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Beginner Seeking Guidance ( Need to sharpen my mind )

  1. Apr 27, 2006 #1
    Ok, simply put, i am 21, working in a warehouse that i am not even closely challenged, and i feel as if i am getting dull.

    As unfortunate as it may be, when in highschool learning was low on my rank of importance, and as you can imagine, i don't feel i learned much... Despite it being one of my favorite subjects.

    However, i am strong willed, and feel i need to sharpen my dull sword before i break the blade.. so to say.

    And on to the question.. I wish to buy a book or two that can help me learn. What to learn though? I would Like to learn advanced math, algebra, and the like. In reality, i am sure i would just stare at it and be confused. All that was reachable back when it was fresh, but now after being so careless with my tool i call a brain, a lot of math.. especially written math (for what i did i did lazily in my head, why write it i thought then lol), i am poor at now. However if i buy some beginners math book and blaze through it I'll have wasted 50$ or so.


    I'm looking for those books that teach you new ways to think. I want to think of math in a new way, learn new tricks for old problems, and just go about everything better... and perhaps quicker. If i buy a good book that is too advanced, i can always go down a step and use the same book later on when i am ready.. but if i buy a book that is too dumbed down.. well i don't have any furniture that needs to be propped up lol.



    So any suggestions? I hope i am in the right forum in general.. i searched and searched, and found this little gem which seems to be full of life.. i just hope you are all accepting of a newcomer who is willing but uneducated.


    Oh, and on the purchasing, I'd prefer perhaps Amazon.com or Barns & Noble.


    Thanks to any replies!
     
  2. jcsd
  3. Apr 27, 2006 #2

    J77

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  4. Apr 27, 2006 #3
    how far did you go in high school? did you do trigonometry, plane geometry, polynomials, algebra, any calculus or statistics? does any of that ring a bell? i'm sure there are people on the forum who could recommend a few books but they might be either too easy or over your head right now.

    if you have a good eye you definitely don't have to spend $50 for a math text. www.abebooks.com, for example, has lots of cheap used ones.
     
  5. Apr 27, 2006 #4

    matt grime

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    Let's not recommend engineering texts, or anything that emphasizes analysis. They are not very enjoyable subjects to learn at the best of times and have little to recommend themselves as texts to sharpen the mind whilst being enjoyable.

    Far more accessible would be something like discrete mathematics.

    Start with "A very short introduction to mathematics" by Tim Gowers. Only a few bucks and will give you some idea of what mathematics is. Now, how about sharpening the mind with some books by David Wells; often the solutions to his puzzles require a little mathematics, and they will at least be cheap. Probably to advanced at this stage is Aigner and Ziegler's "Proofs from the book" but it might be one to bear in mind to aim for later. I can't think of any titles that would be perfect for you, but you might want to try and look at books on combinatorics and graph theory (which probably isn't what you think it will be). They allow you to do 'hard' maths quite quickly without having to learn loads of tedious calculus. Here, for example is a famous problem that can be solved with elementary graph theory:

    suppose that 'being friends' is 'symmetric' ie if i am friends with you you are friends with me, then show that in any room with six people in it there will either be three people who are all friends with each other, or there are 3 people who are not friends with each other.

    proof: draw 6 dots on a piece of papre, label them a,b,c,d,e,f. They represent the six people. If person a is friends with person b draw a blue line, and if they are not friends draw a red line, and do that for all pairs of people (points). now i claim that no matter how you join them up there will be a triangle of one colour or the other. a blue triangle means the three people are all friends, a red triangle means they are all not friends. try it a few times with two coloured pens.

    now, can you prove there is always a triangle? the proof is very nice and uses a very nice and obvious idea called the pigeon hole principle. feel free to look it up and try to think how to solve the problem.
     
  6. Apr 27, 2006 #5

    J77

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    :biggrin: :biggrin: :biggrin:

    Only if you're into that kind of thing!

    It might sound crazy, but some people prefer more applied maths :surprised :wink:
     
  7. Apr 27, 2006 #6

    matt grime

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    And they way I put it discrete maths is applied maths. Far more applied than engineering maths of the type taught to undergraduates. I personally think that anyone who thinks solving differential equations is fun is insane. Solving differential equations is not intellectually stimulating. Either the method you know works or you can't do it; it is purely mechanical and mind numbingly tedious. At least discrete mathematics exercises the brain as you try to think up reasons to justify why the number of ways to seat n dinner guests at a round table is the same as the number of ways of seating n-1 guests along one side of a rectangular table.
     
  8. Apr 27, 2006 #7

    J77

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    [​IMG]
    Which is handy if you fall out with one of your friends... :biggrin:

    I concede that the OP may just be looking to learn some maths for fun, but he may also want to know about methods with more application.
     
