Is an MSc in quantitative finance realistic with a BEng Chemical Engineering background? Especially regarding real analysis gap

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My main consideration is it seems quant finance masters require you to have done real analysis. This isn't something that I have not done in any formal academic capacity.
I am happy soughting experience in real analysis indepdently, but my consideration then is how I can translate this independent learning into something that has substance on an application when compared to students who have specifically studied and been assessed on it at university?

However, programs such as MSc Quantitative Finance at ETH Zurich do say they are open to engineers - and I didn't realise real analysis was even studied in any engineering discipline. I wonder though whether this is just my ignorance and some engineering disciplines do indeed include real analysis, and chemical engineering just wouldn't be included in eligible engineering degrees? Or, whether an academic background in real analysis has less weighting than I currently consider it has?

This all leaves me quite confused as to whether I am even eligible to for a quantitative finance masters with this gap in real analysis? Confused especially since other engineers must surely be in the same boat? Any recommendations on how I can possibly bridge this gab in a credible way independently.

TL;DR: Ultimately, my question is - is real analysis the bottleneck to quantitative finance programs that I think it is? A
 
I don't know anything about the program at ETH, but I seriously doubt they are actually doing real analysis. You see this in most of the US MFE programs - they aren't doing math math. A lot of their curriculum is at best applied math, at worst finance/business math. I'm sure your engineering background includes a formal education on single and multivariate calculus, which would probably give you the basics to understand parts of analysis if you ran into it in grad school (mean value, inverse functions, squeeze theorem, whatever, ...)

I came from an engineering background and probably studied at one of the most mathy programs discussed here and we didn't touch too too much into analysis. If you do dip into this area, you can definitely tell where our engineering degrees don't hold as well. But if you can figure out engineering, you can probably figure out math. It is just about effort.
 
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