory. By directed I mean that the result is already established and we're just trying to make it formal by looking for arguments that just verify the fact without , for example , mentioning how one would first consider these arguments and how they would come up while trying to prove the result.
That said , There are other suggestions such as Barry Simon's comprehensive course in analysis. This is a new text which isn't reviewed a lot. The description says it may be suitable for a graduate level course but others say it gives a good introduction to the prerequisites but I'm not sure.
Any other suggestions ?
Edit : thanks for your answers
analysis reference-request soft-question
$endgroup$
This question already has an answer here:
Good First Course in real analysis book for self study
7 answers
I know this question was asked many times but I have some specific questions. I know the usual recommendations but I am afraid of going for Rudin because I've read many reviews that said it wasn't good for self studying. I remember in one review I read the guy said " As you go through the book you get excited about some cool theorems and results only to find that Rudin gives a proof that only does the job and leaves out much of the intuition for you to either find on your own or look for elsewhere".
I don't like this type of texts because when the proof is too directed it becomes unsatisfactory. By directed I mean that the result is already established and we're just trying to make it formal by looking for arguments that just verify the fact without , for example , mentioning how one would first consider these arguments and how they would come up while trying to prove the result.
That said , There are other suggestions such as Barry Simon's comprehensive course in analysis. This is a new text which isn't reviewed a lot. The description says it may be suitable for a graduate level course but others say it gives a good introduction to the prerequisites but I'm not sure.
Any other suggestions ?
Edit : thanks for your answers
This question already has an answer here:
Good First Course in real analysis book for self study
7 answers
analysis reference-request soft-question
analysis reference-request soft-question
edited Jul 26 at 13:57
community wiki
Km356
marked as duplicate by Greek - Area 51 Proposal, cmk, YuiTo Cheng, The Count, Leucippus Jul 27 at 0:51
This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.
marked as duplicate by Greek - Area 51 Proposal, cmk, YuiTo Cheng, The Count, Leucippus Jul 27 at 0:51
This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.
marked as duplicate by Greek - Area 51 Proposal, cmk, YuiTo Cheng, The Count, Leucippus Jul 27 at 0:51
This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.
2
$begingroup$
Robert Burn's "Numbers and Functions" is amazing.
$endgroup$
– dfnu
Jul 26 at 11:40
1
$begingroup$
royden is the standard text for real analysis at the graduate level.
$endgroup$
– Tony S.F.
Jul 26 at 11:44
1
$begingroup$
Tao, Zorich, Bartle (Elements), Bartle (Introduction), Pugh, Hubbard & Hubbard, Abbott, Apostol (Calculus), Apostol (Analysis), Spivak (Calculus), Spivak (Calculus on Manifolds), Munkres, Royden, Rudin, Kolmogorov/Fomin, Stein/Shakarchi... the list goes on. There are many, many choices and they are all heavily recommended in various threads. Use several sources if you find yourself having trouble with a particular section, or ask here.
$endgroup$
– graeme
Jul 26 at 12:26
1
$begingroup$
I will add that the benefit of going through a well-worn text like Rudin's PMA is that there are generally bountiful solutions and hints to be found online, including Professor Bergman's nearly 100 pages of notes, explanations, and supplementary exercises to accompany Rudin.
$endgroup$
– graeme
Jul 26 at 14:19
$begingroup$
math.stackexchange.com/questions/2725690/…, math.stackexchange.com/q/594640/53259, math.stackexchange.com/q/2096062/53259,
$endgroup$
– Greek - Area 51 Proposal
Jul 26 at 20:19
add a comment |
2
$begingroup$
Robert Burn's "Numbers and Functions" is amazing.
$endgroup$
– dfnu
Jul 26 at 11:40
1
$begingroup$
royden is the standard text for real analysis at the graduate level.
$endgroup$
– Tony S.F.
