Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Where to start self study of higher mathematics?

  1. Jan 26, 2006 #1
    Where to start self study of higher mathematics???

    I am a student who just finished high school and i am gonna go to college this fall. I got like 7 months to shape up my maths and physics cuz my country got only 10 years of school. I wanna ask if i could self study on all the advanced topics like number theory and abstract algebra and differential equations juz by a handful of books and physicsforums and the web.

    Well, the main question i wanted to know is whether it is possible to learn higher mathematics juz by self studying. I have been giving it a shot for about 3 years now and the author juz jumps with the "it is obvious that" and so on. I dont know enough of maths to understand what the author says or i am too stupid.

    I hope no one laughs but i am asking for help out of despair and do forgive me if i posted it in the wrong place. Thanks.
    :confused: :confused: :confused: :frown: :frown:
     
  2. jcsd
  3. Jan 26, 2006 #2

    shmoe

    User Avatar
    Science Advisor
    Homework Helper

    It's certainly possible to study advanced math on your own, just get some books and start working. The more you can work out on your own, the better off you'll be but there's no shame at all in asking for help here if you need help understanding a concept. Just trying to explain what it is you don't understand can sometimes help your own understanding.

    Here's a thread with some number theory text suggestions, https://www.physicsforums.com/showthread.php?t=85248
     
  4. Jan 26, 2006 #3
    Well, it would help if you told us what you do know.

    You should know calculus fairly well before you do differential equations, but if you do, then any number of straightforward texts like Boyce and DiPrima or Zill will do.

    Algebra on the other hand really doesn't have many prerequisites. Artin's Algebra works well.

    And for Number theory, knowledge of a little algebra is helpful, but after that, LeVeque's fundamentals of Number Theory is good.

    And as for points where the author says: "it obviously follows", these points are indeed not obvious to everyone. So take some time, think about it, write some stuff down if you have to, until you understand why it follows. I do believe it is possible to learn on your own, but it does take time and effort. The less time you spend learning this stuff the more shallow your understanding will be.
     
  5. Jan 26, 2006 #4
    One recommendation for books, regardless of the topic, is to find ones that either have a great deal of worked out answers in the back, or a large number are online through a search. It's pretty pointless to work out a problem and not whether you did it correctly or not. Usually, university textbooks handle this best, since a good number have solutions manuals or many professors post homework solutions.
     
  6. Jan 26, 2006 #5
    you should be able to learn Calculus, Linear Algebra, Abstract, Number THeory, Set Tehory, Graph Theory/Combinatorics, Basics of DIffential Equations and Dynamical Systems....the first bit of analysis, simple geometry, computational geometry all on your own.

    The best bet is to look at some universities course webpages like MIT open course website. "ocw". And look at the assignments and topics

    James Stewarts Calculus should be a good startng point. Any Number THeory book more or less will give you a good foundation in Number Theory.
     
  7. Jan 26, 2006 #6
    The MIT site is awesome, I'm working on trying to do an independant study to teach myself some of differential equations and open course ware has practically all you need for the course including lecture videos.
     
  8. Jan 26, 2006 #7
    Thanks for the help.

    Can someone tell me what they teach in first year american college courses? Are they hard? Thanks again!
     
  9. Jan 27, 2006 #8

    JasonRox

    User Avatar
    Homework Helper
    Gold Member

    It's going to be a big challenge.

    Self-study isn't easy when you have no directions.
     
  10. Jan 27, 2006 #9

    benorin

    User Avatar
    Homework Helper

  11. Jan 29, 2006 #10
  12. Jan 30, 2006 #11
    First Year Canadian studies teach:
    Linear Algebra-Vectors, Matrices, 3D transformations, Solving Systems of LEs
    Calculus- Integration, Differentation, Applications of Both(area,length,volume, flow,rate[eg population growth] ),plotting, basics of functions,Trig/NaturalLog,Limits

    2nd half Lagrange Multipliers Multivariables, Basics of Solving DiffQs, Series(Taylor) & Sequences, and some more stuff can't remember

    Statistics-never took first year and I don't like stats.
     
  13. Feb 4, 2006 #12

    mathwonk

    User Avatar
    Science Advisor
    Homework Helper
    2015 Award

  14. Feb 5, 2006 #13

    JasonRox

    User Avatar
    Homework Helper
    Gold Member

    They are lecture notes, so they won't be as thorough as a good text.

    I'd say follow those notes while following a good text. That should be a good indication that you know what's going on.
     
