What is Modern Analysis and Abstract Analysis? [closed]

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Mostly I encounter textbooks named Analysis, Mathematical Analysis,... But recently, i encountered a book named A Course In Modern Analysis.

Please explain the difference between Modern Analysis and "Classical" Analysis. Also, please give some information about what Abstract Analysis means.

It's quite weird to me that the number of Modern Analysis textbooks is very small.

analysis

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edited Jul 18 at 23:01

amWhy

189k25219431

asked Jul 18 at 15:24

Le Anh Dung

708318

closed as primarily opinion-based by Mostafa Ayaz, Michael Lugo, José Carlos Santos, Alan Wang, Parcly Taxel Jul 19 at 1:10

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.

• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  How about this one?
  – John Ma
  Jul 18 at 15:31
  

  
  
  
  


• 
  
  
  

  
  2
  

  
  
  
  
  
  

  
  There's usually not much difference, as these are mostly non-precise descriptive terms. Probably "classical analysis" would have an emphasis on calculation methods (inequalities, integral evaluations, asymptotic methods, etc.) and "modern analysis" would have an emphasis on soft analysis topics making use of metric and normed spaces. And of course, there are some strong counterexamples to this classification!
  – Dave L. Renfro
  Jul 18 at 15:36
  

  
  
  
  


• 
  
  
  

  
  2
  

  
  
  
  
  
  

  
  A little anecdote: When I was at the university, there department had rules that every other year there was to be a graduate level course in modern analysis and in the other years there had to be a graduate level course in classical analysis. When I took those courses, the professor asked to teach the course on modern analysis believed that everything that had happened after 1850 (or whenever, it's not really important) was modern enough, and the professor asked to teach the course on classical analysis believed everything that had happened before 1950 (again, I ...
  – Henrik
  Jul 18 at 15:41
  

  
  
  
  


• 
  
  
  

  
  2
  

  
  
  
  
  
  

  
  ...don't remember and it's not important) was classical enough. So effectively what we studied in the course on classical analysis had been developed after what we studied in the course on modern analysis.
  – Henrik
  Jul 18 at 15:41
  

  
  
  
  


• 
  
  
  

  
  2
  

  
  
  
  
  
  

  
  @XanderHenderson: Just wait until Dadaism hits math.
  – Asaf Karagila♦
  Jul 18 at 15:56
  

  
  
  
  

 | 
show 2 more comments

up vote
0
down vote

favorite

Mostly I encounter textbooks named Analysis, Mathematical Analysis,... But recently, i encountered a book named A Course In Modern Analysis.

Please explain the difference between Modern Analysis and "Classical" Analysis. Also, please give some information about what Abstract Analysis means.

It's quite weird to me that the number of Modern Analysis textbooks is very small.

analysis

share|cite|improve this question

edited Jul 18 at 23:01

amWhy

189k25219431

asked Jul 18 at 15:24

Le Anh Dung

708318

closed as primarily opinion-based by Mostafa Ayaz, Michael Lugo, José Carlos Santos, Alan Wang, Parcly Taxel Jul 19 at 1:10

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.

• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  How about this one?
  – John Ma
  Jul 18 at 15:31
  

  
  
  
  


• 
  
  
  

  
  2
  

  
  
  
  
  
  

  
  There's usually not much difference, as these are mostly non-precise descriptive terms. Probably "classical analysis" would have an emphasis on calculation methods (inequalities, integral evaluations, asymptotic methods, etc.) and "modern analysis" would have an emphasis on soft analysis topics making use of metric and normed spaces. And of course, there are some strong counterexamples to this classification!
  – Dave L. Renfro
  Jul 18 at 15:36
  

  
  
  
  


• 
  
  
  

  
  2
  

  
  
  
  
  
  

