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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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    I would definitely add being very comfortable with measure-theoretic Probability and Real Analysis.2012-10-23
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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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    Of course, for any given undergraduate program, your mileage may vary.2012-10-23
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    thanx, can you tell which chapters of Linear algebra by Shilov will constitute "graduate level" linear algebra and same for Multi Variable Calculus by Edwards2012-10-23
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    I cannot, because I do not own those books. Perhaps I can find the TOC on Google.2012-10-23
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    @Vikram Looking at previews in Google, I would say that probably none of the chapters in either of those books covers true graduate-level material. Maybe some of the later chapters in Shilov covers some material, but it appears to largely be computational.2012-10-23
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    thank you, but unfortunately you increased my worries/tension( :s hehe..), don't know how much I will have to cover before embarking on Stochastic Calculus... (phew...)!2012-10-24
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    Take a look through Rudin's *Principles of Mathematical Analysis*, particularly chapters 9-11, and also an abstract algebra.bo2012-10-24
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    thanx, I will..2012-10-25
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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