Why little math required for electronics?

[NorthGuy]

Asimov's story was written in 1957 and is as valid then as now.

It's a trend. It started long time ago and it is moving along slowly. I'm sure many thing which would look absurd to Azimov, look quite normal now. The trend will continue until it comes to total absurd, at which point you probably should expect some sort of shake up.

[EEVblog]

So one thing I have been curious about as a beginner, but I have read in The Art of Electronics and in Practical Electronics for Inventors that you don't need to know high-level math to design good circuits, just algebra basically. Now The Art of Electronics is considered a major reference in electronic design, but it doesn't seem to get into things like advanced calculus-based math. My question then, is why does acquiring an electrical engineering degree require so much math? Is it just to understand the underlying theory regarding WHY circuits work the way that they do, but otherwise isn't actually needed to create the circuits, or is it really needed for high-level circuit design? Or is it that the kind of circuit design performed by electrical engineers is different somehow...?

The majority of electronics design work would be applied engineering (I know the term applied engineering can have a specific meaning, but it's just a point), or practical engineering if you will.
This means that most solutions are solved by practical means without much recourse to anything beyond fairly basic applied theory and math. e.g. ohms law, the concepts of integration etc, rather than actually having to derive ohms law or solve an integral.
Solving problems and troubleshooting is also usually approached (at least initially) from an applied practical aspect as well, again without much recourse to anything beyond fairly basic applied theory and math. Usually the first pass practical approach will solve your issue and you move on, rarely if ever having to resort back to the heavy math to solve something.

e.g. there are hundreds of thousands of chips out there, all with highly details practical datasheets on how to implement that part and complete systems. And if something goes wrong you don't immediately resort back to Maxwell's equations to try and figure out what went wrong, you try more basic stuff first.

This is why it's so common to hear career engineers say they have never needed to practically apply the advanced math they were taught.

I highlighted the word "majority" above because there are obviously some (many) fields and jobs where you'd use the heavy math all the time, but it's certainly the exception rather than the rule.

Of course that's not any sort of argument for whether or not the advanced math should be taught, it's just pointing out that yes, as per the OP "Why little math required for electronics?" can be true.

As for the argument should it be taught or not, of course it should. There are basically three levels of engineering education:
1) Trade level - Very little to no math.
2) Diploma level - Usually some advanced math, but mostly more practical stuff.
3) Degree level - You go the Full Maxwell

Choose your own adventure, all of them (or even none) can lead to a successful career in electronics design.

And within those there are some degrees that go much more advanced than others, and likewise for diploma and trades.

[EEVblog]

You can build a bridge or a house without knowing any maths, but if you want to be sure it will be safe and long lasting while at the same time not using more materials than you need to meet the specs, then you need the math and theory to calculate strength and resonance modes, etc.

I get the purpose of the analogy here, and don't want to take away form that message, but want to add that it's not always applicable to electronics design.
In many cases you don't ensure a product is safe and long lasting (or whatever) by going into the mathematical theory and modelling of the components and the construction. Instead you usually follow rigorous practical testing methodology, probably some statistics, and looking at and analysing existing data.
One could even argue that statistics is a more valuable skill in practical electronics design that any of the physics theory.

[tggzzz]

One could even argue that statistics is a more valuable skill in practical electronics design that any of the physics theory.

That way lies the "because the computer says so" justification for a decision. Even now that can be a real problem because sometimes nobody knows the reason by design. Think "machine learning", which is currently fashionable because it can be cheaper than people.

There are such systems in the USA that cause people to be locked up in prison, and nobody can specify why it makes such recommendations. Yes, it is probably racist.

From a engineering standpoint, the problem is that nobody knows how close a system is operating to the edge of the envelope. Inevitably such faults will be passed off as operator error.

Summary: beware of using stats as a drunkard uses a lamp post - for support rather than illumination.

[rstofer]

Certainly; my thinking was more, if I could either work and make say $60K/yr as an engineer doing a job I love or make $300K/yr doing a job I don't much care about or even hate, I'd prefer the $60K engineering job. But yes, to make really serious money, you need to either go into management or be a successful entrepreneur.

I would ALWAYS go for the money!  Working for somebody else is just another form of prostitution, I might as well get paid.  I never wanted to work hard enough to be an entrepreneur.