  
  A little anecdote: When I was at the university, there department had rules that every other year there was to be a graduate level course in modern analysis and in the other years there had to be a graduate level course in classical analysis. When I took those courses, the professor asked to teach the course on modern analysis believed that everything that had happened after 1850 (or whenever, it's not really important) was modern enough, and the professor asked to teach the course on classical analysis believed everything that had happened before 1950 (again, I ...
  – Henrik
  Jul 18 at 15:41
  

  
  
  
  


• 
  
  
  

  
  2
  

  
  
  
  
  
  

  
  ...don't remember and it's not important) was classical enough. So effectively what we studied in the course on classical analysis had been developed after what we studied in the course on modern analysis.
  – Henrik
  Jul 18 at 15:41
  

  
  
  
  


• 
  
  
  

  
  2
  

  
  
  
  
  
  

  
  @XanderHenderson: Just wait until Dadaism hits math.
  – Asaf Karagila♦
  Jul 18 at 15:56
  

  
  
  
  

 | 
show 2 more comments

up vote
0
down vote

favorite

up vote
0
down vote

favorite

Mostly I encounter textbooks named Analysis, Mathematical Analysis,... But recently, i encountered a book named A Course In Modern Analysis.

Please explain the difference between Modern Analysis and "Classical" Analysis. Also, please give some information about what Abstract Analysis means.

It's quite weird to me that the number of Modern Analysis textbooks is very small.

analysis

share|cite|improve this question

edited Jul 18 at 23:01

amWhy

189k25219431

asked Jul 18 at 15:24

Le Anh Dung

708318

Mostly I encounter textbooks named Analysis, Mathematical Analysis,... But recently, i encountered a book named A Course In Modern Analysis.

Please explain the difference between Modern Analysis and "Classical" Analysis. Also, please give some information about what Abstract Analysis means.

It's quite weird to me that the number of Modern Analysis textbooks is very small.

analysis

share|cite|improve this question

edited Jul 18 at 23:01

amWhy

189k25219431

asked Jul 18 at 15:24

Le Anh Dung

708318

share|cite|improve this question

share|cite|improve this question

edited Jul 18 at 23:01

amWhy

189k25219431

edited Jul 18 at 23:01

amWhy

189k25219431

edited Jul 18 at 23:01

amWhy

189k25219431

189k25219431

asked Jul 18 at 15:24

Le Anh Dung

708318

asked Jul 18 at 15:24

Le Anh Dung

708318

asked Jul 18 at 15:24

Le Anh Dung

708318

708318

closed as primarily opinion-based by Mostafa Ayaz, Michael Lugo, José Carlos Santos, Alan Wang, Parcly Taxel Jul 19 at 1:10

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 Mostafa Ayaz, Michael Lugo, José Carlos Santos, Alan Wang, Parcly Taxel Jul 19 at 1:10

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.

• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  How about this one?
  – John Ma
  Jul 18 at 15:31
  

  
  
  
  


• 
  
  
  

  
  2
  

  
  
  
  
  
  

  
  There's usually not much difference, as these are mostly non-precise descriptive terms. Probably "classical analysis" would have an emphasis on calculation methods (inequalities, integral evaluations, asymptotic methods, etc.) and "modern analysis" would have an emphasis on soft analysis topics making use of metric and normed spaces. And of course, there are some strong counterexamples to this classification!
  – Dave L. Renfro
  Jul 18 at 15:36
  

  
  
  
  


• 
  
  
  

  
  2
  

  
  
  
  
  
  

  
  A little anecdote: When I was at the university, there department had rules that every other year there was to be a graduate level course in modern analysis and in the other years there had to be a graduate level course in classical analysis. When I took those courses, the professor asked to teach the course on modern analysis believed that everything that had happened after 1850 (or whenever, it's not really important) was modern enough, and the professor asked to teach the course on classical analysis believed everything that had happened before 1950 (again, I ...
  – Henrik
  Jul 18 at 15:41
  

  
  
  
  


• 
  
  
  

  
  2
  

  
  
  
  
  
  

