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rAgAv
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 Posted: Wed Jun 25, 2008 8:40 am Post subject: Programming skills required by mathematicians? |
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Hello,
I'm a highschool graduate and I'm going to major in Mathematics this
Fall. I would like to have a foundation in programming so that it
would be useful in my later career as a mathematician with interests
in logic, numerical analysis, formal systems and that sort.
I don't know enough technicalities to seek the right sort of
programming that I should learn now. I wish to hear advice on what
sort of programming skills a pure mathematician would find useful.
Regards.
PS - At the moment, I know only the basics of C++. |
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Nasser Abbasi
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| Posted: Wed Jun 25, 2008 11:00 am Post subject: Re: Programming skills required by mathematicians? |
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"rAgAv" <ragav.payne@googlemail.com> wrote in message
news:7479d8a6-9aba-418f-9bb3-073fc3bd802e@j33g2000pri.googlegroups.com...
| Quote: |
Hello,
I'm a highschool graduate and I'm going to major in Mathematics this
Fall. I would like to have a foundation in programming so that it
would be useful in my later career as a mathematician with interests
in logic, numerical analysis, formal systems and that sort.
I don't know enough technicalities to seek the right sort of
programming that I should learn now. I wish to hear advice on what
sort of programming skills a pure mathematician would find useful.
Regards.
PS - At the moment, I know only the basics of C++.
|
You probably need to learn how to use a CAS system and how to program in it.
This could be a useful skill to have over the years.
There are many CAS systems out there, find out you like, and learn its
programming and commands.
http://en.wikipedia.org/wiki/Computer_algebra_system
Nasser |
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translogi
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| Posted: Wed Jun 25, 2008 12:05 pm Post subject: Re: Programming skills required by mathematicians? |
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On Jun 25, 12:40 pm, Frederick Williams
<frederick.willia...@tesco.net> wrote:
| Quote: |
rAgAv wrote:
[...] I know only the basics of C++.
And you haven't been put off computer programming for life?
|
I am still a favourite of old fashioned Q basic.
I think it is good to know the basics in a simple way.
It maybe slower than C++ but it is easy.
And you can make very sophisticated programs with it.
At the moment writing a condenced detachment theorem creator.
It does work, not quickly (But still faster than me) not nice and
shiny (no grahics and so)
But still it works. (except that it still has some unresolved
problems)
and it really shows that logic is nothing else than the manipulation
of meaningless symbols...
Ps do it in the interpretor, not in the compilor and add lots of tests
that interrupt the program when something was not the way you thought
you programmed it.
Good luck |
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Jaap Spies
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| Posted: Wed Jun 25, 2008 4:20 pm Post subject: Re: Programming skills required by mathematicians? |
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rAgAv wrote:
| Quote: |
Hello,
I'm a highschool graduate and I'm going to major in Mathematics this
Fall. I would like to have a foundation in programming so that it
would be useful in my later career as a mathematician with interests
in logic, numerical analysis, formal systems and that sort.
I don't know enough technicalities to seek the right sort of
programming that I should learn now. I wish to hear advice on what
sort of programming skills a pure mathematician would find useful.
Regards.
PS - At the moment, I know only the basics of C++.
|
You should take a look at Sage:
http://www.sagemath.org/
Sage is built by and for mathematicians!
Sage is a free mathematics software package.
It combines the power of many existing open-source
packages into a common Python-based interface.
Jaap Spies |
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Frederick Williams
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| Posted: Wed Jun 25, 2008 4:40 pm Post subject: Re: Programming skills required by mathematicians? |
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rAgAv wrote:
| Quote: |
[...] I know only the basics of C++.
|
And you haven't been put off computer programming for life?
--
He is not here; but far away
The noise of life begins again
And ghastly thro' the drizzling rain
On the bald street breaks the blank day. |
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rAgAv
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| Posted: Wed Jun 25, 2008 5:46 pm Post subject: Re: Programming skills required by mathematicians? |
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Thanks guys, for all the comments and suggestions!