The even better news about going for the money is the fact that you can put a bunch away for retirement.  That's why, 15 years into retirement, my life style hasn't diminished at all.  Arguably, I am better off after retirement.

Even though my education is primarily in electronics, I never worked a day in that particular part of the electrical engineering sandbox.  Instead, I worked on power systems in industrial applications and managed some high tech facilities.  A good career in a related field while still allowing me to enjoy the hobby of electronics without confusing it with making a living, working for somebody else.

Everybody has their own approach to what they want to do for a living and how far up the chain they want to go.  It's just a choice to make...

[EEVblog]

One could even argue that statistics is a more valuable skill in practical electronics design that any of the physics theory.

That way lies the "because the computer says so" justification for a decision. Even now that can be a real problem because sometimes nobody knows the reason by design.

Sure but in the majority of the time in practical electronics design you are simply not using advanced math and physics level stuff to analyse if your circuit/project is going to work or not, you just likely aren't for practical reasons, design are so complex combining so many complex chips and other components that you can't possible do that except on niche stuff. YMMV of course, we are talking majority applications here.
Hence why I said that statistics is arguably a more valuable skill in practical electronics design that any of the physics theory, because it potentially gets used in more situations in practical product design.

[EEVblog]

Everybody has their own approach to what they want to do for a living and how far up the chain they want to go.  It's just a choice to make...

Some people just aren't going to have a personality that is compatible with climbing that ladder 

[CatalinaWOW]

One could even argue that statistics is a more valuable skill in practical electronics design that any of the physics theory.

That way lies the "because the computer says so" justification for a decision. Even now that can be a real problem because sometimes nobody knows the reason by design.

Sure but in the majority of the time in practical electronics design you are simply not using advanced math and physics level stuff to analyse if your circuit/project is going to work or not, you just likely aren't for practical reasons, design are so complex combining so many complex chips and other components that you can't possible do that except on niche stuff. YMMV of course, we are talking majority applications here.
Hence why I said that statistics is arguably a more valuable skill in practical electronics design that any of the physics theory, because it potentially gets used in more situations in practical product design.

I agree that statistics are more frequently applied than vector calculus - in circuit design.  But serious statistics and noise requires advanced math also to be sure that it is applied correctly.  Not to do, that is more often just algebra, but knowing when the algebra is appropriate requires more background. 

Math requirements vary with area of focus, and if you are like most your area of focus will change over time, either due to your interests or when jobs evaporate in one area and you move on to another.  Antennas and waveguides - again the day to day stuff is just algebra, but understanding why that algebra is applicable or not is vector calculus.  Doing thermal design can be done with computer programs, or in simple cases with algebra, but most programs will give stupid answers if you don't understand boundary conditions, the impact of time sampling and a few other things which can come with either a lot of experience, or for most people a substantially shorter time learning the math.  This pattern repeats over a great many subsets of the engineering problem set.

You don't have to have advanced math to do a great many engineering jobs, but it has been my experience that those tools enhance understanding and help avoid errors.  Even if you are going to have a computer do all the grunt work you need to know what to tell it to do.  And when the computer answer doesn't converge the tools for understanding why not, and what to do about it are maybe not necessary, but they are useful.  Cut and try can be slow and frustrating.

[GregDunn]

you can also simply accept the stuff that has already been proven over and over and move on ...

Every year millions of students get questions on their finals to prove this or that theorem. Why ? Do math teachers really have no imagination ? Those theorems are sometimes thousands of years old and have been proven by billions of students through the ages. Do they really think there is need to prove it once again ? are they still unsure about them ?

If you are an athlete (say triathlon or body builder) - why lift those weights?  Surely there's a forklift or device to do that already.  Why run training laps on a track?  You're going nowhere and just burning energy.  Is there really a need to prove that you can do something millions of other people have already done before?

No, the whole point is to improve yourself by using techniques which have worked for hundreds of years.  Endurance and strength will give you an edge against the competition - math and familiarity with the processes of solving problems will enable you to do designs and handle complex issues without struggling to find a specific answer which already has been worked out.

[tggzzz]

you can also simply accept the stuff that has already been proven over and over and move on ...

