Electronics and Mathematics

[rstofer]

But I wouldn't major in math.  I don't know what mathematicians do for a living.  Other than teach...  I went to school to get a job!

Most of them apply the maths they learned, the problem identification and the problem solving techniques/disciplines they learned to... real world problems.

They went to university to do something they enjoyed and to get jobs.

Yes, the math is important.  But it needs to be taken in the context of the OPs situation.  Starting a hobby!  Can a new hobbyist get anywhere without years of math?  Of course!  Can an engineer?  Nope!

Nowhere did I ever want to get into the stupid argument of 'degrees are worthless'; they're not.  Yes, there are talented technicians who can do some clever engineering.  But when it gets down to it, on average, the degreed engineer makes more money.  One company I worked for, one of the largest in the world, didn't think much of BS degrees.  Sure, they were required, as a minimum, but to really get anywhere you had to have at least an MS.  Oddly, the major wasn't as important.

So, let's take this back on track.  Can a hobbyist get anywhere in electronics without years of math?  In my view, YES!  There are tools to take the drudgery out of crunching numbers and the equations are pretty well known.  But it's also true that some amount of math will be required.

And by experimentation, I wasn't talking about 'random walk' or 'Mozart's Monkeys'.  I was thinking about the simple RC low pass filter I was playing with the other day.  From the equation f_c=1/(2*PI*R*C), I can predict the corner frequency and I know the roll-off of a simple RC filter.  I can model the filter in LTspice using ideal components, I can measure it's response using real components with my Analog Discovery (using the neat Network Analyzer Tool) and I can work out the math by hand.

Now, from the equations, I can surmise that changing the value of R or C will move the corner frequency and I can predict how far.  But it's just as useful to change the resistor and measure the results.

Experimentation, not random walk.  Knowledge gained from both sides:  the math and the experiment.  Fortunately, it will work out (at modest frequencies).

The very type of experimentation we did in lab classes.  Calculate, build, measure and explain the differences.

[rstofer]

But I wouldn't major in math.  I don't know what mathematicians do for a living.  Other than teach...  I went to school to get a job!

As an electronics engineer dealing with digital signal processing you need the maths background, say you wanted to do an odd ball sized FFT that isn't radix 2 or radix 4 in VHDL, you've got to work it out from first principles because the FPGA vendors don't have the tools to do it for you, they just have a few IP libraries based on radix 2 or 4 and some newer pipelined algorithms.
What do mathematicians do for a living ? DSP algorithms, image processing, pattern matching and recognition, software defined radio, OFDM modulators and demodulators, carrier aquisition, GPS etc etc. DSP is one branch of electronics where I would say you need the maths background.

Yup, the math guys come up with all the algorithms.  But they don't build the gadgets!  That's left to engineers and technicians.  Scientists figured out how to get to the Moon but engineers made it happen!  Six times!

I like math and science but I really like to build stuff.

When I was a kid and my folks were promoting the idea that I should study math (as a field), I asked "What do mathematicians do?".  They said mathematicians sat in a room and solved math problems.  I came up with the image of an old man with thick glasses and a visor sitting at  a desk with one of those old fashioned desk lamps writing in a ledger and decided right then and there that I wasn't going down that path.

[IanB]

When I was a kid and my folks were promoting the idea that I should study math (as a field), I asked "What do mathematicians do?".  They said mathematicians sat in a room and solved math problems.  I came up with the image of an old man with thick glasses and a visor sitting at  a desk with one of those old fashioned desk lamps writing in a ledger and decided right then and there that I wasn't going down that path.

Here are some mathematicians (sitting at their desk, with glasses even) describing some mathematical concepts:




These examples are obviously presented for a non-mathematical audience, but you can imagine perhaps that similar levels of conceptual thinking are required to solve real world problems in engineering. If you cannot imagine, visualize and conceptualize, you will find it very difficult to succeed as an engineer.

