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Where should I start in math?

  1. Apr 15, 2004 #1

    JasonRox

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    Where should I start if I want to pick up on Relativity, and Quantum Mechanics?

    Is advanced calculus necessary?

    I plan on learning Non-Euclidean, which I already know the concept, but I would like to know more.

    Anything else?

    Thanks.
     
  2. jcsd
  3. Apr 15, 2004 #2

    Integral

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    I do not know how you could study those specialized fields in isolation. To understand either you need to understand Newtonian Mechanics. To understand Newtonian Mechanics you need at least Calculus and Differential Equations. Partial Differentals are necessary to go very far in any field of Physics.
    If you are interested in General Relativity then Differential Geomerty is essential.
     
  4. Apr 16, 2004 #3
    Hi there. It would certainly be ambitious to try and learn general relativity and quantum mechanics outside of a university enviroment.

    I would instead do what I did before coming to university and attempt to get a good qualitive understanding of the more advanced concepts of physics. Read popular science books, anything by Feynman, and definitely the Elegant Universe by Briane Greene.

    Special relativity can be easily understood on a qualitive level, as can a basic overview of quantum mechanics. General relativity can like most things in physics be explained in a set of compact equations. But it will require years of intense study of very complicated maths to understand how to interpret and use those equations.

    I hope you do succeed in your goal, but bear in mind it will take a very long time, a lot of hard work, and dedication.
     
  5. Apr 16, 2004 #4

    JasonRox

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    I am fortunate enough to learn quickly, but I understand your concern for learning this type of material.

    I'm going to university for Physics and Mathematics, and I just can't wait that long. It is about 2 years away, for the classes I am patiently waiting to take.

    I don't plan on mastering it on my own, and of course I would e-mail or talk to university professors, as if I was one of their students. :biggrin:

    For now, I have to wait for school to finish(2 weeks), and I'll see what I can do in 4-5 months of summer vacation. I plan on looking up more Trigonometry, Calculus, Geometry, and Algebra.

    I have learned everything I know in Calculus(Senior High School Calculus), and Chemistry.

    I seem to do better in learning things in solitude(isolation). The only times I have trouble is when there is a print error, which happens very seldomly.

    In the end, this website will help me with the questions, and help me through all the troubles. :wink:
     
  6. Apr 16, 2004 #5
    JasonRox,

    To understand any of the cool stuff in quantum mechanics takes a lot of math. So, I'd wait on that. But Einstein divided his theory of relativity into two part, Special Relativity and General Relativity. The math for GR is even more daunting than for QM!

    On the other hand, a lot of SR (including some of the most interesting parts), requires only high school algebra and an open mind (a VERY open mind!).

    Enjoy!
     
  7. Apr 16, 2004 #6
    Hi JasonRox,

    I just recently stepped on the path you seem curious in taking yourself. Someone at your level of mathematics education can work through Special Relativity with dedication and patience (like jdavel said). I can refer you to a terrific source that I used to comprehend the topic myself. It was an excellent place for me to start:

    Special Relativity, by David W. Hogg. http://physics.nyu.edu/hogg/sr/sr.pdf

    Make it through this book (and I know you can), and you'll have an excellent fundamental knowledge of Special Relativity. I want to stress; from my experience you MUST progress from Special Relativity (SR) to General Relativity (GR) in that order. As far as quantum mechanics I believe they should come after SR but probably before GR...I'm not that far myself.

    Remember that Newtonian Physics (isAsubset of) Special Relativity (isAsubset of) General Relativity. GR takes a lot of math knowledge to comprehend, specifically differential geometry and tensor analysis--this was mentioned.

    Read David W. Hogg!! And check out this website for some derivations of equations: http://www.geocities.com/physics_world/sr/sr.htm . It's hosted by this forum's very own pmb_phy.
     
  8. Apr 17, 2004 #7

    JasonRox

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    Wow!

