Can Prerequisites Lead to Unexpected Passions?

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    Passion Prerequisites
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SUMMARY

This discussion highlights the phenomenon where studying prerequisites can lead to unexpected passions in related subjects. The author shares personal experiences, specifically transitioning from an interest in general relativity to a deep fascination with differential geometry and differential topology after recognizing the need for foundational knowledge. Similarly, the author notes a shift from topology to set theory, emphasizing the interconnectedness of mathematical disciplines. This illustrates the importance of prerequisites in shaping academic interests and pathways.

PREREQUISITES
  • Differential Geometry
  • Differential Topology
  • Topology
  • Set Theory
NEXT STEPS
  • Explore advanced concepts in Differential Geometry
  • Study applications of Differential Topology in modern mathematics
  • Investigate the foundational principles of Set Theory
  • Learn about the relationship between Topology and other mathematical fields
USEFUL FOR

Students, educators, and self-learners in mathematics who are exploring the impact of foundational knowledge on their academic interests and career paths.

andytoh
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Have you ever studied from a subject, realized that you were lacking in some prerequisites, then started reading up on the prerequisites, and then realized that you have become more interested in the prerequisite subject(s) than the original subject?

I have. Years ago, I was very interested in general relativity, but realized I needed to learn more differential geometry to study it. So I started reading differential geometry, and then fell in love with differential geometry. Now my main interests are differential geometry and differential topology, and I don't think about general relativity as much as I used to. Also, a long time ago I was studying topology, but I realized I needed to study more set theory. Then I became very interested in set theory (though I still like topology very much now).
 
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Mathematics news on Phys.org
It's inevitable in any self-studier's life.
 
That's like me trying to look up a word in a dictionary- often to ever get to it because I start looking at definitions of other words along the way!
 

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