I'm getting started learning engineering math. I'm really interested in physics especially quantum mechanics, and I'm coming from a strong CS background.
One question is haunting me.
Why do I need to learn to do complex math operations on paper when most can be done automatically in software like Maple. For instance, as long as I learn the concept and application for how aspects of linear algebra and differential equations work, won't I be able to enter the appropriate info into such a software program and not have to manually do the calculations?
Is the point of math and math classes to learn the big-picture concepts of how to apply mathematical tools or is the point to learn the details to the ground level?
Just to clarify, I'm not trying to offend any mathematicians or to belittle the importance of math. From CS I recognize that knowing the deep details of an algorithm can be useful, but that is equally important to be able to work abstractly. Just trying to get some perspective on how to approach the next few years of study.
Best Answer
Both. One is difficult without the other. How are you going to solve equations that Maple can't solve? How are you going to solve it, exactly or numerically? What's the best way to solve something numerically? How can you simplify the problem to get an approximate answer? How are you going to interpret Maple's output, and any issues you have with its solution? How can you simplify the answer it gives you? What if you are only interested in the problem for a particular set of values/parameters/in a particular range? What happens if a parameter is small? How many solutions are there? Does a solution even exist?
Using a CAS without knowing the background maths behind the problems you're trying to solve is like punching the buttons on a calculator without knowing what numbers are, what the operations mean or what the order of operations might be.