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Which topics are considered "graduate-level" for the following subjects:

  • Linear algebra
  • Multivariable calculus

On Internet, it is said that you need "graduate level" Linear algebra and multi-variable calculus for understanding Stochastic calculus, but topics are not mentioned.

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    @gt6989b, thanx, but subject/topics that you mentioned are my step number 2, but I also learned from net that you need some LA and MVC, how much is my question, I am an engineer, if I already know this "how much", then I cam happily start with RA and Measure theory2012-10-23

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Basically, you need to understand the abstract properties of Linear Algebra, e.g. group theoretic properties, etc. This is in contrast to "undergraduate" Linear Algebra, which focuses primarily on computational aspects and some basic algebraic properties (e.g. rank-nullity theorem, etc.).

For graduate-level multivariable calculus, you need to understand rigorous proofs regarding integration and differentiation in $\Bbb R^n$, as well as analytic properties of differential forms. This differs from undergraduate multivariable calculus, which again is typically computational, and focuses on vector calculus and use of Green's/Stoke's Theorems, rather than their construction and proof.

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    My last comment got mangled when I fat-fingered my phone. It should end "and also an abstract algebra book."2012-10-25