How Many Of You Had To Teach Yourself The Math?

[phaeton]

Seriousry.

Math was pure tedium when I was in high school. I programmed my
computer to do my math homework for me. As a result, I didn't learn
much. I'm paying the price now. In fact, the first few times I've tried
getting started in electronics as a hobby over the last 10-15 years, it
was the math that kicked my ass and made me give up. The first example
in AoE (1 foot wide power cable powering NYC) makes me feel like a
class A dunce.

Well dammit, I think I've wasted enough time. I've got a couple of
books from a local used book store that specifically deal with
algebra/trig/calculus and such that applies to electronics. Going
through the first chapter, so far I've surprised myself in how much I
*did* learn, and still remember, but surely I've got a long uphill
struggle ahead.

I'm sure that I'm quite the black sheep in all this (the geek that
hates math), but is there any hope? Have any of you learned the math
from basic algebra up?

Thoughts?

Suggestions?

Insults?

thx

-phaeton

 

[Homer J Simpson]

I'm sure that I'm quite the black sheep in all this (the geek that
hates math), but is there any hope? Have any of you learned the math
from basic algebra up?

When I went to college we had a lecturer for all math courses - except trig.
I asked why and was told that one year they had to do without a lecturer and
the results went up! Too bad they never tried it for the other courses.

It's a matter of finding the right books. I have a fondness for "Mechanics
via the Calculus" by P.W. Norris and Mathematics for the Million by Lancelot
Hogben but that's me. Try your library - and Amazon.

 

[Jon Slaughter]

Seriousry.

Math was pure tedium when I was in high school. I programmed my
computer to do my math homework for me. As a result, I didn't learn
much. I'm paying the price now. In fact, the first few times I've tried
getting started in electronics as a hobby over the last 10-15 years, it
was the math that kicked my ass and made me give up. The first example
in AoE (1 foot wide power cable powering NYC) makes me feel like a
class A dunce.

Well dammit, I think I've wasted enough time. I've got a couple of
books from a local used book store that specifically deal with
algebra/trig/calculus and such that applies to electronics. Going
through the first chapter, so far I've surprised myself in how much I
*did* learn, and still remember, but surely I've got a long uphill
struggle ahead.

I'm sure that I'm quite the black sheep in all this (the geek that
hates math), but is there any hope? Have any of you learned the math
from basic algebra up?

Thoughts?

I too sucked in HS. I was into computers though and then got into computer
graphics. I couldn't understand any of it. I didn't know what cos or sin
ment or even what = really ment. This was about when I was 16-18 or so.
There was a local library sale and I picked up some books on algebra, trig,
and geometry for a few bucks. After having them for a few months and trying
to learn 3D programming I then realized I would make myself work through the
books. I really wanted to know what a matrix was and what a dot product was
and such. Then for the next few months I worked through the books. I forced
myself to understand and figure out what was going on. I didn't know how to
multiply fractions.

They had something like, say

3 9 27
- x - = --
4 5 20

I had no idea what that ment and how they got it but I realized very quickly
what htey were doing is multiplying the top to get the new top and
multiplying the bottom to get the new bottom.

For addition it was harder. I'd read what they were saying but just didn't
really understand it. I had to sit down and look at what they started and
what they ended up with and try to figure out how to do that and then test
what I thought they did.

Eventually I picked it up quite quickly and it wasn't hard at all. Its very
simple stuff but you just have to work at it. I then moved on to college and
got a degree in applied math. It really is amazing stuff and very fun to do
once you realize it's not hard but just requires some attention.

Make sure though that you start from the basics if you don't have a good
foundation. If your foundation is weak everything you build on top of it
will be weak too. i.e., it won't do you much good to jump into calculus if
you don't know "precalculus"(which is pretty much just a sum of everything
before). Being very strong in algebra should make it much easier as
everything is based off that. Calculus is very simple ideas that are taken
to the "extreme". The fundamental concept in calculus is limits. Limits are
very simple to understand if you put in a little effort. Once you understand
that then you can easily understand derivatives and integration. This about
all you really need to know to do well in electronics. Its not even
necessary but sheds some more light on the more basic concepts(i.e.,
functions).

