Mathematicize said:Hi all,
I would like to study Combinatorics and learn more combinatorial problem solving techniques (I especially liked combinatorial proofs but I still have a lot to learn in this area). I know the basics: addition rule, multiplication rule, permutations, combinations, combinations with repetition... and a little about generating functions.
Thanks for all help!
- I would like a proof based book that includes details and gives a solid justification for each derivation/step in the problem/proof (I really dislike reading math texts that would have been so much easier to understand if the author would just give more justifications)
- I would like to learn a lot of the "tricks" or "ingenuity" behind these problems.
reenmachine said:I want to become a mathematician.
At 26 years old though , a lot of people are trying hard to discourage me.I will have to start from scratch (undergraduate level) and go from there.
I tried to self-teach but I find it very difficult to learn math randomly , you always get stuck on Y because you didn't learn X while X is very easy to learn but you don't know that it's X that you have to learn to solve Y so you end up trying to find X by yourself but it took centuries to humanity to solve it while it takes half an hour to learn and understand it once you have in front of your eyes. (exagerration but not so far from the truth of trying to learn by one's self).
RJinkies said:reenmachine - I tried to self-teach but I find it very difficult to learn math randomly , you always get stuck on...
Well what things have you been trying to learn, or maybe what textbook or math puzzle book are you attempting?
There are a lot of people who hit the getting stuck roadblock, and it's quite natural, but with almost anything in math and physics, with a bit more patience and simply spending more time on something, and going back regularly, even if 10-30 min a week, you can snap out of it.
Sometimes it takes weeks, sometimes years but if your interest is there, you'll self-study one day. Just knowing a little piece well, and being interested enough to come back to the book for 30 minutes at a time, and then browsing again, every week for another 30 minutes, you can kickstart the habit
a. where you'll get a better grasp of ideas and concepts from just random browsing and getting the 'gist of things' far more than you might realize
b. actually saying, maybe i'll start on this book properly, at the beginning and go for being slow and complete, but trying extra hard to being consistent with your reading or pondering of examples, and realizing that you don't need to get far. Be patient, spend more time with things.A lot of hurdles with self-studying math can just be something so simple as not realizing that you needed to spend three times as long reading that article/chapter fragment. that 14 minutes didnt work, but 71 minutes unlocked some secrets...
im still kicking myself for not reading sherman stein's calculus book in the house, when i was still struggling with algebra. I got frustrated with the book that some chapters were crystal clear and a few just seemed 'unclear' to me. I gave up.
Also i didnt realize how important it was to just try out what the author *really* intended.
If he wrote 36 pages for chapter one, why not read *all* 36 pages?
Why not read it slowly enough to give the author a 'decent' chance?
Maybe his examples are extremely extremely useful, figure those out *deeply*
Hey, why did the author plop 64 questions at the end? Gee that's a lot! Wait a minute, what happens if i did all 64 of them?
That's the sort of thing that broke things for me with self-study.
Don't fall into the trap that the school system teaches you, the bad habit that it always needs to be a race. Make one chapter of that textbook, your life. Forget about the whole book. Drop the idea that you need to rush through the book and skim through 70% of it, sure a lot of teachers do that to cram things into 12 weeks or 15 weeks ,but why should you?
Make sure you got math books that are slightly easy to read, and some that actually do challenge you too. One day some subjects will be eye-opening if you can read one math book, and then slowly, use 2 more textbooks to read together...
So you're seeing some ideas open up in three different ways, and see how each explanation is unique...
What's murky in one book, can be clearer in another book.
but real accomplishment is when you can read all three chapters in all three books, and they all start to help each other, rather than feel like three different universes, all frustratingly different and confusing.If you are fascinated with something, don't let friends or teachers get you down. You might be interested in something, but who says that you got to be an expert from day one with it?And who says that self-study isn't so hot when you do it randomly...
If you got a book, you start at the beginning. There's nothing random at all about taking an extremely small sliver of it and trying to learn it well. Take small bites, take a lot time to chew, eat regularly...
mathwonk said:Univ de Montreal has Andrew Granville, and outstanding number theorist. I don't know the other faculty but if Andrew went there it should be good.
mathwonk said:I hope you know I am not to blame for the new lame name for this thread. The brilliantly witty tag "Who wants to be a mathematician?" has been changed without my consultation. Has tolerance of a sense of humor departed this realm?
mathwonk said:Better work takes longer of course, but unfortunately the frequency of publications is often influenced greatly by the deadline for renewing your grant or for promotion. I.e. people are forced to publish works in time for those events to occur. Since most grants are for 3 years or less, it is very hard, if not impossible to work on a project taking longer than that, except for very well established or secure people.
In some departments it is expected to publish at least one paper a year, and in some areas many more than that is usual.
My first project took about 5 years, but i was young and naive and even so was having to fend off people telling me that I was not publishing fast enough. Everyone I know who has done a big 5 year project has had the same problems.
Ideally one wants to complete some significant piece of work before publishing it, but there may be a race with someone else working on a similar project to be first. If on waits too long priority may be lost. Ideally one does not care about this and just tries to do the best science possible, but the support for pure science is not so great. A good journal will often reject a paper that has only partial results on a given problem, even decent partial results.
Sometimes the people receiving the most recognition in the form of promotions, grants, etc, are publishing large numbers of minor works. There are department chairmen who evaluate their personnel merely by counting the number of papers published. But this is perhaps within a restricted setting. Worldwide, top recognition usually follows the best work.One should try not to be guided too much by these mundane considerations, insofar as one can avoid it, but you have to pay your bills, in order to be able to work.
reenmachine said:Suppose you are working on something very hard , something that will probably require 5+ years to complete or at least advanced to a significant degree , do you still have the time to work a something more trivial that you can publish just in order to satisfy people that are pressuring you to publish?Mostly uninteresting work but just good enough to publish it.
About publishing , suppose you're in some decent math department , how do the publishing process works exactly? Does being published = who you know/who knows you or is it guaranteed you are going to get published if you have a job in a math department? If your work doesn't get published where is your work going?
mathwonk said:it is smart to have several smaller works to publish while working on a bigger one, but it takes a bit of savvy to manage that.
mathwonk said:here is my summary vita.
dkotschessaa said:Or is there another book that might give me a good crash course? Or should I just get the textbook itself?
mathwonk said:absolutely! hear hear! what else could possibly be learned here? popularity is its own curse. If we let this thread go to a million views it may never die!
But on the general principle that it is better to actually answer a question than to make smart alecky remarks, I recommend the OP go to my web page where there are several free algebra books posted for download.
http://www.math.uga.edu/~roy/
by all means read as much as possible. you can only do so much but whatever you do helps.
mathwonk said:But on the general principle that it is better to actually answer a question than to make smart alecky remarks, I recommend the OP go to my web page where there are several free algebra books posted for download.
Sankaku said:I am sorry you saw it as a "smart alecky remark." It was intended as useful advice. Asking for textbook information in a textbook forum seems like a logical step, no?
