Mathematica Improving Math Analysis for Research Project: Advice Needed

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Mathematical analysis is crucial for success in mathematical physics, particularly in understanding concepts like Hilbert space, which is essential for quantum mechanics. A solid foundation in various areas of analysis—including functional analysis, real and complex analysis, abstract algebra, and operator theory—is important for grasping advanced physics topics. While Hilbert space may not be extensively covered in many undergraduate programs, a thorough review of mathematical analysis is recommended to prepare for graduate-level studies. The interconnectedness of analysis, algebra, and topology underscores their significance in the broader context of mathematics and physics. Engaging in serious study over the summer to strengthen analysis skills is a proactive approach to addressing any gaps in understanding.
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I just finish my final year of undergrad in maths and physics and decided to do mathematical physics next year as my research project. My physics (theory) grad are good mostly A+'s.

However, I have one concern, I underestimated Mathematical analysis... and deservedly got a C+ for it X_X...

I would like to know how you guys rate the importance of mathematical analysis? I know Hilbert space is very important in QM and am planning to take it next year. I am thinking doing a serious study on analysis during my summer break to get up to cratch.

What do you guys think?
 
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Definately, there are so many areas of analysis that are very important to learn some of the physics properly, you've already mentioned Functional analysis in respects to QM but you should also have a solid grasp of Real, COmplex, Abstract Algebras and OPerator theory.
 
Analysis and Algebra should ranks top in mathematics. At least whatever I am studying involved Analysis, Algebra and topology.

This is the tree of analysis in maths
topology is the base of Analysis.
Analysis is base of functional Analysis, Differential Geometry, Differential Equations, Operator Theory, Tensor, probability, statistic, etc

however, I don't think Hilbert Space is covered in many undergraduate programme. Nonetheless, you should review Analysis very carefully if you want to study Mathematical Physics.
 

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