I flew down to San Diego last night to participate in the Statewide Information Communication Technologies (ICT) Industry Advisory Committee. It helped me to remember how important ICT education is. We had a great group of folks at the meeting, with a lot of passion and experience in supporting the students of California to becoming our next generation of “computer nerds”.

But it also brought back to me, about how our education system isn’t keeping up and changing for the needs of our next generation. Technology is our future, and of any industry sector (other than potentially energy), it is the use or abuse of technology will make the biggest difference to the future of human kind. And educational content standards, and the related curriculum, can either be what will give our students the knowledge that will be needed when they graduate; or force irrelevant content on them, leading to more disillusion with our education system; and at the same time lead to more unemployment.

One of the first things we can do is to truly update our Math standards. Common Core has made some improvements, by having more emphasis on statistics than what many math curricula previously had…. But there is still a lot of content learned that is not relevant to most people/jobs. For example, Common Core requires students to know imaginary numbers (aka complex numbers). But there is a reason why they are called “imaginary”…. And I have yet to see where someone use these in their job. (And for those who do, they could learn these in college and be none the worse!) But Common Core does not even mention “binary” nor “hexadecimal” nor “Boolean” (in fact “logic” only appears briefly in 3 standards!) These are concepts used in all aspects of technology, that are far more relevant to every student than imaginary/complex numbers.

But maybe there is a chance of some change, in California at least. California is working on new Computer Science standards… If California categorizes these as math standards, and allow students to take a computer science course in place of Algebra I, as a graduation requirement… Then we might have a chance of having relevant math as an option in our schools; and have better prepared students for the jobs of the future. (Actually, these are the jobs of today!!!)

Electrical impedance is a complex number.

Anyone working with radio or audio electronics is dealing with complex numbers, aware or not. 🙂

I have always heard that complex numbers were involved in parts of electronics. Although, now that I have researched it a little more, it appears that electrical impedance isn’t inherently a complex number, but that simply it is often easier to model it using complex numbers than other methods. (See https://electronics.stackexchange.com/questions/128986/why-use-complex-numbers-to-represent-amplitude-and-phase-of-ac)

So, I’m still not convinced that it is more relevant to require students to know complex numbers than to understand binary and base systems or formal logic with Boolean algebra. I believe it is far more likely students will run into these discreet math concepts than complex numbers. Or maybe math should be specialized sooner, so that those who are going into traditional engineering get the traditional mathematics path, and those going into ICT get a discreet mathematics path, and those going into nearly any other field get a statistical/probability path. Data from the Bureau of Labor statistics backs this up also, with the number of jobs in ICT being far higher than traditional engineering.

Electrical impedance is simply the vector sum of Inductive Reactance (aka Xl which resides on the positive Y-Axis), Capacitive Reactance (aka Xc which resides on the negative Y-Axis), and Resistance (aka R which resides on the positive R-Axis), where Xl and Xc are vectors 180 degrees opposite of each other, where they subtract from eachother and cancel each other if they are equal. R is then simply a horizontal line vector 90 perpendicular to the net Xc+Xl vertical vector line.

To arrive at impedance (aka Z), simply take the pathagorean sum of the hypotenuse of the Xc+Xl vector and R vector which mathimatically is:

Z = SQRT(R^2 + (Xc+Xl)^2);

Electrical engineers like to express this as the complex number equation “Z = R – jXc” when the LCR node is net capacitive, and as “Z = R + jXl” when the LCR node is net inductive, or as “Z=R” when the LCR is purely resistive as in the case of electrical resonance.

F#ck thinking thinking that way. Complex numbers just confuse the issue. Really, there are NO imaginary numbers involved in computing impedance. Both Xc and Xl are not imaginary at all but are very real and easily measured in absolute terms as is R.

To compute Xc:

Xc = 1/(2*pi*F*C), where F is frequency in cycles and C is capacitance in Farads.

To compute Xl:

Xc = (2*pi*F*L), where F is frequency in cycles and L is capacitance in Henries.

Resonance always occurs where Xc=Xl, meaning where 1/(2*pi*F*C) = (2*pi*F*L). Solving for resonant frequency F, the formula for resonance becomes:

F = 1/2*pi*L*C.

The idea of not teaching a student Basic Algebra is ridiculous. The more math you know, the better. Teaching Computer Science is not about teaching a set of programming languages but rather teaching how to apply computer soutions to real world problems which in turn ALWAYS involves algegra. For example, something as simple as a basic balance sheet report or general ledger report generated by a computer program involves algebra first and foremost, and a computer language secondarily.

It is precisely because programming always involves algebra (at least of a certain form), that I think that computer science can be an effective method for students to learn algebra.