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

[autre]

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)

 

[micromass]

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.

 

[autre]

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?

 

[pmsrw3]

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.

 

[CellCoree]

I understand the importance of building a strong foundation in mathematics, especially in higher level courses. While it is possible to excel in these courses without studying real analysis, it may be more challenging and may limit your understanding and application of mathematical concepts. Real analysis provides a rigorous and in-depth understanding of calculus and other mathematical concepts, which can be beneficial for students pursuing careers in quantitative methods of economics and finance.

However, it is also important to note that there are many different branches of mathematics, and real analysis may not be directly applicable to all areas of study. It is possible to appreciate and excel in mathematics without taking a course in real analysis, as long as you have a strong understanding of other mathematical concepts relevant to your field of interest.

That being said, taking a course in real analysis can provide a deeper understanding and appreciation for mathematics as a whole. It can also provide valuable problem-solving skills and analytical thinking that can be applied to other areas of study.

In terms of being at a disadvantage compared to more theoretical math students in upper level courses such as Theory of PDE, it ultimately depends on your individual strengths and weaknesses in mathematics and your ability to apply mathematical concepts to real-world problems. However, taking a course in real analysis may give you a stronger foundation and a better understanding of the underlying principles in these higher level courses.

In summary, while it is possible to excel in higher level math courses without studying real analysis, it is recommended to have a strong understanding of this subject in order to fully appreciate and apply mathematical concepts in your field of interest. It is also important to continue exploring your interests in mathematics outside of the classroom environment.