    Now I'm confident that I'm going down the right path.

    I knew that Special Relativity was a "pre-requisite" to General Relavity.

    Here is was I plan on doing.

    -Do some work on Newtonian Physics, and get a thorough knowledge of the topic, or, in other words, a full understanding of it.

    -Special Relativity will be the next step.

    -Quantum Mechanics, as suggested earlier.

    -General Relativity, which I hope is done in the next 2-3 years.

    During the process I will exercise math skills all the time. I will tend to lean the topic of math according to the science topic that is next, so my math tools are ready.

    I will keep everyone updated on the process, with my questions of course.

    I know this sounds weird coming from someone who has never took any science classes before. Ever since I stopped watching television, I started reading about science (mostly astronomy, cosmology, physics). I read over 20 books since January.

    Another thing I do most of the time is that I try to do calculations in my head before I push the equal button on the calculator. It works great most of the time, but practice makes perfect. I usually like to get a rough number when working with many digits, or what not. While reading, or listening, you can't always assume what they are doing is right, and pulling out the calculator every second is neither convenient nor effective.

    Anyways, thanks for all the tips. :smile:

    Note: I've been eyeing The Universe in a Nutshell, but it seems like it will go through all the basic stuff I probably already know. I have Theory of Everything, and A Brief History of Time from Hawkings. If you got a personal review about it, I'm up for it.
     
    Last edited: Apr 17, 2004
  9. Apr 17, 2004 #8

    chroot

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    If you actually want to learn science, throw away the paperbacks and buy textbooks. Be prepared, though -- you're not going to read 20 textbooks in four months, that's for sure. You'll be lucky if you suffer through a couple in a year.

    - Warren
     
  10. Apr 17, 2004 #9

    Integral

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    Also, throw away, (well shelve it anyway) the calculator. Numbers are not the main objective when learning physics. You need to learn to retain the algebraic expression of all quantities until you have solved for the variable you are interested in. Then you have an expression which can be easily examined for proper dimension, and even further meaning in the expression. Going to the final number is frequently not the interesting part of the solution.
     
  11. Apr 17, 2004 #10
    Amen! Ever since I started my second year of physics/mathematics, I haven't used a calculator.

    The few times I need to calculate something numerically, it's either in an Excell sheet for a lab or for astronomy I simply do it by hand, it usually goes quicker then using some damn casio!
     
  12. Apr 17, 2004 #11

    Dr Transport

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    Chroot has a point, to appreciate the subject matter of a text, it takes time. Even though I have a PhD in semiconductor physics, I have to read and work thru a book 2 or 3 times before I have it down and can digest it throughly. To go back and reread my early texts also helps me remember. I could not tell you how many times I have read and reread my quantum mechanics book.

    dt
     
  13. Apr 17, 2004 #12

    JasonRox

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    Throwing away the paperbacks was dilemma that I was facing in the past few days.

    I was thinking to just keep a few, just for entertainment purposes.

    What you are saying is that I should just go to nearest University, and shop there for books.

    Sounds like a plan. :)
     
  14. Apr 17, 2004 #13
  15. Apr 17, 2004 #14
    Don't throw away books! That is surely a travesty :eek: :smile:

    But yes, paperbacks are good to learn ABOUT physics (which isn't bad, because nobody wants to snuggle up in bed with a textbook and a paper and pencil), but if you want to learn how to do physics you will surely need a textbook
     
  16. Apr 21, 2004 #15
    I think I can relate considering throughout highschool I have always liked the idea of learning things independently myself. Having now finish 2 years of highschool Physics (Mechanics and E/M) I think I have a greater appreciation of the difference between "reading about Physics" and "learning physics"

    Like everyone has already said, books like "The Elegant Universe" and "Universe in a Nutshell" are nice for presenting a overview conceptual idea of what certain subjects in physics involve, but real understanding comes from understanding equations and math that is behind the basics of physics.