  
  ...don't remember and it's not important) was classical enough. So effectively what we studied in the course on classical analysis had been developed after what we studied in the course on modern analysis.
  – Henrik
  Jul 18 at 15:41
  

  
  
  
  


• 
  
  
  

  
  2
  

  
  
  
  
  
  

  
  @XanderHenderson: Just wait until Dadaism hits math.
  – Asaf Karagila♦
  Jul 18 at 15:56
  

  
  
  
  

 | 
show 2 more comments

• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  How about this one?
  – John Ma
  Jul 18 at 15:31
  

  
  
  
  


• 
  
  
  

  
  2
  

  
  
  
  
  
  

  
  There's usually not much difference, as these are mostly non-precise descriptive terms. Probably "classical analysis" would have an emphasis on calculation methods (inequalities, integral evaluations, asymptotic methods, etc.) and "modern analysis" would have an emphasis on soft analysis topics making use of metric and normed spaces. And of course, there are some strong counterexamples to this classification!
  – Dave L. Renfro
  Jul 18 at 15:36
  

  
  
  
  


• 
  
  
  

  
  2
  

  
  
  
  
  
  

  
  A little anecdote: When I was at the university, there department had rules that every other year there was to be a graduate level course in modern analysis and in the other years there had to be a graduate level course in classical analysis. When I took those courses, the professor asked to teach the course on modern analysis believed that everything that had happened after 1850 (or whenever, it's not really important) was modern enough, and the professor asked to teach the course on classical analysis believed everything that had happened before 1950 (again, I ...
  – Henrik
  Jul 18 at 15:41
  

  
  
  
  


• 
  
  
  

  
  2
  

  
  
  
  
  
  

  
  ...don't remember and it's not important) was classical enough. So effectively what we studied in the course on classical analysis had been developed after what we studied in the course on modern analysis.
  – Henrik
  Jul 18 at 15:41
  

  
  
  
  


• 
  
  
  

  
  2
  

  
  
  
  
  
  

  
  @XanderHenderson: Just wait until Dadaism hits math.
  – Asaf Karagila♦
  Jul 18 at 15:56
  

  
  
  
  

1

1

How about this one?
– John Ma
Jul 18 at 15:31

How about this one?
– John Ma
Jul 18 at 15:31

2

2

There's usually not much difference, as these are mostly non-precise descriptive terms. Probably "classical analysis" would have an emphasis on calculation methods (inequalities, integral evaluations, asymptotic methods, etc.) and "modern analysis" would have an emphasis on soft analysis topics making use of metric and normed spaces. And of course, there are some strong counterexamples to this classification!
– Dave L. Renfro
Jul 18 at 15:36

There's usually not much difference, as these are mostly non-precise descriptive terms. Probably "classical analysis" would have an emphasis on calculation methods (inequalities, integral evaluations, asymptotic methods, etc.) and "modern analysis" would have an emphasis on soft analysis topics making use of metric and normed spaces. And of course, there are some strong counterexamples to this classification!
– Dave L. Renfro
Jul 18 at 15:36

2

2

A little anecdote: When I was at the university, there department had rules that every other year there was to be a graduate level course in modern analysis and in the other years there had to be a graduate level course in classical analysis. When I took those courses, the professor asked to teach the course on modern analysis believed that everything that had happened after 1850 (or whenever, it's not really important) was modern enough, and the professor asked to teach the course on classical analysis believed everything that had happened before 1950 (again, I ...
– Henrik
Jul 18 at 15:41

A little anecdote: When I was at the university, there department had rules that every other year there was to be a graduate level course in modern analysis and in the other years there had to be a graduate level course in classical analysis. When I took those courses, the professor asked to teach the course on modern analysis believed that everything that had happened after 1850 (or whenever, it's not really important) was modern enough, and the professor asked to teach the course on classical analysis believed everything that had happened before 1950 (again, I ...
– Henrik
Jul 18 at 15:41

