The discussion centers around the relationship between graduate-level mathematics and the understanding of undergraduate mathematics, specifically whether studying advanced topics like real analysis enhances comprehension of foundational subjects such as calculus and algebra.
Participants express differing views on the extent to which graduate-level math enhances understanding of undergraduate math. There is no consensus on whether advanced study guarantees a better grasp of foundational topics, and the discussion remains unresolved.
Participants highlight the importance of prerequisite knowledge and the potential for forgetting earlier material if not revisited. The discussion reflects varying experiences and perspectives on the relationship between different levels of mathematical study.
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.DrSteve said: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 said: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?symbolipoint said: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.
Orson said: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.Orson said: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?
bacte2013 said:In terms of algebra, do you mean studying books like Lang and Hungerford will be beneficial than the introductory books like Herstein and Artin?
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.Orson said: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?