Every year millions of students get questions on their finals to prove this or that theorem. Why ? Do math teachers really have no imagination ? Those theorems are sometimes thousands of years old and have been proven by billions of students through the ages. Do they really think there is need to prove it once again ? are they still unsure about them ?

If you are an athlete (say triathlon or body builder) - why lift those weights?  Surely there's a forklift or device to do that already.  Why run training laps on a track?  You're going nowhere and just burning energy.  Is there really a need to prove that you can do something millions of other people have already done before?

No, the whole point is to improve yourself by using techniques which have worked for hundreds of years.  Endurance and strength will give you an edge against the competition - math and familiarity with the processes of solving problems will enable you to do designs and handle complex issues without struggling to find a specific answer which already has been worked out.

I didn't make the point about stats  clearly enough.

Apart from that, I still disagree; a few examples of practical engineering....

Filter design needs and uses maths all the time, especially DSP filters.

Microwave engineering is all about visualising and then solving EM felds, with a computer doing the heavy lifting and the tuning.

EMI ditto, without the computer doing  the heavy lifting, because the problem's geometry is too poorly characterised.

Control theory in systems containing feedback is all about maths,  unless you don't care about stability or have.slugged the system so much that it is operating far more slowly than possible. That's true for purely digital or software systems as well, of course.

Whenever an analogue circuit misbehaves, having the maths guides the intuition towards finding the cause. (And almost all circuits are analogue, but that's a different discussion!)

And that's just a few examples from the top of my head.

Of course often it is possible to avoid maths in simple cases that are repititions of standard practice., But to think that maths isn't routinely used in practical engieering is simply false.

[0culus]

Computers are fundamentally "garbage in, garbage out" machines. Without the human who knows how the math works for debugging problems, they are pretty worthless.

[tggzzz]

One could even argue that statistics is a more valuable skill in practical electronics design that any of the physics theory.

That way lies the "because the computer says so" justification for a decision. Even now that can be a real problem because sometimes nobody knows the reason by design.

Sure but in the majority of the time in practical electronics design you are simply not using advanced math and physics level stuff to analyse if your circuit/project is going to work or not, you just likely aren't for practical reasons, design are so complex combining so many complex chips and other components that you can't possible do that except on niche stuff. YMMV of course, we are talking majority applications here.
Hence why I said that statistics is arguably a more valuable skill in practical electronics design that any of the physics theory, because it potentially gets used in more situations in practical product design.

I agree that statistics are more frequently applied than vector calculus - in circuit design.  But serious statistics and noise requires advanced math also to be sure that it is applied correctly.  Not to do, that is more often just algebra, but knowing when the algebra is appropriate requires more background. 

Math requirements vary with area of focus, and if you are like most your area of focus will change over time, either due to your interests or when jobs evaporate in one area and you move on to another.  Antennas and waveguides - again the day to day stuff is just algebra, but understanding why that algebra is applicable or not is vector calculus.  Doing thermal design can be done with computer programs, or in simple cases with algebra, but most programs will give stupid answers if you don't understand boundary conditions, the impact of time sampling and a few other things which can come with either a lot of experience, or for most people a substantially shorter time learning the math.  This pattern repeats over a great many subsets of the engineering problem set.

You don't have to have advanced math to do a great many engineering jobs, but it has been my experience that those tools enhance understanding and help avoid errors.  Even if you are going to have a computer do all the grunt work you need to know what to tell it to do.  And when the computer answer doesn't converge the tools for understanding why not, and what to do about it are maybe not necessary, but they are useful.  Cut and try can be slow and frustrating.

Yes.

I'd summarise those points as "GIGO" and "blind fumbling'. Most people operate like that in most walks of life   I aspire to higher

[rstofer]

One could even argue that statistics is a more valuable skill in practical electronics design that any of the physics theory.

That way lies the "because the computer says so" justification for a decision. Even now that can be a real problem because sometimes nobody knows the reason by design.

Sure but in the majority of the time in practical electronics design you are simply not using advanced math and physics level stuff to analyse if your circuit/project is going to work or not, you just likely aren't for practical reasons, design are so complex combining so many complex chips and other components that you can't possible do that except on niche stuff. YMMV of course, we are talking majority applications here.
Hence why I said that statistics is arguably a more valuable skill in practical electronics design that any of the physics theory, because it potentially gets used in more situations in practical product design.