  15. Feb 5, 2006 #14

    mathwonk

    User Avatar
    Science Advisor
    Homework Helper
    2015 Award

    have you read them? or are you making conjectures?

    you are right of course that they are lecture notes, and thus have some differences from polished books, primarily fewer problems and no index, but i suggest they may in fact be superior to some books available, in terms of insight and thoroughness.

    i.e. these notes are in fact more thorough than many texts, since a guiding principle the author used in writing them was never to sat anything is "obvious" or to leave any tedious calculation as an exercise.

    i would be interested in your reaction to actually reading them, as i have been recommending them for some time with good responses from phd students (at berkeley, upenn, rice, uga) studying for prelims.
     
    Last edited: Feb 5, 2006
  16. Feb 5, 2006 #15

    JasonRox

    User Avatar
    Homework Helper
    Gold Member

    Well, I do admit to only glancing at them. You recommended them in another thread, relating to those of 843, 844 and 845.

    I look at the 843 lecture notes.

    I was reading the beginning to just get a feel of the author, and see how he writes. I found that it's not what I would want as a beginner.

    I totally agree with that it would be great for a Ph. D. student. It quickly goes through everything, which I believe why it wouldn't be good for a beginner.

    I've went through lots of books at second hand bookstores and the ones at the university library. I noticed that Graduate Texts are also thorough, but also quick. You can follow at the beginning, but they will bring in new concepts faster than you can swallow them.

    Anyways, that's my take on it. Maybe I should give it a read when time permits.

    Of course, I did bookmark them for reference. :approve:
     
  17. Feb 6, 2006 #16

    mathwonk

    User Avatar
    Science Advisor
    Homework Helper
    2015 Award

    probably you are right aboit those pre PhD notes going too fast for beginners. what do you think of michael artin's book: Algebra? that was written for MIT sophomores.

    It may also be a bit terse, but he really knows his stuff if you can hang with him.
     
  18. Feb 6, 2006 #17

    mathwonk

    User Avatar
    Science Advisor
    Homework Helper
    2015 Award

    to learn as much as possible in a finite amount of time, i recommend anything by richard courant, like "what is mathematics", or his calculus books.
     
  19. Feb 6, 2006 #18

    JasonRox

    User Avatar
    Homework Helper
    Gold Member

    I've never read or seen Artin's book at the moment. I hear his name roaming around on PF as a recommended author for math books though. His name is certainly familiar.

    I have I.N. Herstein's text for Abstract Algebra, but I'm not positive whether or not they relate. I think Herstein's text has been good so far for me. I also have Gallian's text for Abstract Algebra too, but I find it a little incomplete and that it lacks rigor in some topics (that I read so far).
     
  20. Feb 8, 2006 #19
    Leopold,

    Listen, there is nothing wrong with asking for help. I am no math wiz myself but I'm doing the same thing as you so I think I can help.

    I'm going back to school this fall for physics, and I haven't been doing really any math other than everyday kind of stuff since my first year of college; which was about 11 1/2 years ago. Anyhow I took AP calc in highschool, and then my first year of college, but I literally remember nothing, I didn't even remember algebra. About 2 months ago I started trying to re-teach myself what I forgot and teach myself things I never learned.

    At first I tried to use a calculus book, but that was useless, I had the same problem as you; I didn't understand everything they were talking about, so I went back to the beginning. I started with a quick review of pre-algebra concepts, then I went to algebra 1, after that I started getting into more difficult problems in algebra. Right now I'm starting to re-learn what I need for trig and calc.

    Now, since you're fresh out of school you probably don't need to start as far back as I did, but begin with the basics, then move up slowly. There are also a lot of great sites on the web that help with math, one good site for help with algebra, and the base concepts that you'll need to move on to higher math is http://www.purplemath.com/.

    A good claculus site, that breaks everything down peice by peice so you can start at the beginning, or go to what you are wondering about is http://www.karlscalculus.org/index.shtml.

    I know it's hard sometimes to understand what the authors are trying to say when you're self teaching. The problem is that they understand what they are writing about about so a lot of times they forget to explain things better. Anyhow, I hope this helps you.
     
  21. Feb 13, 2006 #20
    Hi Leopold

    In addition to the sites already recommended, I thought you may want to have a look at this one: http://tutorial.math.lamar.edu/sitemap.aspx.

    I found the notes on this site very detailed (scroll down the page, past the 'cheat sheets'), and they also cover a variety of levels, ranging from pre-calculus algebra and basic trigonometry to multivariate calculus, differential equations, etc.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Where to start self study of higher mathematics?
  1. Where to start? (Replies: 5)

  2. Mathematics self-study (Replies: 6)

  3. Where to Start? (Replies: 2)

Loading...