Two things to note though is that sometimes the problem with understanding
something is the context and time. Either it has to be put in the right
words for you to understand or sometimes it just takes time for it to sink
in. Don't be afraid to read something 10-20 times to get it. When working
through math books you might have to spend 10x longer on a chapter than
reading a work of fiction. Once you get get the foundation built you will
get better at it and it won't take as long. The majority of mathematics is
really learning a language and how to use it. You already know most of the
concepts such as limits, integration, derivatives, functions and such. Its
just a matter of understanding and refining them in an intellectual way and
being able to have a language where you can communicate those ideas with
others.

If you are serious about mathematics then it will pay off. It will open up
many doors for you. You will even see mathematics in things that you might
never have though they had anything to do with it. Math is everywhere. Math
isn't just numbers but its training your brain to think about things in an
intellectual way.

Again though, you have to realize that its not hard because its hard but
simply that it takes time... it does get easier though. In fact, your brain
might give up after you having to force feed it some concepts and then just
shut down where nothing makes sense. But give it a little free time then
try it again. Your brain will realize that you mean buisiness and then will
try to make it easier.

Its all up to you though. If you really want it then you can have it. Don't
expect it to be easy though, atleast first. There are many resources on the
internet too that can help you. You can goto sci.math and post questions(no
matter how basic) if you get stuck, but don't ask for help until you have
tried many times to understand. The reason for this is many times you will
get the result without doing anything. Your subconscious will work on the
problem and eventually solve it. Many times I had no clue about how to do
something and spend many hours on it only to wake up the next day with the
answer(which is very rewarding). If you always ask for help then you will
only end up using that as a crutch and never really learn to figure things
out for yourself. (and this is probably the hardest part of math) It will
get easier though.

Have fun and good luck,
Jon

 

[Claude]

Seriousry.

Math was pure tedium when I was in high school. I programmed my
computer to do my math homework for me. As a result, I didn't learn
much. I'm paying the price now. In fact, the first few times I've tried
getting started in electronics as a hobby over the last 10-15 years, it
was the math that kicked my ass and made me give up. The first example
in AoE (1 foot wide power cable powering NYC) makes me feel like a
class A dunce.

Well dammit, I think I've wasted enough time. I've got a couple of
books from a local used book store that specifically deal with
algebra/trig/calculus and such that applies to electronics. Going
through the first chapter, so far I've surprised myself in how much I
*did* learn, and still remember, but surely I've got a long uphill
struggle ahead.

I'm sure that I'm quite the black sheep in all this (the geek that
hates math), but is there any hope? Have any of you learned the math
from basic algebra up?

Thoughts?

Suggestions?

Insults?

thx

-phaeton

I worked as an electronics technician all my life and later with
computers, routers and networks. The only time I ever had to use math is
in test taking for higher level work. You need math to take the tests,
not for working with electronics. Now if you are into engineering and
circuit design that may be another thing. I think they just used math as
a screening tool. Now they use degrees to screen people. You can be a
complete idiot but as long as you have a degree you get the job.



--

If a group's goal is the complete destruction of free people
then extermination is the only choice and shouldn't be delayed.
Only defective human beings cannot live and let live.


Claude Hopper

 

[notbob]

circuit design that may be another thing. I think they just used math as
a screening tool.

Engineering design absolutely needs math, make no mistake. Yes, as an
eng tech, I can confirm that one can do 95% of the job without math.
Learning how to diagnose and troubleshoot is a matter of experience
and creative/critical thinking. But, working out the fine details is
in the math.

Now they use degrees to screen people. You can be a
complete idiot but as long as you have a degree you get the job.

That's why engineers need technicians!

nb

 

[Jon Slaughter]

Engineering design absolutely needs math, make no mistake. Yes, as an
eng tech, I can confirm that one can do 95% of the job without math.
Learning how to diagnose and troubleshoot is a matter of experience
and creative/critical thinking.

I'm afraid that is math. Math doesn't have much to do with numbers but with
concepts and ideas... with figuring things out and trying to understand
them. Some people get distracted by the numbers but really they are just
used because its the easiest way to express math and its something everyone
has a fundamental concept of. i.e., without critical and creative thinking
you don't have math.

But, working out the fine details is

in the math.

yep. Thats the truth. I have a friend that has a degree in EE that can't
make an LED blink. He makes 50k a year and I probably know more about
electronics then he does. I doubt he could build a simple regulated power
supply even if he a schematic.

He once tried to build an 8w guitar amp from a kit he ordered and it didn't
work. I had to fix it for him and that was before I knew much about anything
in EE(I knew the basics of what a resistor, cap, inductor and such did from
physics but never really did to much with amplifiers or tubes or anthign lik
ethat). I was supprised though that he got as far as he did with it. Its
just you would/should expect more from someone like that. The said fact is
that he was probably avg.


