Mathematician vs applied mathematician

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SUMMARY

The discussion clarifies the distinctions between pure mathematicians and applied mathematicians, emphasizing that pure mathematicians focus on theoretical aspects, theorems, and proofs, while applied mathematicians concentrate on practical applications, computations, and algorithms. For graduate school, pursuing pure mathematics is advantageous for those interested in mathematics, whereas applied mathematics is preferable for those aiming for physics. The conversation highlights that applied mathematicians can secure lucrative positions in industries such as finance, while pure mathematicians typically earn lower salaries. Key areas mentioned include real analysis for pure math and numerical analysis for applied math.

PREREQUISITES
  • Understanding of theoretical mathematics concepts, particularly theorems and proofs.
  • Familiarity with applied mathematics, including computations and algorithms.
  • Knowledge of real analysis as a foundational topic in pure mathematics.
  • Awareness of numerical analysis as a key area in applied mathematics.
NEXT STEPS
  • Research graduate programs in pure mathematics and their admission requirements.
  • Explore the applications of numerical analysis in various industries.
  • Investigate career opportunities for applied mathematicians in finance and technology sectors.
  • Study the differences in coursework between pure and applied mathematics programs.
USEFUL FOR

Students considering graduate studies in mathematics or physics, educators in mathematics, and professionals evaluating career paths in pure or applied mathematics.

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whats the main differences and which one one would help get into grad school? I am looking into pure math and quite possibly physics as well.
 
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(Pure) Mathematician- Stresses more on the theoretical and abstract aspects of mathematics. Deals more with theorems and their proofs than computations. (Usually, when you say "mathematician", you usually mean this type)

Applied Mathematician- Stresses more on the applications of mathematics to some other fields. Deals more with computations and algorithms than theorems and proofs.

Note that these are very simplified distinctions between those two professions. As for grad school, I think pure math would be good if you're thinking of going to grad school in math, and applied math would be good if you're thinking of going to physics (but again, that's probably not the case all the time).
 
PieceOfPi outlined the main differences. If you want to do physics in grad school, applied maths would be a better route to go. You must have pure maths if you want to do pure maths in grad school. Applied mathematicians-- if they study the right fields-- can get high paying jobs in industry, banks etc. As far as I know, pure mathematicians don't get paid that much.

Pure maths is like real analysis. Applied maths is like numerical analysis (assuming you know those fields).
 

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