Math, Math and more Math(The Basics?)

[Bumpeh]

I've been doing some thinking about the different levels of mathematics I've gone through in high school.

For a little context, I'm a current undergraduate student highly debating majoring in astrophysics. I just finished Calculus I with an A- and I'd consider myself very proficient in it. I enjoyed working with derivatives and integrals and a few simple differential equations. I know I really need to brush up on my trigonometry, perhaps even my geometry, but when it comes to Calculus I'm fairly proficient, which is good since it's a fundamental math for physics.

In elementary school, the teachers drilled in our heads that we needed to know our multiplication tables and long division cause we won't be able to use calculators in real life. Calculators were shunned in elementary school. When I got to high school, the attitude was a little different, but still intent on saying calculators were the devil. Now I'm in college, and there's an extremely different attitude. Sure, in calculus you can't use a graphing calculator because a graphing calculator would defeat the purpose of the learning what Isaac Newton created for finding the slope of a tangent and secant line and the area under a curve, but you can still use your scientific calculator all you want.

I've been using Khan Academy to brush up on some basic math skills like algebra and such, and I'm curious to those of you in higher physics classes or those of you that have graduated and are working in physics, perhaps as an engineer or a physicist, theoretical or otherwise-

How much do you really use the simple mathematics in grade school, like the multiplication table and long division, when you simply have a calculator that can do it for you? I've looked over some physics equations and done some work and it just seems ridiculous to try to work that out on paper because 1, you run the risk of making a lot of mistakes with that much work and 2, it's wasting valuable time when you can just punch the numbers into your calculator.

I never really learned the multiplication tables and long division never stuck with me, are these things I should go back and focus on? Even though I'm already a veritable wiz at so far of Calculus? Thanks!

 

[axmls]

In my upper level engineering classes, it's even becoming less oriented towards calculators. Some professors let us use our laptops in exams so we can check our work with MATLAB.

You should have some level of proficiency with mental calculation. You should know all of your basic products (at least from 1*1 to 12*12) by heart. Long division isn't too necessary, but even then, I actually end up doing long division with polynomials sometimes. But no, I don't think there's ever a reason to write out 6827 x 3829 and perform the calculation by hand. Too much can go wrong there. There's just no good reason you shouldn't at least know basic products by heart to speed up your work, though.