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1. consider the Baruch quantnet one.
2. Numerical Analysis, and then Numerical Method for differential equations.
3. PDE teach the way of solving analytically and the theory behind. Numerical method one will teach how to solve them numerically when analytical solution is not available.
In the practise of financial mathematics, analytical tractability is a nice properties for pricing models. But product can be exotic, and thus the most common way is only rely on analytical tractability on calibration but not pricing, if possible. Not to mention that you can imagine that all those equations that can be solved analytically had be solved by researcher already, and thus understanding how things are solved numerically is also very important. In practise.......it is very likely you are either using it, repairing / maintaining it, or developing it......(it = tools), and this is the reason why people always say programming is important in this field.
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