Courses Mathematics Bachelor's Degree: Choices ahead

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The discussion centers on a second-year mathematics bachelor's student contemplating course selections that align with interests in physics. The student is currently enrolled in abstract algebra, measure and integration theory, and probability, expressing uncertainty about future applications of mathematics. The upcoming decision involves choosing between complex analysis and partial differential equations (PDEs), with concerns about the abstract nature of PDEs versus the perceived enjoyment of complex analysis. Additionally, the student is considering whether to pursue geometry on manifolds or opt for applied mathematics courses like numerical analysis or discrete mathematics. The conversation highlights the importance of aligning course choices with specific branches of physics, suggesting that a clearer focus on a particular area of physics could aid in making informed decisions about mathematics coursework.
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I am studying mathematics as bachelor in my second year. At the moment I am taking abstract algebra, analysis (measure and integration theory) and probability course. I don't know exactly what I want to do with maths but the applications in physics always have fascinated me. The next term I have to choose between complex analysis and PDEs. I don't really know which alternative is more appropriate. PDEs look important in physics but I am afraid that it would be just abstract manipulations without much imagination. Complex analysis looks fun but I am not sure if it is relevant for me.
Furthermore I want to ask if geometry on manifolds is a good choice or I should go with something from applied maths like numerical analysis or discrete mathematics.
 
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All of those choices are relevant to different branches of physics. If you specified aparticular branch of physics, it may be easier to make a choice. Physics is not just physics but has many subfields, just like math does.
 

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