Mathematics Bachelor's Degree: Choices ahead

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SUMMARY

The discussion centers on the academic choices faced by a second-year mathematics bachelor's student, currently enrolled in abstract algebra, measure and integration theory, and probability courses. The student is contemplating whether to pursue complex analysis or partial differential equations (PDEs) next term, with a particular interest in their applications in physics. Additionally, the student is considering geometry on manifolds versus applied mathematics topics like numerical analysis or discrete mathematics, emphasizing the importance of aligning mathematical studies with specific branches of physics for better decision-making.

PREREQUISITES
  • Understanding of abstract algebra concepts
  • Familiarity with measure and integration theory
  • Basic knowledge of probability theory
  • Awareness of the applications of mathematics in physics
NEXT STEPS
  • Research the applications of complex analysis in physics
  • Study the significance of partial differential equations in modeling physical phenomena
  • Explore geometry on manifolds and its relevance to theoretical physics
  • Investigate numerical analysis techniques for solving real-world problems
USEFUL FOR

Mathematics students, physics enthusiasts, and educators seeking guidance on course selection and the relevance of mathematical topics to various branches of physics.

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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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