Jul 26 at 11:44
1
$begingroup$
Tao, Zorich, Bartle (Elements), Bartle (Introduction), Pugh, Hubbard & Hubbard, Abbott, Apostol (Calculus), Apostol (Analysis), Spivak (Calculus), Spivak (Calculus on Manifolds), Munkres, Royden, Rudin, Kolmogorov/Fomin, Stein/Shakarchi... the list goes on. There are many, many choices and they are all heavily recommended in various threads. Use several sources if you find yourself having trouble with a particular section, or ask here.
$endgroup$
– graeme
Jul 26 at 12:26
1
$begingroup$
I will add that the benefit of going through a well-worn text like Rudin's PMA is that there are generally bountiful solutions and hints to be found online, including Professor Bergman's nearly 100 pages of notes, explanations, and supplementary exercises to accompany Rudin.
$endgroup$
– graeme
Jul 26 at 14:19
$begingroup$
math.stackexchange.com/questions/2725690/…, math.stackexchange.com/q/594640/53259, math.stackexchange.com/q/2096062/53259,
$endgroup$
– Greek - Area 51 Proposal
Jul 26 at 20:19
2
2
$begingroup$
Robert Burn's "Numbers and Functions" is amazing.
$endgroup$
– dfnu
Jul 26 at 11:40
$begingroup$
Robert Burn's "Numbers and Functions" is amazing.
$endgroup$
– dfnu
Jul 26 at 11:40
1
1
$begingroup$
royden is the standard text for real analysis at the graduate level.
$endgroup$
– Tony S.F.
Jul 26 at 11:44
$begingroup$
royden is the standard text for real analysis at the graduate level.
$endgroup$
– Tony S.F.
Jul 26 at 11:44
1
1
$begingroup$
Tao, Zorich, Bartle (Elements), Bartle (Introduction), Pugh, Hubbard & Hubbard, Abbott, Apostol (Calculus), Apostol (Analysis), Spivak (Calculus), Spivak (Calculus on Manifolds), Munkres, Royden, Rudin, Kolmogorov/Fomin, Stein/Shakarchi... the list goes on. There are many, many choices and they are all heavily recommended in various threads. Use several sources if you find yourself having trouble with a particular section, or ask here.
$endgroup$
– graeme
Jul 26 at 12:26
$begingroup$
Tao, Zorich, Bartle (Elements), Bartle (Introduction), Pugh, Hubbard & Hubbard, Abbott, Apostol (Calculus), Apostol (Analysis), Spivak (Calculus), Spivak (Calculus on Manifolds), Munkres, Royden, Rudin, Kolmogorov/Fomin, Stein/Shakarchi... the list goes on. There are many, many choices and they are all heavily recommended in various threads. Use several sources if you find yourself having trouble with a particular section, or ask here.
$endgroup$
– graeme
Jul 26 at 12:26
1
1
$begingroup$
I will add that the benefit of going through a well-worn text like Rudin's PMA is that there are generally bountiful solutions and hints to be found online, including Professor Bergman's nearly 100 pages of notes, explanations, and supplementary exercises to accompany Rudin.
$endgroup$
– graeme
Jul 26 at 14:19
$begingroup$
I will add that the benefit of going through a well-worn text like Rudin's PMA is that there are generally bountiful solutions and hints to be found online, including Professor Bergman's nearly 100 pages of notes, explanations, and supplementary exercises to accompany Rudin.
$endgroup$
– graeme
Jul 26 at 14:19
$begingroup$
math.stackexchange.com/questions/2725690/…, math.stackexchange.com/q/594640/53259, math.stackexchange.com/q/2096062/53259,
$endgroup$
– Greek - Area 51 Proposal
Jul 26 at 20:19
$begingroup$
math.stackexchange.com/questions/2725690/…, math.stackexchange.com/q/594640/53259, math.stackexchange.com/q/2096062/53259,
$endgroup$
– Greek - Area 51 Proposal
Jul 26 at 20:19
add a comment |
3 Answers
3
active
oldest
votes
$begingroup$
Try "Introduction to Real Analysis" by Donald R. Sherbert & Robert G. Bartle
The book is extremely great and an absolute beginner can read and understand it with immense pleasure, It starts with basic sets function and ends up to Riemann integrals and some glimpse of Topology. No doubt it will help you to make you strong in this field.
