I am an undergraduate student at a university in Sweden who am studying my second semester of a three year undergraduate degree. I have always loved mathematics and had a few years between high school and university to realize that. I am therefore certain that I want to prep myself for advanced studies and try to go for a PhD after a master's degree. What I am wondering is - should I take the recommended programming courses and statistical courses or instead read advanced material such as galois theory or partial differential equations (both graduate level books)? I understand that both probability/statistics and programming can be very useful for mathematicians, but I am highly sceptical of how much of that information I will retain over the coming years of not having any follow-up courses in them and also if I simply cannot just learn them when I find out that I need them.
So I am reaching out to you, Stack Exchange community. Should I skip the probability/statistics and programming to do at a later date when/if I need it? Or should I bite the bullet and just take the courses?
We are talking about 5 courses that are: Numerical Analysis, probability 1, stochastic processes (or statistical analysis), programming 1 and programming 2. Together they make 5/4th of a semester. Comparatively, I could read 5 equal courses on a master's/grad introductory level (springer graduate texts).
Thank you in advance!