I'm actually going to dual major in Physics and Mathematics. I need no
more than good education to stay put with my current ambitions of
becoming a pure thinker with mathematics and physics as my tools of
analysis. But, yes, I posted it here so that I could have an idea of
what I should do the next few idle weeks before college.
I think I'm going to focus on my C++ skills as of now because those
CAS and SAGE and other software were a bit too specific and less
versatile for my interests now.
Actually I came up with this thread after pondering over how the MU-
puzzle presented in "Goedel, Escher and Bach: An Eternal Golden Braid"
could be solved mechanically. It was frustrating to think that your
quest to prove a theorem had a well established methodology but was of
mechanical complexity and had no guarantee of hitting the bottom. I
guess that's where programming comes in. I figured it could be done
simply using C++ (perhaps with a little more expertise than I have
now). But, I was just curious if there was some program out there that
you can use for such things.
As for the books suggested, well, thanks. But, I guess I oculd do with
more books like GEB so that I get an insight into some exciting parts
of pure sciences that would keep me motivated and excited (not exactly
instructing me on how to do stuff) while I learn the real deal through
formal education.
Thanks again. |
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rAgAv
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| Posted: Wed Jun 25, 2008 6:12 pm Post subject: Re: Programming skills required by mathematicians? |
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| Quote: |
While you're there, I suggest concentrating your course work on the
parts that are hardest to pick up on your own. (I'm an experimental
physicist, so for me that was mathematical analysis and asymptotic
methods. For the theoreticians I know, it would be how to hammer in a
nail without bending it. ;)
|
Haha...yes, the main reason why I'm even going to college is to take
all those courses that I can't learn myself. Perhaps to get some
inspiration as well. I'm excited! |
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David N. Williams
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| Posted: Wed Jun 25, 2008 7:18 pm Post subject: Re: Programming skills required by mathematicians? |
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Nasser Abbasi wrote:
| Quote: |
"rAgAv" <ragav.payne@googlemail.com> wrote in message
news:7479d8a6-9aba-418f-9bb3-073fc3bd802e@j33g2000pri.googlegroups.com...
Hello,
I'm a highschool graduate and I'm going to major in Mathematics this
Fall. I would like to have a foundation in programming so that it
would be useful in my later career as a mathematician with interests
in logic, numerical analysis, formal systems and that sort.
I don't know enough technicalities to seek the right sort of
programming that I should learn now. I wish to hear advice on what
sort of programming skills a pure mathematician would find useful.
Regards.
PS - At the moment, I know only the basics of C++.
You probably need to learn how to use a CAS system and how to program
in it.
This could be a useful skill to have over the years.
There are many CAS systems out there, find out you like, and learn its
programming and commands.
http://en.wikipedia.org/wiki/Computer_algebra_system
|
Good advice!
Could I raise a different twist on this question?
Over the years, starting almost at the beginning of the personal
computer revolution, I've seen (at least three) cases of
extremely bright kids, with the potential to become excellent
pure mathematicians or physicists, be seduced into programming,
to the point of not majoring in mathematics or physics, or
dropping out of university early because of high salaries
offered by recruiters or to start their own companies.
Now maybe that's not a bad thing, but it's my prejudice that it
is.
I think it would be good if those kids had their mind space
exposed to some real, pure mathematics to counterbalance the
siren call of programming, before it's too late.
How about reading some self-contained pure math over the summer,
like Landau's "Foundations of Analysis"*, or the appendix to
Kelley's "General Topology" on "Elementary Set Theory"?
I know for a fact that Landau is accessible to at least some
bright high school students, say, who have done AP calculus,
and believe Kelley's appendix to be so as well.