$endgroup$
1
$begingroup$
This also has a good follow-up/alternative, in Bartle's "The Elements of Real Analysis." While it goes through some concepts in one real variable, it's primarily geared towards analysis in $mathbbR^n$.
$endgroup$
– cmk
Jul 26 at 13:42
add a comment |
$begingroup$
I would purchase a copy of Understanding Analysis by Abbott. There are a lot of pictures and the exercises are aimed at undergraduate students.
$endgroup$
add a comment |
$begingroup$
I like "Understanding Analysis" by Abbott, as suggested by @Axion004. Alternatively, you could look at Tao's "Analysis I" and "Analysis II." The series starts from the ground (natural numbers, set theory, real numbers) and, by the end of the last book, works up to the Lebesgue integral. The books feature clear examples and explanations. and many of the simple propositions are left as exercises, which you might like for additional practice.
$endgroup$
add a comment |
3 Answers
3
active
oldest
votes
3 Answers
3
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
Try "Introduction to Real Analysis" by Donald R. Sherbert & Robert G. Bartle
The book is extremely great and an absolute beginner can read and understand it with immense pleasure, It starts with basic sets function and ends up to Riemann integrals and some glimpse of Topology. No doubt it will help you to make you strong in this field.
$endgroup$
1
$begingroup$
This also has a good follow-up/alternative, in Bartle's "The Elements of Real Analysis." While it goes through some concepts in one real variable, it's primarily geared towards analysis in $mathbbR^n$.
$endgroup$
– cmk
Jul 26 at 13:42
add a comment |
$begingroup$
Try "Introduction to Real Analysis" by Donald R. Sherbert & Robert G. Bartle
The book is extremely great and an absolute beginner can read and understand it with immense pleasure, It starts with basic sets function and ends up to Riemann integrals and some glimpse of Topology. No doubt it will help you to make you strong in this field.
$endgroup$
1
$begingroup$
This also has a good follow-up/alternative, in Bartle's "The Elements of Real Analysis." While it goes through some concepts in one real variable, it's primarily geared towards analysis in $mathbbR^n$.
$endgroup$
– cmk
Jul 26 at 13:42
add a comment |
$begingroup$
Try "Introduction to Real Analysis" by Donald R. Sherbert & Robert G. Bartle
The book is extremely great and an absolute beginner can read and understand it with immense pleasure, It starts with basic sets function and ends up to Riemann integrals and some glimpse of Topology. No doubt it will help you to make you strong in this field.
$endgroup$
Try "Introduction to Real Analysis" by Donald R. Sherbert & Robert G. Bartle
The book is extremely great and an absolute beginner can read and understand it with immense pleasure, It starts with basic sets function and ends up to Riemann integrals and some glimpse of Topology. No doubt it will help you to make you strong in this field.
answered Jul 26 at 12:12
community wiki
nmasanta
1
$begingroup$
This also has a good follow-up/alternative, in Bartle's "The Elements of Real Analysis." While it goes through some concepts in one real variable, it's primarily geared towards analysis in $mathbbR^n$.
$endgroup$
– cmk
Jul 26 at 13:42
add a comment |
1
$begingroup$
This also has a good follow-up/alternative, in Bartle's "The Elements of Real Analysis." While it goes through some concepts in one real variable, it's primarily geared towards analysis in $mathbbR^n$.
$endgroup$
– cmk
Jul 26 at 13:42
1
1
$begingroup$
This also has a good follow-up/alternative, in Bartle's "The Elements of Real Analysis." While it goes through some concepts in one real variable, it's primarily geared towards analysis in $mathbbR^n$.
$endgroup$
– cmk
Jul 26 at 13:42
$begingroup$
This also has a good follow-up/alternative, in Bartle's "The Elements of Real Analysis." While it goes through some concepts in one real variable, it's primarily geared towards analysis in $mathbbR^n$.
