Can one excel in higher level math courses without studying real analysis?

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Discussion Overview

The discussion centers on the necessity of real analysis for success in higher-level mathematics courses, particularly in the context of applied mathematics, economics, and finance. Participants explore whether a background in real analysis is essential for understanding advanced topics like partial differential equations (PDEs).

Discussion Character

  • Debate/contested

Main Points Raised

  • One participant questions whether appreciation for mathematics is possible without real analysis, expressing a preference for applied math over theoretical courses.
  • Another participant suggests that the importance of real analysis may depend on the instructor's approach to the upper-level course, noting that their own differential equations course heavily relied on real analysis.
  • A third participant raises the question of whether students with a background in real analysis possess an innate advantage in grasping concepts, even in less theoretical classes.
  • A different participant shares their experience of not having taken a formal analysis course, stating that they feel their understanding of PDEs has not been significantly hindered, as they have learned analysis concepts through applications.

Areas of Agreement / Disagreement

Participants express differing views on the necessity of real analysis for success in advanced mathematics courses. Some believe it is crucial, while others feel it is not a significant barrier to understanding.

Contextual Notes

Participants acknowledge that the relevance of real analysis may vary based on course structure and teaching methods, and there is uncertainty about the extent to which it impacts comprehension of advanced topics.

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Can one truly appreciate mathematics without a course in real analysis? My main interest is in quantitative methods of economics and finance, or applied math. While I find the proofs behind calculus interesting, I can't see myself enjoying a purely theoretical math course. I prefer to explore that interest outside the classroom environment. Will I be at a significant disadvantage vis-à-vis more theoretical math students when I take upper level courses such as Theory of PDE?

(I am an undergraduate economics major)
 
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autre said:
Can one truly appreciate mathematics without a course in real analysis? My main interest is in quantitative methods of economics and finance, or applied math. While I find the proofs behind calculus interesting, I can't see myself enjoying a purely theoretical math course. I prefer to explore that interest outside the classroom environment. Will I be at a significant disadvantage vis-à-vis more theoretical math students when I take upper level courses such as Theory of PDE?

(I am an undergraduate economics major)

It depends on how the instructor approaches the upper-level course. My course on differential equations relied quite heavily on topology and real-analysis methods, so a student that didn't have real analysis would certainly have a major disadvantage.
However, I could see it happening that a course on PDE's does not use real analysis. In any case, it's best to ask the lecturer beforehand whether there will be a problem.
 
Even if the class isn't very theoretical, will students who have RA under their belts have a strong innate advantage in understanding the concepts?
 
I've actually never had a course in analysis per se. Of course, it's possible that I don't know what I'm missing, but I don't feel it's really held back my understanding of, for instance, PDEs. Instead, I think I've absorbed most of the concepts of analysis through their applications.
 

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