I don't know if it's still a thing but just before I retired 15 years ago Six Sigma was sweeping through industry.  They were dragging highly qualified engineers through the quagmire of statistics, kicking and screaming.  I'm pretty sure I can prove that pigs can fly using statistics.  Of course, there may be a vertical bias...

The math tools are so much better today!  I really had to struggle to get through Differential Equations back in the early '70s.  Slide rules just didn't help and the arithmetic soon got ugly.  Today you can solve a wide array of these problems with a computer using something like MATLAB or Octave (GNU opensource).  Now the student has more time to study the application and wastes less time on arithmetic.  When my grandson starts his DE course in the Fall, it will all be based around MATLAB.  And the University has a required MATLAB course, probably as a prerequisite.

These 3 lines of code produce a vector of 'y' values from dy/dt.  It doesn't get much easier than this

Code: [Select]

dydt = @(t,y) (t^3-2*y)/t;  % anonymous function y'=(t^3-2y)/t,y=4.2 at t=1
t = linspace(1,3,40);       % create a vector t values
[t,y] = ode45(dydt,t,4.2);  % ode45 returns a vector of y values from dydt
[/font]

[NiHaoMike]

I'm pretty sure I can prove that pigs can fly using statistics.  Of course, there may be a vertical bias...

It's statistically possible for an ice cube to spontaneously form in a pot of boiling water. The probability is extremely small and very close to zero, but still greater than zero.

[CatalinaWOW]

Many of those who where championing and teaching 6 sigma were examples of those who needed more math background.  There is much meat behind 6 sigma, but like any fad it got diluted, misapplied and otherwise degraded.

[NorthGuy]

It's statistically possible for an ice cube to spontaneously form in a pot of boiling water. The probability is extremely small and very close to zero, but still greater than zero.

Not really. You need external energy for that, and, as we all know, energy cannot come from nowhere.

And this is an example of how applying simple mathematical and physical principles can help you distinguish a hoax from a plausible scenario.

[tggzzz]

It's statistically possible for an ice cube to spontaneously form in a pot of boiling water. The probability is extremely small and very close to zero, but still greater than zero.

Not really. You need external energy for that, and, as we all know, energy cannot come from nowhere.

And this is an example of how applying simple mathematical and physical principles can help you distinguish a hoax from a plausible scenario.

Actually you don't need external energy, provided you are prepared to wait for many times the lifetime of the universe.

[coppice]

why does acquiring an electrical engineering degree require so much math?

All of the math taught at university is to demonstrate the validity of the principles they want you to learn.  You need to know how to manipulate Maxwell's equations to understand why clamp-on ammeters work, why transformers, motors and generators work like they do and why antennas work at all.  You need to do the calculus involved in the physics of semiconductor materials before you see the validity of the simpler algebra involved in biasing a transistor.  You have to do the calculus involved in Fourier transforms to know what different effects come from signal modulation and  Laplace transforms to know that you can avoid all that messy calculus in circuit analysis and replace it with much easier algebra.
The main effect of all this is to reduce the level of abstraction involved in all of this so that intelligent approximations can be used with resorting to any of that godawfull stuff.

I did all that in school but in my career I never used anything more sophisticated than a 4 banger calculator.  I got through half of my undergrad years with only a slide rule.

you can also simply accept the stuff that has already been proven over and over and move on ...

Every year millions of students get questions on their finals to prove this or that theorem. Why ? Do math teachers really have no imagination ? Those theorems are sometimes thousands of years old and have been proven by billions of students through the ages. Do they really think there is need to prove it once again ? are they still unsure about them ?

Doesn't that logic mean that all engineering exams are pointless, as they only ask questions which have already been answered?

[nctnico]

So one thing I have been curious about as a beginner, but I have read in The Art of Electronics and in Practical Electronics for Inventors that you don't need to know high-level math to design good circuits, just algebra basically. Now The Art of Electronics is considered a major reference in electronic design, but it doesn't seem to get into things like advanced calculus-based math. My question then, is why does acquiring an electrical engineering degree require so much math? Is it just to understand the underlying theory regarding WHY circuits work the way that they do, but otherwise isn't actually needed to create the circuits, or is it really needed for high-level circuit design? Or is it that the kind of circuit design performed by electrical engineers is different somehow...?

