Automated Algebra: Efficiency in Calculation

For a couple years in college, I was a math and physics tutor for my university, up until I realized that I didn’t have much patience for people who didn’t want to learn. One of the classes that I tutored for was College Algebra. Business majors have to take an Applied Calculus course for their major, and a prerequisite for Applied Calculus is College Algebra, for obvious reasons.

A difficulty with this setup is that oftentimes, students will decide to major in something like Business in large part because they are trying to avoid taking math courses in college, which is reasonable. For some people, math is an alien language. So when they realize that they will not only have to take math, but they will have to take calculus, which, in the eyes of non-math minded people, is sometimes seen as being similar in complexity to String Theory, these students get a little bit nervous, don’t do well in class, and end up needing tutoring.

This is completely understandable. I’m sure everyone had at least one class that they dreaded taking and just had to white-knuckle it to make it out alive. And that’s what some of the students in College Algebra would do. They would white-knuckle it through College Algebra so that they could then brave the ferocious waters of Applied Calculus. In their minds, the two courses were distinct, separate challenges to overcome, so they were okay with barely surviving College Algebra. But what I often had to explain was that Calculus is impossible without a good understanding of algebra. Algebra is the foundation (okay, I suppose arithmetic is the foundation, but give me this one). Without at least a decent grasp on functions and solving for variables and manipulating equations and all the other algebra stuff, calculus doesn’t make any sense.

But this is not just true of calculus. Algebra is foundational to about every math, physics, and engineering course. For engineers, algebra is second nature. It no longer requires thought. I even had professors in college who would tell us that on tests, we only had to set up the problem, without having to actually solve it all out because they assumed that we knew how to perform algebraic manipulations. It was just a tedious waste of time to actually solve out the problems and only served to demonstrate an ability to do algebra rather than testing us on our actual knowledge of the engineering material.

And I think the same can be said about engineering calculations in the industry. Why waste time solving for a variable by hand? It may not be challenging, but it takes up valuable time and poses the risk of sign errors or other easy-to-make mistakes.

Here’s a simple example. Let’s say I have three resistors in parallel with each other and all of these resistors are in series with one other. If my design specifications require a certain voltage and current in the circuit and three of the four resistors have known values, what does the value of the fourth resistor need to be?

I could solve it by hand.

It’s not difficult by any means, but it is time consuming. How about we try using PTC Mathcad’s symbolic engine to solve the same problem?

This is clearly much more quickly accomplished, and PTC Mathcad worries about the signs and other algebra so you don’t have to. Again, this is a simple example, but I think the point is clear: Don’t waste time and risk errors by actually doing all of the algebra by hand. We all know you know how to do it. Save clutter, save time, save trees, and save errors. Let PTC Mathcad do your algebra for you...

See how you can leverage PTC Mathcad as your Algebra Problem Solver.

Try it out for free with PTC Mathcad Express.