You can infer that there's some uncertainty about the
suitability of Landau for this purpose from these reviews:
rave:
http://www.amazon.com/review/R3R4YQOMY3ARJU/ref=cm_cr_rdp_perm
pan:
http://www.amazon.com/review/R3INMVDAQZODN2/ref=cm_cr_rdp_perm
But maybe something along that line would be a good idea.
Or maybe the OP is already resistant to premature seduction by
programming...
-- David |
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Peter Webb
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| Posted: Wed Jun 25, 2008 8:45 pm Post subject: Re: Programming skills required by mathematicians? |
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"rAgAv" <ragav.payne@googlemail.com> wrote in message
news:7479d8a6-9aba-418f-9bb3-073fc3bd802e@j33g2000pri.googlegroups.com...
| Quote: |
Hello,
I'm a highschool graduate and I'm going to major in Mathematics this
Fall. I would like to have a foundation in programming so that it
would be useful in my later career as a mathematician with interests
in logic, numerical analysis, formal systems and that sort.
I don't know enough technicalities to seek the right sort of
programming that I should learn now. I wish to hear advice on what
sort of programming skills a pure mathematician would find useful.
Regards.
PS - At the moment, I know only the basics of C++.
|
An excellent choice. Whilst its not the simplest language to learn, you have
start already. Its widely available on range of platforms, is completely
general purpose, great for building abstract data structures (trees, hash
tables, matrices etc), and has been around so long and so widely that there
lots of code libraries you can access, on line tutorials etc. |
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Phil Hobbs
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| Posted: Wed Jun 25, 2008 9:09 pm Post subject: Re: Programming skills required by mathematicians? |
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Peter Webb wrote:
| Quote: |
"rAgAv" <ragav.payne@googlemail.com> wrote in message
news:7479d8a6-9aba-418f-9bb3-073fc3bd802e@j33g2000pri.googlegroups.com...
Hello,
I'm a highschool graduate and I'm going to major in Mathematics this
Fall. I would like to have a foundation in programming so that it
would be useful in my later career as a mathematician with interests
in logic, numerical analysis, formal systems and that sort.
I don't know enough technicalities to seek the right sort of
programming that I should learn now. I wish to hear advice on what
sort of programming skills a pure mathematician would find useful.
Regards.
PS - At the moment, I know only the basics of C++.
An excellent choice. Whilst its not the simplest language to learn, you
have start already. Its widely available on range of platforms, is
completely general purpose, great for building abstract data structures
(trees, hash tables, matrices etc), and has been around so long and so
widely that there lots of code libraries you can access, on line
tutorials etc.
|
I agree that C++ is a good choice. You can use all that C (and even
Fortran) numeric code that's out there, and write the program logic in a
comprehensible and extensible way.
To the list of suggested books, I'd recommend adding Polya's "How to
solve it", which is a deceptively simple short text on how to be smart
about "messing about till you find the solution". Good luck at college!
While you're there, I suggest concentrating your course work on the
parts that are hardest to pick up on your own. (I'm an experimental
physicist, so for me that was mathematical analysis and asymptotic
methods. For the theoreticians I know, it would be how to hammer in a
nail without bending it. ;)
Cheers,
Phil Hobbs |
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Herman Rubin
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| Posted: Thu Jun 26, 2008 12:23 am Post subject: Re: Programming skills required by mathematicians? |
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In article <fd0e8605-ee29-4365-a130-e0baedb3d9c0@f63g2000hsf.googlegroups.com>,
translogi <wilemien@googlemail.com> wrote:
| Quote: |
On Jun 25, 12:40=A0pm, Frederick Williams
frederick.willia...@tesco.net> wrote:
rAgAv wrote:
[...] I know only the basics of C++.
And you haven't been put off computer programming for life?
|
| Quote: |
I am still a favourite of old fashioned Q basic.
I think it is good to know the basics in a simple way.
It maybe slower than C++ but it is easy.
And you can make very sophisticated programs with it.
|
One can make very sophisticated programs in any
language with adequate reference capability. One
could program any machine-language combination,
except possibly for timing conditions, on even a
decent programmable calculator with sufficient
memory.
