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Old 9th January 2009
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Default Math resources

I have started to develop some interest in Mathematics and I am working on improving my math. Also, I just realized that although my math isn't weak, its nowhere near the level it needs to be. I find the math in some academic papers almost impenetrable, so math has become a stumbling block. Also, It doesn't help that all this while I was under the impression that math is not important in my chosen field.

- What are the good math resourses on the net?

- What books do you recommend?
- What book(s) you think really helped you grok math?
(while i am mainly interested in math related to CS and under-grad/grad level please free to share any other books/info too)

Thanks.
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Old 9th January 2009
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This is a rather useful link:

http://www.sosmath.com/
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Old 9th January 2009
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Quote:
Originally Posted by ephemera View Post

- What are the good math resourses on the net?
Just Math Sci Net and similar data base searches which will enable you to find the papers you are looking for. For most part unless you are affiliated to a major research university those resources are not freely available to you. This is the comprehensive list of free internet sources
I compiled for the library at my university

The largest collection (450) of links to free Journals can be found on this web-site

http://math.golonka.se/

You may check the impact factor of Journals

http://www.in-cites.com/research/200...15_2001-2.html

and see that most top journals are actually freely available.


The other important links are


http://www.math.ethz.ch/EMIS/ELibM.html

http://www.emis.de/projects/JFM/

http://www.zblmath.fiz-karlsruhe.de/MATH/home

http://front.math.ucdavis.edu/

http://www.ams.org/mathscinet/

http://www.jstor.org/?cookieSet=1

http://www.emis.de/journals/short_index.html

http://www.emani.org/



Quote:
Originally Posted by ephemera View Post
- What books do you recommend?
The question is ill posed. I need to know how much you know, what subject you want to learn and how deep, before I can make any recommendations.


Cheers,
OKO

P.S. In the case you wonder, I am a professional research mathematician
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Old 9th January 2009
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Being just a student, I recommend the one and only http://www.amazon.com/Elements-Discr.../dp/0070381305

Trust me.

I feel very lucky to have been provided with this book by the University.
It contains introductory for most of the things I think you're interested in - set theory, boolean algebra, logic, induction etc.

My apologies for not mentioning any other title but almost all math books I read/use are in greek.
But there are tons of it. Grab some and go for it.

Quote:
P.S. In the case you wonder, I am a professional research mathematician
It would be extremely interesting to know your or ephemera's or anyone else's opinion about the relationship between mathematics and CS.
Thanks

Last edited by anemos; 9th January 2009 at 10:03 PM.
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Old 9th January 2009
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You really should give some indication on what branch of math you are interested in. My area is partial differential equations, but that may be of little interest to you. So what do you want to be able to do with math?
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Old 10th January 2009
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Quote:
Originally Posted by anemos View Post
It would be extremely interesting to know your or ephemera's or anyone else's opinion about the relationship between mathematics and CS.
Thanks
Donald Knuth better know as Leonard Euler of CS has a Ph.D. in Algebra from Caltech. First computer is of course designed by John von Neumann who was a mathematician. I believe that Kan Thomson has a masters in electrical engineering from the University of Michigan. In 70s and 80s before creating separate CS departments about 75% of CS people were educated as electrical engineers and 15% were mathematicians. The rest were from other departments. For instance Greg Lehey has a degree in Chemical Engineering. I think Kaith Bostic was originally Ph.D. student in Biology but DrJ will know better.

This is the book
http://math.ucsd.edu/~ebender/DiscreteText1/index.html

I will use to teach one semester introduction into Discrete mathematics to a class of freshmen majoring in CS at my university. I am planing to use the following for the second semester

http://math.ucsd.edu/~ebender/DiscreteText2/index.html

The above books have some tiny logical mistakes and inconsistencies but I could not find better for the freshman course especially if you take into account the price

Cheers,
Oko

P.S. By the way my area of expertise in wider sense is dynamical systems but that is a huge field and I know just tiny bits of it.

Last edited by Oko; 10th January 2009 at 03:50 AM.
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Old 10th January 2009
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Quote:
Originally Posted by Oko View Post
For instance Greg Lehey has a degree in Chemical Engineering. I think Kaith Bostic was originally Ph.D. student in Biology but DrJ will know better.
Sorry, I don't know about Keith, nor did I know Greg is/was a ChE. That's my background, FWIW.

Quote:
P.S. By the way my area of expertise in wider sense is dynamical systems but that is a huge field and I know just tiny bits of it.
That's generally true. The breadth and depth of human knowledge truly is stunning. The best one can do is to master the fundamentals of whatever field you choose, and then pick up things as you go.

