Topology in many particle systems

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Discussion Overview

The discussion revolves around understanding lecture notes on topology in many particle systems, particularly focusing on the prerequisites and foundational knowledge required to grasp the material. Participants express varying levels of familiarity with the topic and related mathematical concepts.

Discussion Character

  • Homework-related
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant expresses confusion about the lecture notes and requests help, indicating a lack of background knowledge in topology.
  • Another participant asks for more specific questions to provide targeted assistance.
  • A participant mentions not understanding the Hessian matrix and its diagonalization, indicating a gap in prerequisite knowledge.
  • It is noted that the Hessian matrix relates to multi-variable calculus, which is not strictly topology.
  • One participant suggests that the original poster may not be prepared for the material, as it assumes knowledge of multi-variable calculus, typically covered in earlier undergraduate courses.
  • Another participant appreciates the notes and inquires about the author and additional resources, indicating interest in the content despite the challenges faced by the original poster.

Areas of Agreement / Disagreement

Participants generally agree that the lecture notes require a certain level of mathematical background, particularly in multi-variable calculus. However, there is no consensus on how to address the original poster's difficulties, with some suggesting that the material may be too advanced.

Contextual Notes

There are indications of missing foundational knowledge, particularly in multi-variable calculus, which is necessary to understand the lecture notes. The discussion highlights the complexity of the material and the prerequisites that are not met by the original poster.

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Interesting notes, but what exactly do you need help with? You have to be more specific.
 
i basically have no bakground regarding topology that's why i cannot understand even from start:frown:like i don't know what hessian matrix is?
its diagnolization etc.
i started reading these notes many times but coudnt get any thing:cry:
what to do ?
 
tayyaba aftab said:
i basically have no bakground regarding topology that's why i cannot understand even from start:frown:like i don't know what hessian matrix is?
its diagnolization etc.

Well, do you know what a http://en.wikipedia.org/wiki/Jacobian_matrix_and_determinant" is? This isn't topology, it's multi-variable calculus. It's the matrix of the partial derivatives of one set of coordinates with respect to another set of coordinates. (see link for examples)

A Hessian matrix is the same thing, just for the second-order derivatives.
 
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:cry: buttttttttttttttttttttt what about rest of the notes?
:confused:
 
Honestly, I think you're out of your league with those lecture notes. If you get stuck in the second paragraph of the first page on 'mathematical preliminaries' (things you should already know before taking that course), then you're simply not ready for it.

Specifically, multi-variable calculus (which covers Hessians) is first or second-year stuff for a physics undergrad, whereas those lecture notes are for a graduate course.

Nobody is going to even attempt to explain an entire course on a message board. And asking to fill in several years of missing prerequisite knowledge is just absurd.
 
That said, I like these notes. Who wrote them? Are there more where these came from?
 
genneth said:
That said, I like these notes. Who wrote them? Are there more where these came from?

I googled the info at the top of the notes - it's Joel Moore at UC Berkeley.

There are a few more on the Physics 250 site.
 
Link:
http://socrates.berkeley.edu/~jemoore/Physics_250.html
 
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