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Reading Math Books
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gershon.bialer@gmail.com1
science forum beginner


Joined: 28 Jun 2006
Posts: 1

PostPosted: Wed Jun 28, 2006 12:50 am    Post subject: Reading Math Books Reply with quote

What is the best way to read a math book? Do you skim the whole book,
and the go back to, or slowly work through it word by word.

Do you try to work out all the problems? When should you give up trying
to solve the 'elementry' problems?

It just seems like in certain branches of mathematics, there are
problems that are really hard. Even worse, they sometimes lead to even
harder problems. However, this can distract from making progress.

Gershon Bialer
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Russell
science forum Guru


Joined: 25 Mar 2005
Posts: 594

PostPosted: Wed Jun 28, 2006 1:58 am    Post subject: Re: Reading Math Books Reply with quote

gershon.bialer@gmail.com wrote:
Quote:
What is the best way to read a math book? Do you skim the whole book,
and the go back to, or slowly work through it word by word.

Whatever works best. Why just those two alternatives? I find
that I have to go slowly, to get anywhere, but I also try to keep
my eyes open to the scenery as it goes by, so it isn't really
"word by word" either. And yes, I go back. Generally that is
after a chapter or so, certainly not a whole book. Reread,
reread, reread.

Quote:

Do you try to work out all the problems? When should you give up trying
to solve the 'elementry' problems?

It depends on the book. However, it is always a bad idea to
skip problems if your reason for skipping them is you don't
know how to do them. You should at least mark such problems
so you can return to them later. If you have reason to think
that the problem really *is* elementary, why give up? You
can ask for help here.

Quote:

It just seems like in certain branches of mathematics, there are
problems that are really hard. Even worse, they sometimes lead to even
harder problems. However, this can distract from making progress.

Why is that "even worse"? And what is the progress that you
want to make?

Quote:

Gershon Bialer
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Stephen J. Herschkorn
science forum Guru


Joined: 24 Mar 2005
Posts: 641

PostPosted: Wed Jun 28, 2006 2:47 am    Post subject: Re: Reading Math Books Reply with quote

Russell wrote:

Quote:
gershon.bialer@gmail.com wrote:


What is the best way to read a math book? Do you skim the whole book,
and the go back to, or slowly work through it word by word.



Whatever works best. Why just those two alternatives? I find
that I have to go slowly, to get anywhere, but I also try to keep
my eyes open to the scenery as it goes by, so it isn't really
"word by word" either. And yes, I go back. Generally that is
after a chapter or so, certainly not a whole book. Reread,
reread, reread.



And for a subject with many texts, it often helps to have several
sources available.

--
Stephen J. Herschkorn sjherschko@netscape.net
Math Tutor on the Internet and in Central New Jersey and Manhattan
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Abstract Dissonance
science forum Guru Wannabe


Joined: 29 Dec 2005
Posts: 201

PostPosted: Wed Jun 28, 2006 3:14 am    Post subject: Re: Reading Math Books Reply with quote

<gershon.bialer@gmail.com> wrote in message
news:1151455859.750257.173180@75g2000cwc.googlegroups.com...
Quote:
What is the best way to read a math book? Do you skim the whole book,
and the go back to, or slowly work through it word by word.

Do you try to work out all the problems? When should you give up trying
to solve the 'elementry' problems?

It just seems like in certain branches of mathematics, there are
problems that are really hard. Even worse, they sometimes lead to even
harder problems. However, this can distract from making progress.

Gershon Bialer


Working through the problem is definately the way to go. How do you truely
expect to understand the concepts if you don't apply them? Not only that, it
also helps you remember those concepts much easier.

I would suggest that you read through the book slowly if its small then read
through it again with much more intent on learning it and work through the
problems. Try and do them all if you can but you don't have to spend hours
on problems as most are usually designed to be done quickly(depending on the
subject matter and its level). If you cannot do the problems at all then
chances are you are really not understanding the material or are missing
something else. Try working through several similar subjects at the same
time too as it can help stimulate your mind in different ways.