2

2

...don't remember and it's not important) was classical enough. So effectively what we studied in the course on classical analysis had been developed after what we studied in the course on modern analysis.
– Henrik
Jul 18 at 15:41

...don't remember and it's not important) was classical enough. So effectively what we studied in the course on classical analysis had been developed after what we studied in the course on modern analysis.
– Henrik
Jul 18 at 15:41

2

2

@XanderHenderson: Just wait until Dadaism hits math.
– Asaf Karagila♦
Jul 18 at 15:56

@XanderHenderson: Just wait until Dadaism hits math.
– Asaf Karagila♦
Jul 18 at 15:56

 | 
show 2 more comments

1 Answer
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It depends on the age of the book.

"A Course of Modern Analysis" by E. Whittaker, first published in 1902, covers analytic functions, infinite series, Fourier series, Riemann integration etc. - all topics that today we would just call "analysis".

On the other hand "Introduction to Modern Analysis" by S. Kantorowitz, published in 2003, covers measure theory, functional analysis, Banach algebras, spectral theory etc. i.e. a more abstract and generalised treatment of analysis.

share|cite|improve this answer

answered Jul 18 at 15:49

gandalf61

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add a comment | 

1 Answer
1

active

oldest

votes

1 Answer
1

active

oldest

votes

active

oldest

votes

active

oldest

votes

up vote
5
down vote



accepted

It depends on the age of the book.

"A Course of Modern Analysis" by E. Whittaker, first published in 1902, covers analytic functions, infinite series, Fourier series, Riemann integration etc. - all topics that today we would just call "analysis".

On the other hand "Introduction to Modern Analysis" by S. Kantorowitz, published in 2003, covers measure theory, functional analysis, Banach algebras, spectral theory etc. i.e. a more abstract and generalised treatment of analysis.

share|cite|improve this answer

answered Jul 18 at 15:49

gandalf61

5,689522

add a comment | 

up vote
5
down vote



accepted

It depends on the age of the book.

"A Course of Modern Analysis" by E. Whittaker, first published in 1902, covers analytic functions, infinite series, Fourier series, Riemann integration etc. - all topics that today we would just call "analysis".

On the other hand "Introduction to Modern Analysis" by S. Kantorowitz, published in 2003, covers measure theory, functional analysis, Banach algebras, spectral theory etc. i.e. a more abstract and generalised treatment of analysis.

share|cite|improve this answer

answered Jul 18 at 15:49

gandalf61

5,689522

add a comment | 

up vote
5
down vote



accepted

up vote
5
down vote



accepted

It depends on the age of the book.

"A Course of Modern Analysis" by E. Whittaker, first published in 1902, covers analytic functions, infinite series, Fourier series, Riemann integration etc. - all topics that today we would just call "analysis".

On the other hand "Introduction to Modern Analysis" by S. Kantorowitz, published in 2003, covers measure theory, functional analysis, Banach algebras, spectral theory etc. i.e. a more abstract and generalised treatment of analysis.

share|cite|improve this answer

answered Jul 18 at 15:49

gandalf61

5,689522

It depends on the age of the book.

"A Course of Modern Analysis" by E. Whittaker, first published in 1902, covers analytic functions, infinite series, Fourier series, Riemann integration etc. - all topics that today we would just call "analysis".

On the other hand "Introduction to Modern Analysis" by S. Kantorowitz, published in 2003, covers measure theory, functional analysis, Banach algebras, spectral theory etc. i.e. a more abstract and generalised treatment of analysis.

share|cite|improve this answer

answered Jul 18 at 15:49

gandalf61

5,689522

share|cite|improve this answer

share|cite|improve this answer

answered Jul 18 at 15:49

gandalf61

5,689522

answered Jul 18 at 15:49

gandalf61

5,689522

answered Jul 18 at 15:49

gandalf61

5,689522

5,689522

add a comment | 

add a comment |