$endgroup$
– cmk
Jul 26 at 13:42
add a comment |
$begingroup$
I would purchase a copy of Understanding Analysis by Abbott. There are a lot of pictures and the exercises are aimed at undergraduate students.
$endgroup$
add a comment |
$begingroup$
I would purchase a copy of Understanding Analysis by Abbott. There are a lot of pictures and the exercises are aimed at undergraduate students.
$endgroup$
add a comment |
$begingroup$
I would purchase a copy of Understanding Analysis by Abbott. There are a lot of pictures and the exercises are aimed at undergraduate students.
$endgroup$
I would purchase a copy of Understanding Analysis by Abbott. There are a lot of pictures and the exercises are aimed at undergraduate students.
edited Jul 26 at 13:15
community wiki
Axion004
add a comment |
add a comment |
$begingroup$
I like "Understanding Analysis" by Abbott, as suggested by @Axion004. Alternatively, you could look at Tao's "Analysis I" and "Analysis II." The series starts from the ground (natural numbers, set theory, real numbers) and, by the end of the last book, works up to the Lebesgue integral. The books feature clear examples and explanations. and many of the simple propositions are left as exercises, which you might like for additional practice.
$endgroup$
add a comment |
$begingroup$
I like "Understanding Analysis" by Abbott, as suggested by @Axion004. Alternatively, you could look at Tao's "Analysis I" and "Analysis II." The series starts from the ground (natural numbers, set theory, real numbers) and, by the end of the last book, works up to the Lebesgue integral. The books feature clear examples and explanations. and many of the simple propositions are left as exercises, which you might like for additional practice.
$endgroup$
add a comment |
$begingroup$
I like "Understanding Analysis" by Abbott, as suggested by @Axion004. Alternatively, you could look at Tao's "Analysis I" and "Analysis II." The series starts from the ground (natural numbers, set theory, real numbers) and, by the end of the last book, works up to the Lebesgue integral. The books feature clear examples and explanations. and many of the simple propositions are left as exercises, which you might like for additional practice.
$endgroup$
I like "Understanding Analysis" by Abbott, as suggested by @Axion004. Alternatively, you could look at Tao's "Analysis I" and "Analysis II." The series starts from the ground (natural numbers, set theory, real numbers) and, by the end of the last book, works up to the Lebesgue integral. The books feature clear examples and explanations. and many of the simple propositions are left as exercises, which you might like for additional practice.
answered Jul 26 at 13:37
community wiki
cmk
add a comment |
add a comment |
2
$begingroup$
Robert Burn's "Numbers and Functions" is amazing.
$endgroup$
– dfnu
Jul 26 at 11:40
1
$begingroup$
royden is the standard text for real analysis at the graduate level.
$endgroup$
– Tony S.F.
Jul 26 at 11:44
1
$begingroup$
Tao, Zorich, Bartle (Elements), Bartle (Introduction), Pugh, Hubbard & Hubbard, Abbott, Apostol (Calculus), Apostol (Analysis), Spivak (Calculus), Spivak (Calculus on Manifolds), Munkres, Royden, Rudin, Kolmogorov/Fomin, Stein/Shakarchi... the list goes on. There are many, many choices and they are all heavily recommended in various threads. Use several sources if you find yourself having trouble with a particular section, or ask here.
$endgroup$
– graeme
Jul 26 at 12:26
1
$begingroup$
I will add that the benefit of going through a well-worn text like Rudin's PMA is that there are generally bountiful solutions and hints to be found online, including Professor Bergman's nearly 100 pages of notes, explanations, and supplementary exercises to accompany Rudin.
$endgroup$
– graeme
Jul 26 at 14:19
$begingroup$
math.stackexchange.com/questions/2725690/…, math.stackexchange.com/q/594640/53259, math.stackexchange.com/q/2096062/53259,
$endgroup$
– Greek - Area 51 Proposal
Jul 26 at 20:19