The first thing to note is that MATH1041 and MATH1141 are substantially different from one another.
The actual 'get maths out of the way' is MATH1031. This course actually shares some overlap with the regular MATH1131/MATH1231 progression. The content is taught at a much lower level in contrast to MATH1131/MATH1231, and also with less depth. It's not required for many degrees either.
MATH1041 is a course taught at roughly the same difficulty as MATH1031. But as the course name suggests, the focus is on
statistics. It only really assumes mathematical knowledge up to HSC Maths Standard 2, since you don't even have to do calculus in this course (at most they show the integral symbol but never use it). (Which is pretty much all the maths you need to know to learn statistics, provided that you're not interested in the theory behind it all.)
In my opinion, more degrees recommend MATH1041 over MATH1031 simply because they anticipate students to find the basic stats knowledge more useful. However, the statistics content is completely separate from the other maths-focused courses. In fact, MATH1041 is more equivalent to MATH2801/MATH2901, but with basically all the theory taken out. (Will note that some degrees do require students to do both anyway.)
On the other hand, MATH1131 is the more natural continuation of maths, and MATH1141 being its higher counterpart. The former assumes knowledge equivalent to HSC Maths Ext 1. The latter is only recommended if you've succeeded well in Ext 1 + Ext 2, which clearly you have. (Some infographics
here and
here, but these won't matter to you.)
During COVID, the difference between these two courses kinda got blurred. I don't know if there was any significant difference between the two, since they had to do online exams. Prior to COVID though, MATH1131 and MATH1141 were completely identical, up until the final exam. Half of the final exam is identical between MATH1131 and MATH1141, but as for the other half, MATH1141 do receive some notably more difficult problems. By taking MATH1141, you're basically saying "sure, come at me" to these problems. I think in the past, you were rewarded with some scaling for taking it over MATH1131.
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With that out of the way, what should you be picking? For starters, I can confirm according to
this UNSW handbook entry that you can take either-or. You also have room for electives as per
this UNSW handbook entry should you want both. Specifically, 1 science elective or 1 free elective can be used if you want to do both.
Whilst statistics is often highly recommended for its usefulness, a university degree should also have elements of fun in it. (Otherwise you're just gonna hate your time.) So you might want to first ask this question: will you miss maths? If yes, then at the very least MATH1131 would be a good idea. And if you do enjoy the stimulation of maths, then MATH1141 is likely the better option.
Judging by that you feel MATH1041 might 'waste' your Ext 2 knowledge, you probably
are headed down that road. But just ask yourself the question again if you're sure about it. If you really don't have the passion for maths anymore, then MATH1141 could backfire. But if you do, then MATH1141 could be one of the best decisions you make.
I can't really give my own opinion without being biased, since I literally study advanced maths at uni. And consequently would've just said do both regardless of the circumstances. Having said that though, doing both does have its perks. It feeds into any passion for math you have, whilst sacrificing just 1 mere elective to get the usefulness out of the statistics side. The only thing you need to accept is that MATH1041 is literally just a basic statistics course, without any intense maths at all.