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A little about myself:

I did one semester of university maths, consisting half of linear algebra and half of single variable calculus a few years ago, the rest of my studies were across business/finance/economics and I have since taken gap years to work and play so I haven’t finished my undergrad yet still.

During my initial exposure to university level maths, I found limit problems and convergence/divergence topics most interesting, whilst numerical approximations, and hand computing matrices were rather boring albeit exploring techniques in integration was also fun. Linear algebra seemed more fun during analytical stages rather than computational stages. And I’m pretty weak at hand drawing 3D conics for multivariable calculus (contour maps or anything requiring 3D visualization are slow for me to catch onto, not sure if this also means I’ll be weak at visualizing linear transformations.)

I also didn’t do much about sigma notation on sequence/series based maths in high school so in stats it was at first a shock to me, but this increased my interest to self study for them and now I’m comfortable with them, I also liked how maclaurin and taylor series were explained.

I’ve read subject reviews from student forums about how the alumnis found their maths subjects, and the majority of the opinions were that vector(multivariable) calculus was an exceedingly “applied” unit rather than pure, and was therefore boring for them. I don’t know anything about how I might feel towards that opinion nor about whether I’m going to be able to have a stronger focus in Applied or Pure maths.

Given my current situation, and that I plan to major in stochastic calculus for both undergrad and possibly Msc in maths later on down the track with measure theory in mind as well, what should be my sequence of taking the following subjects in order to maximize understanding/ease of learning curve, and what might be some good co-requisites to take together? And which subjects can more easily be self-learned so I don’t have to enroll in them? And from non-stats related math branches, what subjects am I missing that are of relevance?

I can fit a total of 10 maths subjects from the following list into my course before I graduate:

Multivariable(vector) calculus 2nd year

Real analysis 2nd year

Probability 2nd year

Mathematical statistics 2nd year

DE with modelling 2nd year

Linear algebra with applications 2nd year

PDE 3rd year

Intro to computational mathematics (numerical analysis) 3rd year

Advanced ODEs 3rd year

Complex analysis 3rd year

Random processes in the sciences and engineering 3rd year

Time series and random processes in linear systems 3rd year

Financial mathematics 3rd year

Are there anything redundant from these 3 units that need not be repeated:

Financial mathematics

Random processes in the sciences and engineering

Time series and random processes in linear systems

And for the following subjects, which ones are relevant to Measure theory and/or have a probabilistic emphasis, when should I take them after the initial list of subjects:

Algebra and number theory

Algebra and number theory II

Differential Geometry

Functional analysis

Applied mathematical modelling

Fluid dynamics

Anything I may have missed from the above list of subjects?

As for coding, I plan to learn in the next 10 years or so, in this following order of priority:

Matlab, C, R, C++, Python. (Should I change the priority in any ways?)

Thanks in advance!