I've just finished the first year of Mathematics at University. I've already encountered groups, in a soft mini-course that took around half semester. My idea would be to study applied mathematics, even though I'm not entirely sure which particular field.
Next year I could study group theory, algebra and geometry. I thought these are all pretty abstract modules which wouldn't really benefit my applied-maths "curriculum". However I've been speaking to many students and lecturers and some of their answers where contradictory. Many thought that those courses are fundamental also for an applied mathematician and that it is better to specialize after graduation, maybe after the master even.
Do you think that those pure mathematics modules (and in general pure mathematics topics) are essential to an applied mathematician?
In which way could these topics improve the performance and the career of an applied mathematician?
Wouldn't be better just to specialize and study mathematical physics and statistics?
I'm not sure this is the right place for this question, however I'd like to hear your opinion of this.