I always say that the 'AoE' is a book which shouldn't be on the desk of a good electronics engineer. It is good for managers of an electronics R&D department to get a small clue on what is going on 

The level of math needed depends entirely on what kind of circuits you work on. Over the years I have used quite a lot of the math I learned. Usually solving equations but integrals and differentiation as well. Some Fourier and Z-transform where handy to know too.

If you are interested in good books on engineering maths then I can recommend the books 'Modern engineering mathematics' and 'Advanced modern engineering mathematics'.

[rstofer]

I can tell you with absolute certainty that you will need all your math and even more when your grandson enrolls in an ME program.  You will want to add context to what is otherwise dry subject matter and provide real world examples of the applications for this material.  And if you don't remember the quotient rule, well, you better hit the books!

MATLAB is equally useful as a programming language and all of the ideas related to CS are helpful when writing the code.  Better get up to speed on wxMaxima as well.  And C, C++, FORTRAN, Java (?), Pascal, definitely Python and probably some others.

If you're going to coach your grandkids through STEM programs, you better bring your 'A' game.  Old age is not an acceptable excuse.

[Yansi]

Just my little grumpy bit to the plenum: Math is just a tool (one of many) universities use to fuck students with and kick them out of the school (...as soon as possible, because they get payed by the number of students applied to the school - many apply multiple times).

Does it sound downright stupid? Yes, of course. But if they would indeed want to teach the subject in the first place, they would not cut corners on merging a full 4 semester course into a single semester one light-speed course of all but nothing.

And if they mean I should've learn and practice myself, I shouldn't have attended the school in the first place, uh?

Please note that this grumpy opinion on (our local) school system does not by any means state my position against math as a subject. In fact I am quite pissed at the school, because they did not teach us math properly. They did not teach us what in fact may become useful for us to know in the future. Because of this, I still am wrestling badly with laplace transform, know sh!t about z-transform, we had not even single mention of discrete math and our course of control theory & stability analysis is barely usable in practice.

Instead we got many useless but mandatory courses of history, theology, ecology, economy, while the technical subjects were dumbed down to become boring wasted time for many of us.

[tggzzz]

They did not teach us what in fact may become useful for us to know in the future. Because of this, I still am wrestling badly with laplace transform, know sh!t about z-transform, we had not even single mention of discrete math and our course of control theory & stability analysis is barely usable in practice.

No course will ever teach you everything you need to know in your career - unless your career is so boring that everything is static and preordained.

A course should teach you how to continue to educate yourself throughout your career about the specific things that are relevant to your career.

[rstofer]

The Internet is full of tutorials.  Every subject you could possibly name is covered somewhere.  If you don't get the material in the lecture, get it from the Internet.

For those who are serious about math up through Linear Algebra and Differential Equations beginning with Algebra, consider subscribing to CalcWorkshop.com.

Khan Academy covers a LOT of material and there is an EE track.  There are multiple videos on Laplace Transforms with complete explanations.

Things are so much better than back in the '70s.  If you're willing to work, there are plenty of sources for help.  Chegg comes to mind as a 'for pay' source of homework answers.  I have never subscribed but they cover the popular textbooks like Stewart for Calculus.

Try 3blue1brown.com or https://www.mathtutordvd.com/

Calculus is easy, it's the PreCalc material that will eat you alive!

[rstofer]

If you are interested in good books on engineering maths then I can recommend the books 'Modern engineering mathematics' and 'Advanced modern engineering mathematics'.

I went looking at Alibris.com for both books and it seem like Glyn James should be the author except that I see another author for an identically named book and the cost is way up there!

https://www.alibris.com/booksearch?keyword=modern+engineering+mathematics

I thought I would add them to the library but I want to get the right book(s).

[nctnico]

If you are interested in good books on engineering maths then I can recommend the books 'Modern engineering mathematics' and 'Advanced modern engineering mathematics'.

I went looking at Alibris.com for both books and it seem like Glyn James should be the author except that I see another author for an identically named book and the cost is way up there!

https://www.alibris.com/booksearch?keyword=modern+engineering+mathematics

I thought I would add them to the library but I want to get the right book(s).

I have the books written by Glyn James. I didn't know there where other books with the same title.