Anyways, thats life...

 

[Lord Garth]

I too sucked in HS. I was into computers though and then got into computer
graphics. I couldn't understand any of it. I didn't know what cos or sin
ment or even what = really ment. > Jon

So Jon, do you think you can work on your spelling now?

 

[Jon Slaughter]

So Jon, do you think you can work on your spelling now?

Nope, sorry. I tried. Just a huge waste of time for me. I'd rather do
something useful instead.

 

[Chris Lloyd]

Seriousry.

Math was pure tedium when I was in high school. I programmed my
computer to do my math homework for me. As a result, I didn't learn
much. I'm paying the price now. In fact, the first few times I've tried
getting started in electronics as a hobby over the last 10-15 years, it
was the math that kicked my ass and made me give up. The first example
in AoE (1 foot wide power cable powering NYC) makes me feel like a
class A dunce.

Well dammit, I think I've wasted enough time. I've got a couple of
books from a local used book store that specifically deal with
algebra/trig/calculus and such that applies to electronics. Going
through the first chapter, so far I've surprised myself in how much I
*did* learn, and still remember, but surely I've got a long uphill
struggle ahead.

I'm sure that I'm quite the black sheep in all this (the geek that
hates math), but is there any hope? Have any of you learned the math
from basic algebra up?

Thoughts?

Suggestions?

Insults?

thx

-phaeton

I'm currently studying for a degree in Mechatronic Engineering. So far
I've had to use little of the maths that I've learnt with circuit
design. Where its been real handy is with dynamics and analysis. I
guess, from my experience and what other people have said, if you
already know the answer to a physical problem then you probably won't
need math. However math is always handy when trying to transform
natural phenomonae into discrete and quantifiable relationships.

 

[Tim Williams]

Well- you can always go back to basics. Start with a line, then chop it up
into evenly spaced hash marks. Now number the marks. Bingo, number line.
Play around with lengths, add and subtract. Observe how multiplication and
division behave.

Too elementary? Replace numbers with letters that can represent many
numbers. Write things down and observe how they behave; acceptable and
unacceptable rules; move things around. Viola, algebra. Now you are open
to linear and nonlinear (polynomial) equations.

Add another dimension. Don't necessarily graph things on a whole coordinate
system, but fiddle around with Euclidian geometry, of lines and segments,
assemblies such as triangles, and the wide world of geometry involving
circles. Incorporate algebraic representations of the various line segments
and angles. Circles and right triangles beget trigonometry.

Now place things on a Cartesian coordinate plane and, using your rules of
geometry, determine a whole new set of relations; distance, equations of
lines, polar coordinates; if you want to get adventerous, you can even delve
into loci of curves such as parabolas, elipses, etc., and their algebraic
solutions.

The last big, important part of math starts with the limit. What happens
when you make a variable very big, very small, or very close to another
value? What if that variable is part of a ratio? Discover derivative and
integral calculus. You can also go about it from the less abstract
standpoint of position, velocity and acceleration, as Newton himself did.
Establish vector math, vector calculus; expand into three dimensions and
discover the cross product; for more examples from reality, perform
electromagnetic experiments and derive Maxwell's equations from first
principles.

And that's just a miniscule fraction of all the math that has been derived
to date, let alone a further miniscule portion of all the math that is
ultimtely possible!

Ohhh, the world is an exciting place, and so much of it defined in fully
abstracted, fully logical mathematical terms. The only problem is that you
probably don't have nearly the impulse to go and do all that; I know I
don't. Hell, even Euler didn't go and derive that much, and he produced so
much work that it was still being printed currently in journals a half
century after he died!

I certainly don't have the drive to do all this, but I can see the value in
doing so. I tend to skip over reading equations and doing problems (they
are *problems*...what's that tell you? unless I have to, so I've learned
the most from classes on the subjects.

Math is a language, as much as any other; it describes things just a bit
more abstract than spoken language, but it's also immensely precise. As
with any other language, it will take time and effort to speak it.

Tim

 

[Jerry R]

[snip]

Now they use degrees to screen people. You can be a
complete idiot but as long as you have a degree you get the job.

yep. Thats the truth. I have a friend that has a degree in EE that can't
make an LED blink. He makes 50k a year and I probably know more about
electronics then he does. I doubt he could build a simple regulated power
supply even if he a schematic.

