Does Graduate Level Math Enhance Understanding of Undergrad Math?

[Orson]

Does learning graduate level math make one better understand undergrad math?

For example, after taking real analysis, does one better understand calculus?

 

[DrSteve]

Certainly, but conversely, you have to understand calculus to understand real analysis. In other words, graduate courses are not a shortcut to undergraduate learning.

 

[symbolipoint]

Certainly, but conversely, you have to understand calculus to understand real analysis. In other words, graduate courses are not a shortcut to undergraduate learning.

He might have not meant that way, anyway. Studying prerequisite course, and then study a following course which springs from that prerequisite, can often help to understand the prerequisite course better. That may be how he meant his question.

 

[symbolipoint]

A little more specific - although not at all "graduate level", studying Intermediate Algebra, having as prerequisite Introductory Algebra, will help to understand Introductory Algebra much better. As DrSteve described, just studying Intermediate without first studying Introductory, will not be of much help in either of those "Algebra" levels.

 

[bacte2013]

A little more specific - although not at all "graduate level", studying Intermediate Algebra, having as prerequisite Introductory Algebra, will help to understand Introductory Algebra much better. As DrSteve described, just studying Intermediate without first studying Introductory, will not be of much help in either of those "Algebra" levels.

In terms of algebra, do you mean studying books like Lang and Hungerford will be beneficial than the introductory books like Herstein and Artin?

 

[Orson]

A little more specific - although not at all "graduate level", studying Intermediate Algebra, having as prerequisite Introductory Algebra, will help to understand Introductory Algebra much better. As DrSteve described, just studying Intermediate without first studying Introductory, will not be of much help in either of those "Algebra" levels.

Sounds reasonable. But what I am wondering is.. say you take calculus 1 and 2 and get a B in each, a decent grade, but not fully mastering the material the way you would like. Then you take Advanced Calculus/ real analysis as a junior or senior in undergrad and then again in graduate school. if after getting say an A or B in those subjects, would you have extreme command over calculus 1 and 2?

 

[micromass]

Sounds reasonable. But what I am wondering is.. say you take calculus 1 and 2 and get a B in each, a decent grade, but not fully mastering the material the way you would like. Then you take Advanced Calculus/ real analysis as a junior or senior in undergrad and then again in graduate school. if after getting say an A or B in those subjects, would you have extreme command over calculus 1 and 2?

Not really, if anything, you'll forget a lot about it.

 

[Hercuflea]

Sounds reasonable. But what I am wondering is.. say you take calculus 1 and 2 and get a B in each, a decent grade, but not fully mastering the material the way you would like. Then you take Advanced Calculus/ real analysis as a junior or senior in undergrad and then again in graduate school. if after getting say an A or B in those subjects, would you have extreme command over calculus 1 and 2?

Probably not unless you go back and re-study it. You need an extreme command of those subjects before you can get an A or B in graduate real analysis.

 

[symbolipoint]

In terms of algebra, do you mean studying books like Lang and Hungerford will be beneficial than the introductory books like Herstein and Artin?

Sounds reasonable. But what I am wondering is.. say you take calculus 1 and 2 and get a B in each, a decent grade, but not fully mastering the material the way you would like. Then you take Advanced Calculus/ real analysis as a junior or senior in undergrad and then again in graduate school. if after getting say an A or B in those subjects, would you have extreme command over calculus 1 and 2?

The Calcululs situation, possibly; but I meant for the Algebra situation example, that level which you learn either in high school, or the remedial but same equivalent stuff you learn in a community college.

 

[The Bill]

The courses which helped me understand Calculus I and II material the most were Physics courses. Mostly because in those courses, I was using the same methods as in Calc I and II, applied in slightly different ways, and taken a bit further mechanically, but not conceptually.