Please advise! what kind of training I am lackfor math?

Dear all,

I have long been headache about this problem... please help me! let me try
to explain my problem to you:

For years I have been headache about reading math notations. A concept, if
it is put in straightforward way, I can understand. But if it is put in a
math notation, or even advanced math notation, I will feel dizzy when I read
it. I cannot avoid feeling dizzy if I meet math formulars having more than 3
lines. But I am in graduate school and must accquaint myself with maths. For
some reason, in my research field, information theory and signal processing,
if there is no math, the research may be regarded as low quality; hence high
quality journals are full of maths. I can never fully understand a paper
full of maths.

I guess my problem is my lack of exposure to math and lack of systematical
education in math. I thought I will be a programmer and all my past time was
devoted to programming. But later I found programming is kind boring so I
end up need to use math.

In fact I am quite good in terms of grades in math classes; but I have only
studied very few math courses: calculas, linear algebra, complexity
analysis, probability, all in undergraduate and introductory graduate level.

So I am at a very akward stage now: if give me undergraduate math to read, I
feel too easy and boring, if give me difficult math to read as those in
Information Theory Transactions, I feel dizzy...

Can anybody recommend some procedures/reference books to give me a treatment
for my current sickness? Can anybody give a booklist that any big guy in the
field would recommend as a must-read as a systematic treatment to math for
researchers in math-related engineering/science area?

Thank you very much,

-Walala

walala wrote:

> Dear all,
> 
> I have long been headache about this problem... please help me! let me try
> to explain my problem to you:
> 
> For years I have been headache about reading math notations. A concept, if
> it is put in straightforward way, I can understand. But if it is put in a
> math notation, or even advanced math notation, I will feel dizzy when I read
> it. I cannot avoid feeling dizzy if I meet math formulars having more than 3
> lines. 

   ...

> Can anybody recommend some procedures/reference books to give me a treatment
> for my current sickness? Can anybody give a booklist that any big guy in the
> field would recommend as a must-read as a systematic treatment to math for
> researchers in math-related engineering/science area?
> 
> Thank you very much,
> 
> -Walala

OK, Buddy: we're much alike. My problem with math is not doing it -- I
find that straightforward -- but reading it. I tend to skim, and that's
fatal. When I need details and not just gist (which is most of the time,
unfortunately), I decipher it instead of reading it. I use the symbols
as a guide to the pathway that the writer tries to lead me down, and I
walk it, every step. Most of the time, that seems to work.

Jerry
-- 
Engineering is the art of making what you want from things you can get.
�����������������������������������������������������������������������

In article <bven6i$6k6$1@mozo.cc.purdue.edu>,
 "walala" <mizhael@yahoo.com> wrote:

> Can anybody recommend some procedures/reference books to give me a treatment
> for my current sickness? Can anybody give a booklist that any big guy in the
> field would recommend as a must-read as a systematic treatment to math for
> researchers in math-related engineering/science area?

One fact is that everyone learns and understands in a different way. 
Some people understand things by reading. Some people understand things 
when they listen, or when they do them. I personally understand things 
as soon as I write them down. It may be as simple as that: Find out what 
is your method of learning things and use that method.

walala wrote:

>For years I have been headache about reading math notations. A concept, if
>it is put in straightforward way, I can understand. But if it is put in a
>math notation, or even advanced math notation, I will feel dizzy when I read
>it. I cannot avoid feeling dizzy if I meet math formulars having more than 3
>lines. But I am in graduate school and must accquaint myself with maths. For
>some reason, in my research field, information theory and signal processing,
>if there is no math, the research may be regarded as low quality; hence high
>quality journals are full of maths. I can never fully understand a paper
>full of maths.
>
>I guess my problem is my lack of exposure to math and lack of systematical
>education in math. I thought I will be a programmer and all my past time was
>devoted to programming. But later I found programming is kind boring so I
>end up need to use math.
>
>In fact I am quite good in terms of grades in math classes; but I have only
>studied very few math courses: calculas, linear algebra, complexity
>analysis, probability, all in undergraduate and introductory graduate level.
>
>So I am at a very akward stage now: if give me undergraduate math to read, I
>feel too easy and boring, if give me difficult math to read as those in
>Information Theory Transactions, I feel dizzy...
>
>Can anybody recommend some procedures/reference books to give me a treatment
>for my current sickness? Can anybody give a booklist that any big guy in the
>field would recommend as a must-read as a systematic treatment to math for
>researchers in math-related engineering/science area?
>
The notation of mathematics is merely its *language*.  As with a natural 
language, one learns it best through active use.  That is, you will get 
used to notation by writing it down yourself.  Start by using more 
notation in your exercises, or in the writing up of other proofs that 
you know (e.g., from textbooks).  In fact, when you read through a paper 
the second time (the first time should be just an attempt to get the 
basic idea), do so with pen and paper at hand.  Work through proofs to 
learn to understand the paper.  And try to use notation in your own 
writing more and more.  Eventually, you will become more comfortable 
with notation.  However, I suspect that you (as most) will need to use 
this approach throughout your career.

