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    Hello there!

    I am going to begin my undergraduate physics course in October. I am presently in my gap year and want to spend the time in studying more mathematics.

    Mathematical content in physics and engineering course seem to ignore the rigor and formalism pure mathematics. However, I want to learn "Mathematics", not just "Applied Mathematics".

    I am seeking advice on how I should organise my gap year study so that I get a rigorous introduction to mathematics. I am presently studying calculus and basic analysis.

    Please suggest a suitable sequence of mathematical topics for me.

    Thanks in advance.
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    First and Second Order (Homogeneous and Non-) Differential Equations.

    Vectors (a must for Physics).

    Matrix Algebra.

    Fourier Series/Transform.

    Laplace Transform.

    You won't even need all of that for your first year. I do an Electronic Engineering degree at a good uni and the Mathematics involved was barely above A-Level in the first year. Second year, different story!!
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    (Original post by Omio)
    Hello there!

    I am going to begin my undergraduate physics course in October. I am presently in my gap year and want to spend the time in studying more mathematics.

    Mathematical content in physics and engineering course seem to ignore the rigor and formalism pure mathematics. However, I want to learn "Mathematics", not just "Applied Mathematics".

    I am seeking advice on how I should organise my gap year study so that I get a rigorous introduction to mathematics. I am presently studying calculus and basic analysis.

    Please suggest a suitable sequence of mathematical topics for me.

    Thanks in advance.
    Linear algebra and differential equations..
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    So what does the equation in your sig mean?
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    (Original post by electriic_ink)
    So what does the equation in your sig mean?
    I'd be interested to know this too :holmes:
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    The most important thing in terms of preparation is: integration; vectors, matrix multiplication and a good understanding of polar coordinates will also help.

    If you're interested, in the first year I've covered:
    hyperbolic functions, convergence of series, Taylor series, complex numbers (standard, polar & trig forms & solving complex equations), limits of functions, matrices (Gaussian elimination, inverse, eigenvalues and eigenvectors, diagonalisation of square & non-square matrices), vectors (including 2D, cylindrical and spherical polar coordinates), ordinary differential equations (first-order separable, homogeneous & linear; second-order linear homogeneous & non-homogeneous), Fourier series, partial derivatives, separable partial differential equations (first and second-order), multi-dimensional integration (Cartesian and polar), line integrals... plus a fair bit of repetition of A-levels.
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    (Original post by electriic_ink)
    So what does the equation in your sig mean?
    the Schrödinger equation
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    Schrodinger you sick, sick man.
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    If you want to study analysis, the order in which we're taught at Cambridge for the first analysis course, which seems pretty natural is:

    Sequences
    Series
    Continuity
    Differentiability
    Taylor's Theorem
    Integration

    I'd say linear algebra is something that you might want to consider looking into, as well as perhaps group theory (or more generally [abstract] algebra). There's nothing wrong with studying them all at the same time, and in fact these three major areas (analysis, linear algebra, group theory) which maths students meet are not dependent on one another.
 
 
 
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