  9. Apr 27, 2006 #8

    matt grime

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    I wouldn't tell computer scientists (or indeed geologists, statisticians, cryptologists, crystallographers, chemists, phyisicists and engineers of many kinds) that discrete mathematics doesn't have as many applications as whatever you consider applied maths to be if it doesn't include discrete mathematics. I imagine IBM would be more interested in employing you if you knew how to solve knap-sack problems (an example of which is kakuro, the 'new' sudoku that appears in, for example The Guardian) than Laplace's equation, or the heat equation in the disc (all of which are approximations at any rate).


    But sure, you can spend ages learning calculus both integral and differential and be the very model of a modern major general. It might take a long time to get to anything interesting (and realistic), such as the conformal mapping theorem, or Navier-Stokes, and in the mean time you're studying an engineering text written in dry formal symbols and doing exercise 1-100 about differentiating some functions.
     
  10. Apr 27, 2006 #9

    J77

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    :biggrin:

    I know what you're saying - in fact, I advised someone interested in AI to start with discrete maths courses, just the other day.

    The text I originally suggested isn't totally hand-holding and ''dry'' in its approach - I could've suggested James or such...

    I'll have to try that kakuro - tho' it's harder to get The Guardian since I left England :smile:
     
    Last edited: Apr 27, 2006
  11. Apr 27, 2006 #10

    Gokul43201

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    Anecdote : The Tata Institute of Fundamental Science in India has a Math department with an even poorer opinion of DE that Matt - they refuse to offer a class for it to their students, and instead point them to the next building. If you are a Math grad student and you want to learn Differential Equations at the Tata Institute, you go to the Physics Dept !

    As for books, I suggest an introductory Number Theory book. All you need, to get started is middle school math, and no person in his/her right mind can say number theory is boring ! :biggrin:
     
  12. Apr 27, 2006 #11

    nrqed

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    I would suggest that you do the following. If there is any university or college within a reasonable distance, you should go to their library and spend a few afternoons looking at books. You will have a large selection free of charge. You won't be able to borrow them but you could spend hours reading them and see what suits you (in style and in level). If you find a chapter in one book particularly interesting or a calculation interesting you could even photocopy a few pages and read at home. *then*, if you find a book that matches what you are looking for, you could look it up on Amazon or Barnes and Noble or eBay for a used copy.
    I think this makes much more sense than paying 40-50$ (or more) for a book that you are not sure is th eright level for you.

    My two cents

    Patrick
     
  13. Apr 28, 2006 #12

    J77

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  14. Apr 28, 2006 #13

    Gokul43201

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  15. Apr 28, 2006 #14

    J77

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    :biggrin:

    You would have thought that the maths page of tifr.res.in and math.tifr.res.in were the same thing :wink:
     
  16. Apr 28, 2006 #15

    berkeman

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    Welcome to PF, Arezs. I don't have any suggestions for general math books -- as mentioned above, it would help us to know how far you got in high school math to help guide our suggestions.

    But I do have a couple of fun books to suggest that you check out. The first is a pair of books that really helps you to get the math part of your brain working, and actually comes in handy in everyday life (even working in a warehouse):

    "Rapid Math Tricks and Tips" by Julius
    and "More Rapid Math Tricks and Tips" by Julius
    Available at Amazon.com for a good low price as a pair:
    http://www.amazon.com/gp/product/0471575631/ref=pd_bxgy_text_b/002-3040013-2570433?_encoding=UTF8

    The second book I'd suggest is a basic electronics book that is a real gem. If you have any interest at all in learning about basic electronics (and maybe opening up a new career path as an electronics technician if you decide to go on and take some Junior College or trade classes), then I'd suggest:

    "The Art of Electronics" by Horowitz and Hill
    http://www.amazon.com/gp/product/05...002-3040013-2570433?s=books&v=glance&n=283155

    You should definitely check out this 2nd book at a library before you buy it though, to be sure that it looks interesting to you. The math is pretty straightforward -- mostly graphs, adding and multiplying, some sin() and cos() simple trig functions, etc. And it gives you a very practical set of applications of math, so you aren't just trying to learn stuff in a vacuum.
     
  17. Apr 28, 2006 #16

    mathwonk

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    to sharpen ones mind, point it at something abrasive.
     
  18. Apr 28, 2006 #17

    mathwonk

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    in 1970 i was working in a meat packing house.
     
  19. Apr 29, 2006 #18
    lol
    "Knowing what is big and what is small is more important than being able to solve partial differential equations."
    Stan Ulam
     
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