By the way, a well-written paper should also explain the gist of the 
argument without the obscurity of mathematical notation;  it seems to me 
that authors are often too lazy to take this step, or they are incapable 
of doing so.  And academic culture tends tolerate this trend.  In 
particular, when I make a presentation (which is usually in the field of 
operations research), I often consciously try to *avoid* the use of 
notation in my slides:  the important part is concepts and results I am 
trying to convey.  Proofs can be outlined in the presentation;  parties 
interested in details can read the paper.  I have found that graduate 
students in particular appreciate this approach, but I suspect the 
appeal is more general than that.

Always, the important contribution of a work is its content, not its 
notation.

-- 
Stephen J. Herschkorn                        herschko@rutcor.rutgers.edu

In article <bven6i$6k6$1@mozo.cc.purdue.edu>,
 "walala" <mizhael@yahoo.com> wrote:

> Dear all,
> 
> I have long been headache about this problem... please help me! let me try
> to explain my problem to you:
> 
> For years I have been headache about reading math notations. A concept, if
> it is put in straightforward way, I can understand. But if it is put in a
> math notation, or even advanced math notation, I will feel dizzy when I read
> it. I cannot avoid feeling dizzy if I meet math formulars having more than 3
> lines. 

The way to read math is slowly, one line at a time. When presented with 
three lines, just read the first one. Understand it. If need be, take 
pencil and paper and work out to your own satisfaction what they are 
saying. Then go on to the next line.  

The trick is to learn to read math very slowly.





But I am in graduate school and must accquaint myself with maths. For
> some reason, in my research field, information theory and signal processing,
> if there is no math, the research may be regarded as low quality; hence high
> quality journals are full of maths. I can never fully understand a paper
> full of maths.
> 

Signal processing? Yup. All math.

"Jerry Avins" <jya@ieee.org> wrote in message
news:401ae873$0$2665$61fed72c@news.rcn.com...
> walala wrote:
>
> > Dear all,
> >
> > I have long been headache about this problem... please help me! let me
try
> > to explain my problem to you:
> >
> > For years I have been headache about reading math notations. A concept,
if
> > it is put in straightforward way, I can understand. But if it is put in
a
> > math notation, or even advanced math notation, I will feel dizzy when I
read
> > it. I cannot avoid feeling dizzy if I meet math formulars having more
than 3
> > lines.
>
>    ...
>
> > Can anybody recommend some procedures/reference books to give me a
treatment
> > for my current sickness? Can anybody give a booklist that any big guy in
the
> > field would recommend as a must-read as a systematic treatment to math
for
> > researchers in math-related engineering/science area?
> >
> > Thank you very much,
> >
> > -Walala
>
> OK, Buddy: we're much alike. My problem with math is not doing it -- I
> find that straightforward -- but reading it. I tend to skim, and that's
> fatal. When I need details and not just gist (which is most of the time,
> unfortunately), I decipher it instead of reading it. I use the symbols
> as a guide to the pathway that the writer tries to lead me down, and I
> walk it, every step. Most of the time, that seems to work.
>
No, Jerry buddy, we aren't alike. You feel doing math is straightforward for
you... But I am not. Maybe I will need more math courses to catch up with
you. But currently I feel eitherr reading and doing math are difficult for
me... Have you tried some paper in IEEE Transaction on Information Theory?