When I was doing the elementary courses(calc, trig, alg, etc..) I never did
any problems but happen to be able to do quite well. I could easily remember
formulas and do problems very easily. It was ultimately a bad habit and it
carried on to harder courses and I ended up having to spend much more time
working through the problems and it was hard at first. I remember spending
8 hrs on each problem, about 5 total, for homework each week in a topology
course. It got easier as time went on and I struggled more at the beginning
than the end... Its just a matter of getting your brain to focus and the
only way to do that is put in the time.... once you do it will get much
easier.
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Shmuel (Seymour J.) Metz1
science forum Guru


Joined: 03 May 2005
Posts: 604

PostPosted: Wed Jun 28, 2006 10:13 pm    Post subject: Re: Reading Math Books Reply with quote

In <1151455859.750257.173180@75g2000cwc.googlegroups.com>, on
06/27/2006
at 05:50 PM, gershon.bialer@gmail.com said:

Quote:
What is the best way to read a math book?

That depends on the reader.

Quote:
Do you skim the whole book,
and the go back to, or slowly work through it word by word.

I typically read it word for word, but may go back to an earlier
section when appropriate.

Quote:
Do you try to work out all the problems?

I typically try the ones that look interesting.

Quote:
When should you give up trying to solve the 'elementry' problems?

If it's really elementary then you should persevere; if you're stuck,
ask for hints.

Quote:
It just seems like in certain branches of mathematics, there are
problems that are really hard.

In every branch of Mathematics. But a text for college students won't
normally give such problems as exercises without a warning.

--
Shmuel (Seymour J.) Metz, SysProg and JOAT <http://patriot.net/~shmuel>

Unsolicited bulk E-mail subject to legal action. I reserve the
right to publicly post or ridicule any abusive E-mail. Reply to
domain Patriot dot net user shmuel+news to contact me. Do not
reply to spamtrap@library.lspace.org
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Lee Rudolph
science forum Guru


Joined: 28 Apr 2005
Posts: 566

PostPosted: Wed Jun 28, 2006 11:52 pm    Post subject: Re: Reading Math Books Reply with quote

gershon.bialer@gmail.com writes:

Quote:
What is the best way to read a math book? Do you skim the whole book,
and the go back to, or slowly work through it word by word.

In the summer of 1967, the NSF gave me $600 (a princely sum at
the time) as an "undergraduate research fellowship", to do whatever
my faculty sponsor advised--that being, in the event, to read
Chevalley's _The Classical Groups_ (with an eye, supposedly, to
later helping him understand infinite-dimensional sort-of-Lie
groups and their sort-of-Lie algebra, exponential maps, and
so on). When I returned to college to begin my junior year
that fall, my sponsor was on leave, so that rather than reporting
to him for the NSF's required termination of the grant, I was
for some reason told to speak with Salomon Bochner instead.
At the end of my few minutes of terrified hemming and hawing,
he gave me this advice (I put it in quotation marks although
I can't swear it's quite verbatim; imagine it in an appropriate
accent): "You should read mathematics backwards, from the end
to the beginning." Then he dismissed me. I think we never spoke
at any other time.

Lee Rudolph
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Robert B. Israel
science forum Guru


Joined: 24 Mar 2005
Posts: 2151

PostPosted: Thu Jun 29, 2006 3:27 am    Post subject: Re: Reading Math Books Reply with quote

In article <1151455859.750257.173180@75g2000cwc.googlegroups.com>,
<gershon.bialer@gmail.com> wrote:

Quote:
It just seems like in certain branches of mathematics, there are

In every branch, as Shmuel said...

Quote:
problems that are really hard.

.... and that's why we like it.

Quote:
Even worse, they sometimes lead to even
harder problems.

.... even better.

Quote:
However, this can distract from making progress.

.... or promote it, as the case may be.

Robert Israel israel@math.ubc.ca
Department of Mathematics http://www.math.ubc.ca/~israel
University of British Columbia Vancouver, BC, Canada
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