I'm just outside Washington DC at the moment reviewing proposals submitted by academics for funding. Though the topic area is in what I do, the panel had over 20 people on it, with (micro)biologists, chemists, materials scientists, (bio)chemical engineers, physicists, and many others. All had important roles in understanding completely the 40+ proposals we reviewed There just is no way any substantially smaller group could have done as good a job -- we needed the mix of skills and specialties that people had within the larger disciplines -- and this is in one niche science and technology area.

The same is true for math. It is an enormous field, and the best anyone can do is to learn the small part of it that applies to your interest. But do learn the fundamentals, and learn it well.
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Old 10th January 2009
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Quote:
Originally Posted by DrJ View Post
The same is true for math. It is an enormous field, and the best anyone can do is to learn the small part of it that applies to your interest. But do learn the fundamentals, and learn it well.
The last mathematician who new whole mathematics known to human kind
during his life time was Euler who died in 1783. The last human being who new significant chunks of mathematics was John (Janos in Hungarian) von Neumann. He had papers published in Functional Analysis, Ergodic Theory, Operator Algebras, Game Theory, Numerical Analysis, Set Theory, Quantum Mechanics, and of course he built the first computer. He died 1957. His daughter still lives in Boston.

Last edited by Oko; 10th January 2009 at 07:53 AM.
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Old 10th January 2009
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Quote:
Originally Posted by DrJ View Post
You really should give some indication on what branch of math you are interested in. My area is partial differential equations, but that may be of little interest to you. So what do you want to be able to do with math?
I admit my question is at best very vague. But, I know what I need to do (go for an MS), but I am not prepared to go down that path as of now.
Anyway, the reason I asked for www/book recommendations is because I not sure where to look for math info.
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Old 10th January 2009
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Quote:
Originally Posted by anemos View Post
...relationship between mathematics and CS.
I find it hard to answer this question, mainly because i am (obviously) no authority on this matter.
Practically speaking, for the typical working programmer, not much.
But, there is plenty of interesting stuff out there that's only available in the form of research papers; an interesting idea or maybe a better/faster algorithm that you could use in your application. Now, I suppose for a research paper to have some credibility it needs to have a solid mathematical foundation. But, its this math that makes it impervious to us ordinary mortals.
Also, it can be argued that even if you don't actually use it, it's still good to know it.
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Old 10th January 2009
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Quote:
Originally Posted by ephemera View Post
Practically speaking, for the typical working programmer, not much.
Although true that you can deploy MySQL without knowledge or relational
algebras do you think I would like to hire data base developer who do not know it?

Oko

P.S. *SQL are NOT fully relational DB which sucks IMHO.
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Old 11th January 2009
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I probably have one of the worst levels of education in mathematics, out of everyone on this forum.... so anything I can write should probably be taken with a grain of salt. But honestly, the only thing I've needed to know about math in order to work with programs, is how to read what's in front of me, and to understand how numbers can work together. The only real exceptions to the above statements, have usually involved some form of cryptography or a derivative subject; where the need for math can really kick in.


One could argue, that virtually everything interesting in Computer Science can fit (more tersely) into Mathematics at some level, CS is in of it self, a branch of math I believe.



Many of the things that I've read about data structures and algorithms over the years, are really not that different then what I've found on topics related to mathematics or physics; just a different application of thought. The software side of computer science needs to address the issue of design and maintainability of the software, which is probably not necessary in most other branches of mathematics. The parts that seem to fall into math & logic, should be easy enough to come to grips with, but a good education in math is well worth it!!!



Quote:
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The study of mathematics should be fun for it's own sake; applying it, more of an exercise in making life easier.
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Old 16th January 2009
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Wolfram mathworld http://mathworld.wolfram.com/ is a good online source
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Old 18th January 2009
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ephemera:

Quote:
while I was under the impression that math is not important in my chosen field
which field is that ? CS - Computer science I suppose ... which area exactly ..
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Old 18th January 2009
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Quote:
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... which area exactly ..
Umm, that's the problem, I don't have an answer to that. And I don't know exactly what to ask.
I guess its a bit like a newbie programmer who's probably just figured out how to use pointers asking how do I learn kernel prog., or maybe the guy from ancient China who's managed to learn to use a sword asking how do I become a Ninja...
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Old 21st January 2009
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Quote:
Originally Posted by sverreh View Post
This is a rather useful link:

http://www.sosmath.com/
Thanks -- this should help me a lot! For my CS degree, I need to get a Math minor. But, I'm struggling to remember my high school algebra and geometry from 10 years ago! This site should help me brush up.
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Old 3rd April 2009
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Quote:
Originally Posted by anemos View Post
...the relationship between mathematics and CS.
Thanks
Check out this article by S Yegge: http://steve-yegge.blogspot.com/2006...ogrammers.html
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