Good Resources / Best way to self study mathematical methods.

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    (Original post by atsruser)
    for strong graduate students!!! Not really introductory stuff, is it?
    I wouldn't say the Mechanics one is for strong graduates, it should make a good companion through an undergraduate degree.

    Many of the others, yes.
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    (Original post by mik1a)
    I wouldn't say the Mechanics one is for strong graduates, it should make a good companion through an undergraduate degree.

    Many of the others, yes.
    Anyway, it is too much for me to understand. (Looked through the online version.)
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    Many many thanks!!
    (Original post by atsruser)

    Is there some prerequisite that you need to learn first?
    - Are you procrastinating in opening the books due to fear, as it seems too daunting?
    - Are you not sure where to start?
    This is the main problem so far.
    - Do you lack the right resources (books, videos, etc)?
    I find it extremely difficult to choose right materials from the plethora of resources.

    Once you know why you are having trouble, you can start to solve the real problem.

    Note that these days, it is entirely feasible for someone intelligent to learn a huge amount of maths/physics on their own - there are countless internet resources, and fora where you can pose questions. Much of it will come down to the time that you can devote to the subject. You need a lot of time to read and solve problems.

    No. You'll need lots of different books. Read as many different books as you can - sometimes it's just nice to go from one to another when you get bored of the first, sometimes one book will be weak on a particular area, but good on others.

    Note that there are many free maths/physics book these days. I can recommend some if you wish.
    That would be great. One on mathematical analysis (not Rudin's) please.

    Handy hint: if you want to learn theoretical physics properly, I'd split your time about 70%/30% towards mathematics initially - the mathematics will take longer to learn than the physics, IMHO.
    Will I be in a good shape if I follow the following as the general guideline to learn mathematics?
    https://courses.maths.ox.ac.uk/

    I am not sure how should I go on with this path. Could you please lend me some piece of advice? Thank you!!!

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    (Original post by tangotangopapa2)
    My current financial situation will not let me go to regular university (unless I wait 3 years to be eligible for student finance) so I think OU is the only option for me as I can study whilst working.

    I wish to become a theoretical physicist and I am aiming to get into Oxford University for my graduate course.

    I am finding it hard to choose between mathematics and mathematics & physics. (Latter would require me to do practicals, find laboratory and so on)

    Undergraduate in mathematics would lead to graduate in Theoretical Physics, wouldn't it?

    I am 18 yo atm and currently have A* in Mathematics, A in Physics and A in Further Mathematics. (I taught myself all of this in approximately 4 months.)
    I also have AS equivalents in Biology and Chemistry.

    How is course quality like at OU?
    Does it worth waiting 3 years instead? (to go to proper University)

    Any suggestion would be highly appreciated.
    Thanks in advance.
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    (Original post by tangotangopapa2)
    I came to the UK three months ago and decided to study Physics. In order to get into University, I needed A-levels, so I decided to teach myself Physics, Maths and Further Maths in less than two months, which proved to be harder than I had expected. My summer exams are going on and each paper tells me that I was not prepared enough for it. Resits are not in my options. Even if I manage to get acceptable grades, UCAS process is daunting. There is a section called reference and I can not (will not be able to) find a reference as I have no teacher to do this for me. In fact I am my teacher and I can not do this for myself.


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    (Original post by tangotangopapa2)
    Many many thanks!!
    This is the main problem so far. I find it extremely difficult to choose right materials from the plethora of resources. That would be great. One on mathematical analysis (not Rudin's) please.
    Sorry for the delay. Here's a brief list. It's very incomplete though:

    1. Mathematical methods for physics - Nearing.

    Available online. Very nice, detailed, intuitive approach to the subject of the title.

    2. Lebl - Real Analysis.

    Available online. There are many real analysis texts available. I like this one as it is quite short and comprehensible.

    3. Advanced Calculus - Schaum.

    Not legally available online. Nice and fairly detailed overview of a large set of useful maths (real/complex analysis, multivariable/vector calculus, Laplace/Fourier transforms/series, etc), with lots of nice solved problems. Look at the contents on Amazon. One of my goto books when I've forgotten something basic and need a reminder.

    4. Introduction to Linear Analysis - Kreider, Kuller, Ostberg, Perkins.

    Classic, classic text on rigorous treatment of linear operators, linear DEs (methods of solution, wave/heat equations etc), Laplace transforms, Fourier series, and much more. Sadly out of print, and more useful once you're at "2nd year" level. Maybe available second hand, but steal someone else's copy if necessary.

    5. Complex Analysis - Schaum.

    Not legally available online. You probably want another intro text (not sure which), but this provides lots of worked examples and problems, and has a pretty good, if brief, theoretical treatment of a lot of stuff.

    6. 3000 Solved Problems in Calculus - Schaum.

    Not legally available online. Contents well described by title. Single/multivariable calculus + stuff on limits, and some on vectors.

    You also need a linear algebra text, but I don't know of any really good ones. Maybe someone else can make a suggeston. Again many available online.

    Will I be in a good shape if I follow the following as the general guideline to learn mathematics?
    https://courses.maths.ox.ac.uk/
    Yes. Learn all of that and you could skip straight to a PhD. It'll take a few years of full-time study though.
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    You may want to take a look at MIT OpenCourseWare.
    https://ocw.mit.edu/index.htm

    One good linear algebra book to look at after taking MIT Linear Algebra is Linear Algebra Done right.
    http://www.linear.axler.net/
 
 
 
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