    Get a good textbook, read through it, and do every single problem that you can. Like driving a car, physics can only be learned by doing it yourself. Don't take anything in the textbook for granted. Derive equations yourself. If you think at any point that you are making an assumption about some concept or system make sure you understand why you are making that assumption.

    I think that the best attitude to have when learning basic (newtonian) physics is to always believe in what you learn. What I mean by this is if you get into the 3rd chapter of your book and you are presented a new concept, always compare it to what has come before and see how it fits. In a precisely defined, ideal system there are no exceptions to the rules, so start raising questions if you see them.

    Always seek to fully understand a concept. The instant you find yourself just plugging numbers into equations always make sure you step back for a second to contemplate the meaning of what you are doing.
     
    Last edited: Apr 21, 2004
  17. Apr 21, 2004 #16

    JasonRox

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    That's the problem I was getting.

    While reading "coffee" books, I was getting ideas all the time. At first I thought they must have came up with these ideas already, and through them out, but I never read about it. I realized my idea must be new. Also, the more I read, the more information I found that backed it up.

    I can't just tell my idea to the world because it is pretty significant, which is why I need to learn relativity. I know for a fact that it involves changing it (relativity), but then how do I change it if I know nothing about it? How do I know my idea makes any sense without thorough knowledge of what is behind the words? Maybe the problem has been solved, but it hasn't been answered in any of the books I read.

    After this, I quickly realized (obviously) that books with words will not teach you anything about numbers. It can, but then that is a whole other story.

    Anyways, we will see where this gets.

    The only problem I got is that there is no one (physically) that I can talk to or discuss things with. I have told people (who know nothing about math/physics) about some of my ideas (which I will not discuss) and they understand it, but how do I prove it. Believe it or not, I have observational proof, so far.

    It's just a huge block for me not being able to do anything about it.

    I enjoy Physics, so far, and I really enjoyed Calculus. (I actually use Calculus to prove maximums/minimums and come up with equations for certain business applications.)

    I just finished looking through the physics courses offered at the university I'm going at. They mention nothing about General Relativity, in any of the course outlines. Special Relativity is mentionned in a second year class (2-3 years from now) and it is probably just an introduction to it, just so you get an understanding of it. An Introductory Quantum Mechanics course starts in the 3rd year, and the other 2 are in the fourth.

    That seems a little long to me. It is almost I have to attend 3rd classes (pretend I'm a student for the class) during 1st year, just to attend the class for pleasure or leisure.

    We will see.

    Who knows? Maybe my idea will get thrown out the door at Newtonian Mechanics.
     
  18. Apr 21, 2004 #17

    chroot

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    It doesn't matter if your idea is significant or not -- scientists are not normally the type to steal credit for someone else's work. If you can demonstrate that the idea was your first (even some dated paperwork or correspondence with another person -- i.e. us -- is enough proof), people will certainly give you credit for it.

    - Warren
     
  19. Apr 21, 2004 #18

    chroot

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    An even more burning question: how do you know "for a fact" that you need to change relativity, if you don't even yet know relativity?

    For the recond, general relativity involves quite daunting mathematics, and is not usually taught until graduate school.

    - Warren
     
  20. Apr 22, 2004 #19

    JasonRox

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    Well I can't explain that it is a fact.

    If comes out true, relativity is not the only thing that has to be changed.

    I'm not doing this just because I want to work with my ideas. I'm doing this because it is a lot more interesting than Accounting. Accounting requires no thought or brain, and it is driving me nuts right now.

    The fact that I have ideas will just make me pay more attention because I might need that information, or what not to, solve the puzzle.

    Well I gotta go.

    PS. I do realized that the Science world is different from the Business world. People share ideas, not steal them.
     
  21. Apr 27, 2004 #20

    arivero

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    On "stand alone mode", what about getting a copy of Newton's and trying to proof some theorems, etc? Just to get confidence, and also you get calculus in the way :-)
     
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