He once tried to build an 8w guitar amp from a kit he ordered and it
didn't work. I had to fix it for him and that was before I knew much about
anything in EE( I knew the basics of what a resistor, cap, inductor and
such did from physics but never really did to much with amplifiers or
tubes or anthign lik ethat). I was supprised though that he got as far as
he did with it. Its just you would/should expect more from someone like
that. The said fact is that he was probably avg.

I worked with a guy that has an MSEE. He was trying to make a +/-15vdc
power
supply from a single +15vdc. This is what he came up with:
(view in courier)


+15 >------+--------> +15v
|
|
[1uF]
|
|
GND >------+--------> 0
|
|
[1uF]
|
|
+--------> -15V

....jerry

 

[Bill Bowden]

I'm currently studying for a degree in Mechatronic Engineering. So far
I've had to use little of the maths that I've learnt with circuit
design. Where its been real handy is with dynamics and analysis. I
guess, from my experience and what other people have said, if you
already know the answer to a physical problem then you probably won't
need math. However math is always handy when trying to transform
natural phenomonae into discrete and quantifiable relationships.

I took Calculus in college and got a passing grade of "D". The only
thing I remember is the derivative of X^2 is 2X, but I'm not sure what
that means. I think it has something to do with the slope of the line
at some point on a curve, but I forget.

So, what significance does 2X have in terms of X^2?

-Bill

 

[Homer J Simpson]

I worked with a guy that has an MSEE. He was trying to make a +/-15vdc
power
supply from a single +15vdc. This is what he came up with:

I tried to take 3rd year college math (grad, div and curl etc). Couldn't do
it. But my teacher told me he tried to put an auto battery charger kit
together and burned all the copper off the board! I guess we all have our
skills.

 

[Homer J Simpson]

So, what significance does 2X have in terms of X^2?

IIRC, the slope of the X^2 curve is 2X at all points.

 

[[email protected]]

Seriousry.

Math was pure tedium when I was in high school. I programmed my
computer to do my math homework for me. As a result, I didn't learn
much. I'm paying the price now. In fact, the first few times I've tried
getting started in electronics as a hobby over the last 10-15 years, it
was the math that kicked my ass and made me give up. The first example
in AoE (1 foot wide power cable powering NYC) makes me feel like a
class A dunce.

Well dammit, I think I've wasted enough time. I've got a couple of
books from a local used book store that specifically deal with
algebra/trig/calculus and such that applies to electronics. Going
through the first chapter, so far I've surprised myself in how much I
*did* learn, and still remember, but surely I've got a long uphill
struggle ahead.

I'm sure that I'm quite the black sheep in all this (the geek that
hates math), but is there any hope? Have any of you learned the math
from basic algebra up?

Thoughts?

Suggestions?

Insults?

thx

-phaeton

Only one suggestion: Keep going!! Higher mathematics is exquisitely
beautiful, elegant, and powerful.

Hang in there. Everything gets easier, eventually. During high
school, I didn't enjoy the math courses, usually, to say the least.
And some of it seemed VERY difficult, to me. But, somehow, when I
started studying Calculus, and Physics, in my first semester of
Electrical Engineering, even huge algebraic equations suddenly seemed
almost trivially easy. I remember being amazed, especially since I
had once gotten a "D" in Algebra 1, in high school.

SOME stuff just has to be learned the hard way, or needs time to "soak
in" right. During my first university semester, it once took me eight
hours to fully-understand a single page in my Calculus textbook. If
that's what it takes, do it. It will be WELL worth it.

I believe that, essentially, everyone has to "teach themself" the math
(and everything else). I learned at least 80% of my course-work on my
own, and maybe 20% from the lecturers (but maybe only because I usually
went to the lecture before I studied the material, myself. Otherwise it
might have been 99%/1%.).

Anyway....

After you learn Calculus, one of the really-big "payoffs" is that you
can then learn about Differential Equations. THAT'S when the REAL fun
begins. (And no, I'm not being sarcastic.)

Then, you can/should also learn about Fourier Series, and Fourier and
Laplace Transforms, and signals and systems theory, and then
probabilistic signals and systems. (You'll be able to find the
Transfer Function to characterize a system by simply injecting a little
pink noise into the system. [That can be very handy to use for
industrial processes, for example.]) Digital Logic, or Symbolic Logic,
is also good stuff to learn, and is quite easy.