[rstofer]

These examples are obviously presented for a non-mathematical audience, but you can imagine perhaps that similar levels of conceptual thinking are required to solve real world problems in engineering. If you cannot imagine, visualize and conceptualize, you will find it very difficult to succeed as an engineer.

But we're not talking about engineering.  We're talking about a hobby!  Just a hobby!  Not a profession...

Yes, I took physics and we spent some time on waves.  Light, sound, water, whatever.  Actually, physics is my favorite subject.

As to Numberphile - I really like their series.  I also like their proof that 0.999... (repeating an infinite number of times) is EXACTLY 1.000... (repeating an infinite number of times).  Turns  out the matter came up last semester in my grandson's Precalc course when dealing with rational numbers.  Given the decimal representation (with some repeating sequence), find the fractional representation.  Having seen the proof made it a lot easier to explain what was going on.

The proof is trivial BTW;

10 times 0.9999... is 9.9999... then subtract
  1 times 0.9999... is 0.9999...
-----------------------------------
  9 times 0.9999.... is 9.0000... then divide both sides by 9
  1 times 0.9999...  is 1.0000...  EXACTLY

Of course it only works with an infinite number of digits but, still, it's clever.

[tatus1969]

  9 times 0.9999.... is 9.0000...

I get 8.9999 here?

[rstofer]

  9 times 0.9999.... is 9.0000...

I get 8.9999 here?

Carry the repeating decimals out to infinity and after subtraction all you have left is 9.000...  That's the interesting part of the proof.  If there are an infinite number of decimal digits and you multiply by 10, you still have an infinite number of decimal digits.  So, after you subtract, they're all gone!



It's fair to say there is some debate about this as there is with many topics.

[rstofer]

Whether you go for the 0.999... = 1 or not, here's how the idea works for finding fractions:

Say you have the repeating decimal 3.45454545... and call it x

100 x = 345.454545...
  -1 x =    -3.454545...
-------------------------
  99 x = 342

x= 342/99 which, when you use a calculator is 3.454545...

You can extend the idea for the case of n repeating digits, just multiply by 10ⁿ

3.456456... multiply by 1000 and solve for 999 x

[IanB]

x= 342/99 which, when you use a calculator is 3.454545...

One final step: fractions are usually expressed in their simplest form. Divide top and bottom by 9 to give 38/11, or 3 and 5/11.

[b_force]

From a physics point of view, fractions are non existing numbers, because it gives you infinite amount of accuracy/tolerance.
Which is by definition impossible.

For the same reason, a number is only as good as the accuracy which it is calculated from.
So if you multiply two 2 digit numbers, you don't get a 4 digit result, but only a two or even one digit result.
I see a lot of people doing that wrong.

[JacquesBBB]

From a physics point of view, fractions are non existing numbers, because it gives you infinite amount of accuracy/tolerance.
Which is by definition impossible.

This  is certainly not true in quantum physics where you have spin 1/2 everywhere.

It is also not true because of resonances. Motions are locked in exact ratio of frequencies. Like for example the
spin/orbit resonance of Mercury around the Sun where Mercury rotates exactly 3 times  during 2 revolutions around the Sun.

[CatalinaWOW]

A lot depends on what you mean by beginning and what you mean by hobby.

Playing with microcontrollers, PA amplifiers and the such requires little math, and can't actually be improved a lot by applying complex math.

On the other end I had a friend who got involved with sonar as a hobby.  The first step was replicating the original Raytheon consumer depth finder (a spinning disk with a light on the periphery that was triggered by the return pulse).  Little math required at that step.  But very shortly he was trying to implement a 3D imaging sonar.  Something at the very bleeding edge of sonar technology.  Lots of very complex math involved in all steps of the system, from transmitter array through the display.  Some folks just bite off an awful lot right from the start.

Hobbyists have led the way in many areas of technology, and those hobbyists often need very advanced math on a daily basis.