Re: What does it take to get a handle on math?
From: John Creighton (JohnCreighton__at_hotmail.com)
Date: 07/03/04
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Date: 3 Jul 2004 09:38:28 -0700
>In article <5pop38$qqn@dfw-ixnews8.ix.netcom.com>,
>danl999@ix.netcom.com(Daniel Lawton) wrote:
>> I went to a very good bookstore, naively thinking I'd buy a bunch
of
>> math books, read them, and then be able to do what I wanted. Now
>I'm
>> on book 3, still trying to get a grip on advanced calculus, and
I've
>> realized that there are so many specilizations in the math field
that
>> I'm not sure if it's possible to get a handle on the subject.
>You aren't really into specialisations yet. OK, this is a narrow
>subfield, but one that most mathematicians know a lot about.
The original poster is an electrical engineer, and I think by calculus
he would mean system theory in general. I suspect a lot less
mathematicians know this area as comprehensively as you think unless,
they are specializing in some area of it. This is especially true for
those mathematicians that say they hate applied mathematics. I
appreciate pure mathematics and am reading a book on group theory,
("Contemporary Abstract Algebra", Joseph A. Gallian) for my own
interest. I do not know if it will be useful for me but it will give
me a deeper appreciation for things like algebraic coding and
parameter mapping (A.K.A robustness plots).
If I was trying to maximize my efficiency by just learning the
mathematics I new would be relevant to my studies of control systems,
I would read, "Mathematics in Science and Engineering, A series of
monographs and textbooks, Edited by Richard Bellman, University of
Southern California" . In fact I am looking at volume 64 right now,
Stochastic Processes and Filtering Theory. Now this is really advanced
calculus and linear algebra. Now lets take a section from it, say Ito
Calculus. What percentage of mathematicians even know what this is (10
% ?) let alone how it is formulated.
> The
>> engineers I work with keep asking me why I'm bothering to be so
>> thorough and when I expect to have learned enough to do what I want
to
>> do, but I've developed a taste for math and want to be able to
follow
>> general math discussions with good understanding. I've talked to a
>> couple of physics engineers, and find them disdainful of
mathematicians
>> in general.
>That's sad. You can't do decent engineering without a lot of maths.
>But you don't have to go too far. Few mathematicians have read
>Whitehead and Russell's Principia Mathematica (this doesn't even
>prove 1+1=2 until a long way through the book), but a little
>logic doesn't do any harm either. My point is that engineers
>may not need as much rigour as mathematicians, and mathematicians
>don't all need to go as far as Whitehead and Russell.
I agree, unfortunately. Engineers can get by with just the results and
techniques. A lot of the proofs and abstractions can be skipped. But
then look at what is lost in terms of appreciating where it all comes
from. Also recognize that the less or the proofs and theorems known
the harder it is to learn the main results and techniques. An engineer
must find his own balance. To do this the engineer must ask how much
time is he/she going to spend studying mathematics.
>> Everyone seems to have forgotten
>> nearly all of the mathematics they learned to get their degrees.
That
>> makes me wonder if the math training was all necessary in the first
>> place, or just the product of the publish or perish educational
system.
>That's tragic. Much of it was necessary, though perhaps not all.
>What needn't be explicitly remembered is probably still often
>worthwhile in that it helped in understanding other important parts.
Again I agree. As an example, I have forgotten how to do complex
integrals in terms of residues. But I know the main principle and
technique. If I really need it I know what to study and where to find
it.
>> What I want to know is, is it reasonable to keep purchasing math
books
>> and plowing my way through them? Is it possible to come to the
point
>> where you can handle just about any type of mathematical equation
>> without having to study up on that particular topic?
>All engineering involves trade-offs. You have to decide what you
>have time for and whether time is better spent doing something
>else. It's the sort of decision that engineers should be used to
>making.
Again I agree. I personally like mathematics and I think I will always
study some of it in moderation. I think the original post must have
some idea of what he needs to study. If not maybe he should consult
with some university professors in math and engineering.
>> And if I did want to get a grip on math in
>> general, what should the sequence of reading be?
>For engineers, obviously calculus and differential
>equations - not too much manipulations, just enough
>to reinforce the ideas. Lots of linear algebra is
>needed. A bit of abstract algebra and topology might
>be useful, but only take them a long way if you get
>hooked. A bit of graph theory might also be useful.
>I may have missed something useful for engineers.
>But if you get a little way with these, they will lead
>you to further areas if you need them.
Again I pretty much agree. I read part of a topology book. I was
surprised where I ended up using it. The first chapter dealt with some
preliminary set theory stuff and extended to things like demoviers
theorem, to the infinite intersection and union case. I picked up on
the notation and it was very useful to me in proving some result about
probability (I think it was the chain rule). So I know these areas
will yield benefits to the engineer but they are more abstract then
the engineer may need. Ironically I suggested similar areas in
mathematics in the post:
From: John Creighton (JohnCreighton_@hotmail.com)
Subject: Re: Is pure mathematics worth spending tax money for it?
View this article only
Newsgroups: sci.math
Date: 2004-06-12 09:49:42 PST
-----------------------------------------------------------------------
Terry Moore, Statistics Department, Massey University, New Zealand.
Theorems! I need theorems. Give me the theorems and I shall find the
proofs easily enough. Bernard Riemann
Matthew Stoker <matt.stoker@nospam.motoroladotcom> wrote in message news:<40E5E324.74798754@nospam.motoroladotcom>...
> john wrote:
> >
> > I struggle with the same thing. When do I stop? I am in calculus now. I am middle aged.
> >
>
> I'm in the same boat. I'm a Chemical Engineer with an interest in
> Quantum Mechanics, but the math escapes me sometimes. There are plenty
> of books written for the layman, but they gloss over the math and don't
> really provide any insight or deep understanding of the fundamental
> concepts. On the other hand I've muddled through a few more advanced
> books, only to get bogged down in the math or confused by unfamiliar
> nomenclature.
>
> It seems really difficult to find good intermediate-level* textbooks in
> math and other technical fields. In particular, I think to go forward
> requires a buddy with similar interests, so you can help each other
> through when one of you gets bogged down.
I think alot of people would share your frustration. I think though,
quatum mechanics is mostly linear algebra. BTW, I have a Two
undergraduate degrees, A B.Sc wth a physics major and a math minor. I
also have a bachelors of science in engineering (electrical
engineering). I am now doing my masters in control systems (way too
much school). I forget a lot of the physics especially quantum
mechanics
>*Intermediate-level in this case refers to that of a first-year
graduate
> student in a non-related technical field.
I don't know about physics and math but I know in engineering there
are a lot of books that say suitable for and undergraduate but a lot
of professors wouldn't dare give the student's the book. Some examples
I can think of "Nonlinear Control Engineering", D.P. Atherton, Another
book is on robost control, and there is another book that is very
comprehensive which includes fuzzy logic, neural networks, sliding
mode controller etch. So at least in controls engineering there are
numerous books.
BTW when I was at mount A the physics professor had two really good
gradate books on quantum mechanics. The sections he photocopied for
use were not difficult for an undergraduate in physics to understand.
So I think there are lots of books. The best way to find them is to
ask a university professor. They get sent books all the time.
> --
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