"walala" <mizhael@yahoo.com> wrote in message
news:bven6i$6k6$1@mozo.cc.purdue.edu...
> Dear all,
>
> I have long been headache about this problem... please help me! let me try
> to explain my problem to you:
>
> For years I have been headache about reading math notations. A concept, if
> it is put in straightforward way, I can understand. But if it is put in a
> math notation, or even advanced math notation, I will feel dizzy when I
read
> it. I cannot avoid feeling dizzy if I meet math formulars having more than
3
> lines. But I am in graduate school and must accquaint myself with maths.
For
> some reason, in my research field, information theory and signal
processing,
> if there is no math, the research may be regarded as low quality; hence
high
> quality journals are full of maths. I can never fully understand a paper
> full of maths.
>
> I guess my problem is my lack of exposure to math and lack of systematical
> education in math. I thought I will be a programmer and all my past time
was
> devoted to programming. But later I found programming is kind boring so I
> end up need to use math.
>
> In fact I am quite good in terms of grades in math classes; but I have
only
> studied very few math courses: calculas, linear algebra, complexity
> analysis, probability, all in undergraduate and introductory graduate
level.
>
> So I am at a very akward stage now: if give me undergraduate math to read,
I
> feel too easy and boring, if give me difficult math to read as those in
> Information Theory Transactions, I feel dizzy...
>
> Can anybody recommend some procedures/reference books to give me a
treatment
> for my current sickness? Can anybody give a booklist that any big guy in
the
> field would recommend as a must-read as a systematic treatment to math for
> researchers in math-related engineering/science area?
>
> Thank you very much,
>
> -Walala
>
>

I guess I am lack of math thinking... or the buzzword: thinking in math. Are
there any books/courses that can help student to form mathematical thinking?

walala wrote:

> Dear all,
>
> I have long been headache about this problem... please help me! let me try
> to explain my problem to you:
>
> For years I have been headache about reading math notations. A concept, if
> it is put in straightforward way, I can understand. But if it is put in a
> math notation, or even advanced math notation, I will feel dizzy when I read
> it. I cannot avoid feeling dizzy if I meet math formulars having more than 3
> lines. But I am in graduate school and must accquaint myself with maths. For
> some reason, in my research field, information theory and signal processing,
> if there is no math, the research may be regarded as low quality; hence high
> quality journals are full of maths. I can never fully understand a paper
> full of maths.
>
> I guess my problem is my lack of exposure to math and lack of systematical
> education in math. I thought I will be a programmer and all my past time was
> devoted to programming. But later I found programming is kind boring so I
> end up need to use math.
>
> In fact I am quite good in terms of grades in math classes; but I have only
> studied very few math courses: calculas, linear algebra, complexity
> analysis, probability, all in undergraduate and introductory graduate level.
>
> So I am at a very akward stage now: if give me undergraduate math to read, I
> feel too easy and boring, if give me difficult math to read as those in
> Information Theory Transactions, I feel dizzy...
>
> Can anybody recommend some procedures/reference books to give me a treatment
> for my current sickness? Can anybody give a booklist that any big guy in the
> field would recommend as a must-read as a systematic treatment to math for
> researchers in math-related engineering/science area?
>
> Thank you very much,
>
> -Walala

In the UK and NZ it's Maths (plural)

Tom

"walala" <mizhael@yahoo.com> wrote in message
news:bven6i$6k6$1@mozo.cc.purdue.edu...
> Dear all,
>
> I have long been headache about this problem... please help me! let me try
> to explain my problem to you:
>
> For years I have been headache about reading math notations. A concept, if
> it is put in straightforward way, I can understand. But if it is put in a
> math notation, or even advanced math notation, I will feel dizzy when I
read
> it. I cannot avoid feeling dizzy if I meet math formulars having more than
3
> lines. But I am in graduate school and must accquaint myself with maths.
For
> some reason, in my research field, information theory and signal
processing,
> if there is no math, the research may be regarded as low quality; hence
high
> quality journals are full of maths. I can never fully understand a paper
> full of maths.
>
> I guess my problem is my lack of exposure to math and lack of systematical
> education in math. I thought I will be a programmer and all my past time
was
> devoted to programming. But later I found programming is kind boring so I
> end up need to use math.
>
> In fact I am quite good in terms of grades in math classes; but I have
only
> studied very few math courses: calculas, linear algebra, complexity
> analysis, probability, all in undergraduate and introductory graduate
level.
>
> So I am at a very akward stage now: if give me undergraduate math to read,
I
> feel too easy and boring, if give me difficult math to read as those in
> Information Theory Transactions, I feel dizzy...
>
> Can anybody recommend some procedures/reference books to give me a
treatment
> for my current sickness? Can anybody give a booklist that any big guy in
the
> field would recommend as a must-read as a systematic treatment to math for
> researchers in math-related engineering/science area?

