https://github.com/mbrandonw/my-math-notes

All of my math stuff from grad school.
https://github.com/mbrandonw/my-math-notes

computer-science graduate-school homotopy-theory invariants khovanov-homology manifold math physics topology

Last synced: 4 days ago
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All of my math stuff from grad school.

• Host: GitHub
• URL: https://github.com/mbrandonw/my-math-notes
• Owner: mbrandonw
• License: mit
• Created: 2014-09-09T13:08:42.000Z (about 10 years ago)
• Default Branch: master
• Last Pushed: 2018-01-17T01:32:26.000Z (almost 7 years ago)
• Last Synced: 2024-10-12T08:30:55.877Z (about 1 month ago)
• Topics: computer-science, graduate-school, homotopy-theory, invariants, khovanov-homology, manifold, math, physics, topology
• Language: TeX
• Size: 3.74 MB
• Stars: 52
• Watchers: 6
• Forks: 7
• Open Issues: 0
• Metadata Files:
  • Readme: README.md
  • License: LICENSE

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README

        
# My Math

I was in graduate school for a number of years, and this is a collection of the notes/papers I wrote.

## [Homotopy Theory](./homotopy-theory)

Homotopy Theory is the most important field in  all of mathematics, physics and computer science. So, these are some of my notes on it.

## [Low Dimensional Topology](./low-dimensional-topology)

Notes I made while preparing for my [oral exam](./oral-exam).

## [Classifying Spaces and Representability Theorems](./classifying-spaces-and-representability-theorems)

The foundations and statement of the Brown Representability Theorem, a very general result on representing functors as morphisms into a single object. There is a far more general result known as the [Yoneda Lemma](http://en.wikipedia.org/wiki/Yoneda_lemma) that is very applicable to computer science.

## [Computations in Khovanov Homology](./computations-in-khovanov-homology)

Just some examples of how to compute an object known as [Khovanov Homology](http://en.wikipedia.org/wiki/Khovanov_homology).

## [Gauge Theory](./gauge-theory)

I spent one summer trying to learn some physics and this is the resulting notes.

## [Lee's Variant of Khovanov Homology](./lees-variant-of-khovanov-homology)

Notes on Lee's variant of Khovanov homology, which leads to a spectral sequence.

## [Knot Theory](./knot-theory)

Very rough and incomplete notes on some basic knot theory.

## [Oral Exam Syllabus](./oral-syllabus)

Syllabus for my oral exam in graduate school.

## [Spectral Sequences](./spectral-sequences)

An incredibly complicated object arising often in algebra and topology.

## [State Sum Invariants of Links and Manifolds](./state-sum-invariants-of-links-and-manifolds)

Very rough and incomplete notes on some basic state sum invariants of links and manifolds.