i can give some perspective as a (now almost 3rd year :/) math student who has also taken 1st year computer science courses (and a couple of electrical engineering classes with a computer focus):
- firstly if you're going absolutely for employability, arguably compsci is still far suprerior to mathematics. there's just way more software engineering jobs at the moment and although they are becoming highly competitive nowadays, having a compsci degree is still very useful. if you're basically going to uni just to get a job then yeah, probably going for compsci over math will be better
- the good thing about a math degree is that it is highly flexible as you learn a lot of problem solving skills but that's also kind of it's downfall. you could technically have developed the skillset to enter jobs in data science, software engineering, etc after graduating however it will require a bit of extra studying/projects outside of the degree (not to say you wouldn't also have to do this to an extent with a compsci degree). but if you're going to take math alongside another degree, i think it is a good pairing for this reason, since you can combine your skillset developed with math to another area. think about this situation: an employer is hiring for a data science job and two people apply; one with a data science undergrad and another with a math undergrad. they can kind of trust that the person with a data science degree will be somewhat familiar with the tools, programming languages etc needed for the job. on the other hand they know that the other person is good at math, which means that they could possibly know those things but they don't really know. so you can see that there will be a tiny amount more convincing needed, although if you have projects/internships i don't think this is a problem at all.
- also if you're studying math you kinda have to at least lock in for a masters/phd for anything more complicated/research level jobs, like every other science discipline. again it really depends on what your goals are, if you just want to get a job straight out of undergrad there are those options like data science. but if you want to go into more research level roles e.g. some quant roles, algorithmic engineering etc, most of these companies vastly prefer having at least masters level qualifications. simply put an undergraduate in math barely skims the surface of what's possibly as i am finding anew basically every day... graduating with an undergrad basically says "i know the basics and nothing more"; honours says "i can do a bit of research" and masters/phd means you can engage with research at a high level and are really familiar with whatever your favourite subfield is. again this is really up to what your goals are, and you can always find a job without studying further, but just realise you might be locking in at least a few years of postgrad study, if that's what you're interested in doing
okay so basically the rundown is if you just wanna dip with a degree and get a job, compsci is probably better, although if you're just thinking of taking math as a side degree for fun then it can be a really good addition.
now onto the actual differences between the content in uni. keep in mind this is just my experience, combined with a few people i know who are later years in compsci and their experiences with the subject.
- the assessments can be really hit or miss in compsci; some subjects just have you programming random stuff to pass an automarker and what you make realistically is just made for the assessment and doesn't have any real world application, which to me is completly useless and makes the subject quite boring and unmotivated.
- on the other hand some subjects are really fun and have really interesting assessments; e.g. build a cpu, build an encryption and compression system, reverse engineer a codebase with no comments to determine what it does, etc. those are the times when i really enjoyed the content, and it was pretty cool to build stuff that actually worked and i felt like i walked away from those subjects learning something new that i could use in the future.
- in terms of the actual content, i think it is generally quite interesting and at the least, i always felt like my toolbox of programming tricks was growing. i basically learnt up to basic data structures and algorithms (mergesort, stacks and queues and trees, etc), and i do genuinely feel like i became a better programmer as a result of those classes, so at the very least i did take that away. the main reason i didn't want to pursue compsci further was basically because of the above point, i kinda got frustrated with the way the classes were run, but if you really love programming a lot i think you won't find that an issue.
okay now i can talk about math... excuse my yap
- unis basically run 3 different streams of math: stats, pure math, and applied math. stats is kinda self explanatory but honestly ends up being more probability theory than statistics, mainly you work on the theoretical side and just construct hypothesis tests or investigate random processes, etc than doing actual applied testing (which i'm thankful for because it's much more interesting that way. applied math is basically codeword for computations, some of the subjects are just crunching out integrals which is meh. some of them are quite interesting though, for example there are classes on dynamics related stuff, fluid mechanics, computational methods (analysing rate of convergence of different approximations) etc. pure math is probably as you expected, proof based subjects. these are by far the most theoretical (although stats has a suprising amount of theory, it skimps on the rigour), you work with abstract objects and proof statements about classes of things, its quite fun
- the content difficulty will certainly ramp up as the degree continues. i would say applied math is the "easiest" subfield in general however this is not strictly true, the derivations and notation does get kinda crazy and the computations they expect you to do get increasingly longer and annoying, i tend to keep my distance from the applied classes for that reason so i can't say too much. with pure math i'd say the difficulty mostly comes from your proofs really needing to be watertight (you will basically get 0 if your proofs are bad), as well as just the amount of tricks and theorems you need to remember. do i think it becomes impossible? no but there are definetly "trial by fire" subjects where you will need to study a lot to get through, but after you do a couple of these and get used to proof writing, things become a lot easier and you get familiar with all the concepts interweaving between all the classes etc.
- the "trial by fire" subjects are usually group theory/abstract algebra and real analysis. these kinda have a reputation but honestly once you get through it, you do genuinely become so much better at the subject, and usually out of those two subjects you decide which area of math u prefer; analysis/continuous (calculus but rigorous) type stuff or algebra (study of structure)/discrete type stuff.
- i will however say that the workload remains relatively low in terms of assessments, basically quizzes, maybe 1-2 short assignments and a final and that's your typical math class; thus if you keep ahead and know your content well, you can show up on the day, do the quiz/exam and that's about it you passed the subject. imo if you study ahead a little bit, you already get familiar enough to where you can pass through the semester with just weekly keeping up with the lectures and problem sets, it becomes a bit harder if you get stuck along the way though and then you're playing catchup which is no fun
- i would say you will find the content fun if you really enjoy proofs and conceptual things, however if you don't and you just enjoy math for crunching out numbers or similar, you will quickly become demotivated once you realise that uni math very quickly deviates from that after first year. so if you're enjoying say ext2 proof stuff, you'll likely have a good time if you are willing to continue into the depths of proofs and definitions and theorems for the next few years. if you want to have a good introduction to maybe some of the things you study in uni, imo you could (fairly easily with ext 2 skillset if you're willing to) pick up the book by pinter on abstract algebra and learn the basics; you will quickly see the axiomatic and definition/theorem/lemma style that is common in modern mathematics and you can get to see some of the ideas you will study at uni.
ok uhh i got distracted anyway thats all i ahve to say
) but also becos it has a lot of conceptual math im assuming?? so naturally I would pursue higher level of education like a masters or a phd if I lock in for the hsc in 6 days (kill me) anyway according to what you've said im basically getting that doing comp sci would be the better option to pair to pursue quant trading ?