I'm a first year math student.
I'm doing well when it comes to pure math. I understand it, can do proofs, get good grades.
However, I'm shit when it comes to applied math - even the most basic. I often run into equations and exercises which require novel (for me) approaches, and I just can't solve them. I then have to ask other people how to solve them, and I could never think of the approaches they used on my own, even though I understand them.
How do I get better at applied math? Do I just do a shitton of exercises, until I get familiar with all the approaches and methods?
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"Applied math" is a weighted term, couldn't you be more specific?
Raw practice won't necessarily make you good in my opinion. You should never do more than one of the same type of problem unless you really struggled with it.
r u ok?
I'm also a first year math student, and I used to have this same problem. What I learned is that there are only some many different kinds of problems taught and tested over in the first few years of math. With enough practice, you will see all the problems they could ever test you over, and you'll be ready for them on the exam. Keep in mind, I haven't seen the higher level math yet (I'm in calc II) so this might not work up there. But for now, practice, practice, practice.
Being good at applied math is more about applying creative problem solving / "cleverness" and/or using and abusing raw innate talent than following the rigorous rules and established approaches.
Think about how Richard Feynman's mind worked. In his bio he talks about high-school algebra how he found it strange that his cousin was trying to follow the rules/steps his teacher taught him to solve simple algebraic equations to solve "x", when he already knew what the answer should be to make the LHS equal to the RHS by just looking at the equation without doing all the manipulations to isolate x.
A similar mindset should be applied in all applied math problems. Don't focus on mathematical methods and rigour you were taught. Focus on the physical problem you're trying to solve, math is just a tool to help you find the solution.
Solving a variable in an "unsolvable" non-linear algebraic equation? What's the range of the answer you expect that makes physical sense? Plug that in and iterate.
Struggling to converge the parameters optimization of a large process modeled with several PDEs? Calculate the expected steady state values. Why not use the optimization of a lumped parameter ODE system first?
>tl;dr: Don't think like a mathematician. Always keep in mind what physical process the math actually describes.
I didn't...you do realize that in your professional career you'll be thinking as roles from other disciplines far more often than as a mathematician right? That this is required from any normal functioning human being?