I agree with the other posts.

I must say that your problem is very familiar to me too!  So don't be
disheartened.
The idea that this is simply language is a particularly powerful idea.  The
problem is that the language part you're having trouble with is that it's
shorthand!  So you try to read at your own "normal" rate and the shorthand
just doesn't allow that - it's too compact.  Yet, it's still language with a
few new terms thrown in.

The suggestions of others are good ones.  Slow down.  Practice.

Finally, understand this:  many papers are not well written for clarity or
to be understood.  So, in addition to there being issues of language and
shorthand, some stuff is just crap from a presentation point of view and
maybe from a real content point of view as well.  Skip those papers unless
someone tells you they're really important.  You will never read
*everything* anyway - so you may as well be selective.  And, by this I mean
you will never read everything in either: information theory, in circuit
theory, in DSP, in control systems because each topic is just too broad and
has too many articles.

Hint:  look for the referenced articles.  Note that the "classic" papers are
mostly much easier to read than others.  Put your time into the classics and
into the more recent ones that are being often referenced.  Then pick a
single topic and research it very well - using the widest variety of search
methods possible - including Scientific Abstracts if that's still around.  A
careful review of the papers on that one narrow subject will reveal papers
in categories something like this:

- the classics
- a much better notion of what the often-used references are - which should
become part of your research base.
- some very interesting ideas that you haven't seen before
- quite a few papers that aren't very clear and don't seem to mean much in
context of your research - they are off-topic
- some interesting "facts" and proofs that may come in handy in your
research of this topic.


So, you can see from this that it's likely OK to skip the ones that are just
too obscure.  And, you will still have to work at understanding the good
ones!  (but probably not nearly as hard as trying to understand the obscure
papers).

It's also likely that doing this research will cause you to expand your
knowledge of some things:  maybe it will be some parts of set theory,
approximation theory or approaches, linear spaces, etc.  As you add a level
of understanding in these areas, it will be easier to read some of those
papers.

It may seem "not good enough" to be so narrow but it usually helps because
you become more and more familiar with the ideas and will start noticing
variations in notation - "oh! that's just the same old idea but look how
strangely it's written here" ... that sort of thing.   Then, the surprises
of notation will teach you something and will allow you to read other things
more easily, etc.

Now, if you want references, then in what area?  You need to help focus the
helpers too!

Fred

In article <BLOCKSPAMfishfry-0A79E5.17405830012004@netnews.comcast.net>,
fishfry  <BLOCKSPAMfishfry@your-mailbox.com> wrote:
>The way to read math is slowly, one line at a time.

Well, everybody works differently, but I would disagree with this.
One should read the math stuff quickly, but in multiple passes.

On the early passes, try to figure out what notation is being used and
why, where the math is going, what methods were used and the basic idea
of how they got to the results.  Hit your textbooks after each step
if you find a particular notation, assumption or method too opaque.
Perhaps look into some of the citations to see if they explain some of
the concepts better.  Then, after thinking about the stuff for awhile,
and maybe writing out some of equations in your own formulations, the
later passes won't be nearly as slow or frustrating.

I remember checking a book out of the library to read about some DSP
topic.  The chapters on that topic were completely unreadable, so I'd
turn the book back in to the library and check out a different book.
Finally after trying 4 or 5 different unreadable books in succession,
there were no other books on the subject to be found.  So I went back
to the first book I had tried, and found that the words and equations
must have rearranged themselves on the pages while the book was sitting
on the library shelf, because the chapter of interest was now completely
readable.


IMHO. YMMV.
-- 
Ron Nicholson   rhn AT nicholson DOT com   http://www.nicholson.com/rhn/ 
#include <canonical.disclaimer>        // only my own opinions, etc.