Computers are essentially a fixed program, the
hardware, which then has a small initialized amount
of software, quite variable, which enables it to
try to do what the user wants. Keep this in mind;
understand what the hardware can do, which is
different on different machines, and think in those
terms, not the current poorly designed languages.
| Quote: |
At the moment writing a condenced detachment theorem creator.
It does work, not quickly (But still faster than me) not nice and
shiny (no grahics and so)
But still it works. (except that it still has some unresolved
problems)
and it really shows that logic is nothing else than the manipulation
of meaningless symbols...
|
Communication is nothing more than the manipulation of
meaningless symbols as well. We have some established
convention, but are not the 0's and 1's in a computer
representation of what is written here a string of symbols
which by themselves are meaningless?
| Quote: |
Ps do it in the interpretor, not in the compilor and add lots of tests
that interrupt the program when something was not the way you thought
you programmed it.
|
--
This address is for information only. I do not claim that these views
are those of the Statistics Department or of Purdue University.
Herman Rubin, Department of Statistics, Purdue University
hrubin@stat.purdue.edu Phone: (765)494-6054 FAX: (765)494-0558 |
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Jaap Spies
Guest
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| Posted: Thu Jun 26, 2008 1:06 am Post subject: Re: Programming skills required by mathematicians? |
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rAgAv wrote:
| Quote: |
I think I'm going to focus on my C++ skills as of now because those
CAS and SAGE and other software were a bit too specific and less
versatile for my interests now.
|
You must be joking! Sage/Python to specific! You did not look
at the enormous amount of possibilities. Sage/Python comes with
all batteries included.
Jaap |
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rAgAv
Guest
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| Posted: Thu Jun 26, 2008 5:04 am Post subject: Re: Programming skills required by mathematicians? |
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| Quote: |
You must be joking! Sage/Python to specific! You did not look
at the enormous amount of possibilities. Sage/Python comes with
all batteries included.
|
Actually, at first, after seeing the notebook, I was kinda intimidated
and I didn't know if I could learn SAGE all by myself.
But, now, after you said that, I just checked out some tutorials on
what SAGE was and what it does and how it could be learnt (from here -
http://showmedo.com/videos/video?name=2450010&fromSeriesID=245), wow!
I'm gonna learn python as soon as I can!
I think this'll be a great advantage. But, more than that, it seems to
be a lot of fun learning Python and SAGE. Thanks! |
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Guest
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| Posted: Thu Jun 26, 2008 10:57 am Post subject: Re: Programming skills required by mathematicians? |
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On Jun 26, 9:34 am, Han de Bruijn <Han.deBru...@DTO.TUDelft.NL> wrote:
| Quote: |
Herman Rubin wrote:
Computers are essentially a fixed program, the
hardware, which then has a small initialized amount
of software, quite variable, which enables it to
try to do what the user wants. Keep this in mind;
understand what the hardware can do, which is
different on different machines, and think in those
terms, not the current poorly designed languages.
Guess you're still thinking of an IBM mainframe with
APL on it ?
|
No, with parallel computing it is now even more important
to take into account the hardware implementation.
A relatively naive but effectively vectorized algorithm
can beat that highly tuned F77 code from decades ago that
loops all over the place. |
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Frederick Williams
Guest
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| Posted: Thu Jun 26, 2008 11:00 am Post subject: Re: Programming skills required by mathematicians? |
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Phil Hobbs wrote:
| Quote: |
I agree that C++ is a good choice.
|
You must be joking!
| Quote: |
To the list of suggested books,
|
If books are being suggested, then I would recommend two programming
books: Meyer's _Object-Oriented Software Construction_ and Ableson and
Sussman's _Structure and Interpretation of Computer Programs.
--
He is not here; but far away
The noise of life begins again
And ghastly thro' the drizzling rain
On the bald street breaks the blank day. |
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