And you can learn about the discrete-time version of differential
equations, called Difference Equations, and the z-Transform.

With Laplace Transforms and z-Transforms, you can transform
differential and difference equations into (gasp!) algebraic equations.


And knowing about Difference Equations will also make it very easy to
do things with Differential Equations on a digital system, e.g. a
computer.

Maybe you can also study Linear Algebra and learn about sets of
simultaneous equations, for multi-variable systems, which you can then
make into one vector/matrix algebraic equation. Then you can also
learn things involving vector/matrix differential and difference
equations.

I've left a lot out. But that kind of stuff would give you a pretty
good foundation. After that, if you have learned well, "the sky's the
limit".

Good luck! Keep at it!

- Tom Gootee

"He who lives in a glass house should not invite he who is without
sin."

 

[redbelly]

IIRC, the slope of the X^2 curve is 2X at all points.

Yes, that's right.

Mark

 

[Eeyore]

Yes, that's right.

The joy of differentials !

The advent of Mahtcad radically changed ( increased ) my use of more involved
maths in engineering. A very powerful tool indeed.

Graham

 

[vic]

IIRC, the slope of the X^2 curve is 2X at all points.

More generally the slope of X^Y is Y*X^(Y-1) for any integer value of Y
(including negative).

Examples :
1/x -> -1/x^2
x -> 1
x^2 -> 2x
x^3 -> 3x^2

etc ...

vic

 

[Homer J Simpson]

Then, you can/should also learn about Fourier Series, and Fourier and
Laplace Transforms, and signals and systems theory, and then

At college, some students complained to one lecturer that they weren't
getting Laplace Transforms which put them at a disadvantage. He then gave
us a 50 minute rapid lecture on them which took me from zero to 90% - best
lecture I ever heard. It confirmed the old rule that if you can't teach it
in 50 minutes you'll never teach it at all.

 

[Jonathan Kirwan]

I took Calculus in college and got a passing grade of "D". The only
thing I remember is the derivative of X^2 is 2X, but I'm not sure what
that means. I think it has something to do with the slope of the line
at some point on a curve, but I forget.

So, what significance does 2X have in terms of X^2?

Just to add to what others have said...

Yes, the slope. 2X the expression that tells you the slope of X^2 at
any X. So if you were to draw the curve of Y=X^2 and then picked a
point X, say at 3, and then looked at the curve you'd see that the
tangent slope of the Y=X^2 curve at the point located at (3,9) happens
to be 2X or 6.

But that's not really quite so helpful. Start out by thinking in
terms of that point (3,9) for Y=X^2. Imagine you are slightly further
away, say at X=3.1. Y would then be 9.61. What would the slope be
between these two points? Well, it is (9.61-9) / (3.1-3) or .61/.1
which is 6.1. That's not much different from the 6 computed above. So
what if you used X=3.05 to get just a little closer? Well, that would
be Y=9.3025. So what would the slope be between these two points of
(3,9) and (3.05,9.3025)? Well (9.3025-9)/(3.05-3) = .3025/.05 or
6.05. Note that it is closer. It turns out that as we slide that
second point closer and closer, the resulting calculation will show a
slope closer and closer to 6, too.

Generalizing, we have Y1=X1^2 and Y2=X2^2 for the two points and the
slope between them is (Y2-Y1)/(X2-X1). But let's just call the short
distance between X1 and X2 as delta-X or more simply, just dX. Then
we can modify things a little so that we call X2=X1+dX. Then we have
Y1=X1^2 and Y2=(X1+dX)^2=X1^2+2*X1*dX+dX^2. We can then re-express
the slope as (X1^2+2*X1*dX+dX^2-X1^2)/(X2-X1). But this is also just
(2*X1*dX+dX^2)/dX or dX*(2*X1+dX)/dX, which amounts to 2*X1+dX.

Returning to the above calculations, we can now see that when I set
X2=3.05, it was 0.05 away from X1=3. Thus, dX=0.05 in this case. The
above equation suggests that I will calculate the slope as 2*3+0.05,
which would be 6.05, just as I did compute above. Nice. Now what
happens if we let dX go very, very close. Setting dX=0 (that is very
close, yes?), we compute 2*3+0 or 6. Just right.

Anyway, this is quite general. So the expression 2X is true about the
slope of Y=X^2 for all X.

Jon