Do I need ODE and PDE for differential topology?

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SUMMARY

To study differential topology, a strong foundation in ordinary differential equations (ODE) and partial differential equations (PDE) is not a prerequisite. The basic texts, such as "Differential Topology" by Hirsch and "Differential Topology" by Guillemin & Pollack, do not require advanced knowledge of differential equations. A standard introductory differential equations course, typically taken by engineering students, suffices for understanding the fundamentals of differential topology.

PREREQUISITES
  • Basic understanding of differential equations (ODE and PDE)
  • Familiarity with point-set topology
  • Knowledge of mathematical proofs
  • Experience with undergraduate-level mathematics
NEXT STEPS
  • Study "Differential Topology" by Morris Hirsch
  • Explore "Differential Topology" by Guillemin & Pollack
  • Learn about proof techniques in mathematics
  • Investigate applications of differential topology in cosmology
USEFUL FOR

Mathematics students, particularly those interested in pursuing graduate studies in differential topology or applying mathematical concepts to cosmology.

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I am a senior in mathematics studying graduate point-set topoology atm. I am thinking I want to study differential topology in graduate school and maybe apply it to problems in cosmology. Do I need to take more ODE and PDE? I took intro to diff eq- the one that all engineering undergrads take. Is that enough? I would assume not but I may be surprised. Thanks.
 
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You don't need any special knowledge about diff equ. to study the basics of differential topology as in, say, the book by Hirsch or Guillemin & Pollack.
 
And even if you did, it would be a DE course for mathematics students (one that does proofs) and not a DE course for engineers (one that does "what is it useful for?").
 

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