Mathematics & Astrophysics: Importance & Overview

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how much mathematics is important in astrophysics? (which topics mainly?) is astrophysics is a kind of theoretical or observation physics?
 
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Mathematics are an integral part of all Astrophysics. Also astrophysics is a mixture of both theoretical and observational physics. Sometimes a theory is formulated and then observations are made to determine if the theory is solid or not. Sometimes astrophysicists will analyze observational data and draw conclusions from what is actually being observed, so it is a mixture of both. One needs adequate mathematical experience to interpret any data that is gathered as well as forming a theory. Long story short, math is our tool to "visualize" what is happening, what has happened, and what will happen. This is also the case in cosmology or anything related to physical sciences.

Joe