江崎研のTeppei先輩が「理科系の作文技術」の本からまとめてくれました。

# Category Archives: Research

# Algebraic Topology Resources

TODO: more about lecture notes

## Books

## Lecture notes

http://language-and-engineering.hatenablog.jp/entry/20140705/AlgebraicTopologyPDFLectureNotes

## Video

Algebraic Topology by N. J. Wildberger Prof. at UNSW

## Others

# TDA Resources

# Topology Resources (books, lectures, videos)

## Books

- 「位相への３０講」：集合の各要素に対し「近さ」(距離) の概念を導入すれば，位相空間になる。何かの集合や空間を定量的に扱うには，位相の考え方が必要になる。

# Handbook of Discrete and Computational Geometry (3rd Edition, 2016)

http://www.csun.edu/~ctoth/Handbook/HDCG3.html

**Previous editions:**

*Handbook of Discrete and Computational Geometry*, First Edition

J.E. Goodman and J. O’Rourke, editors,

CRC Press LLC, Boca Raton, FL, 1997.

ISBN 978-0849385247 (52 chapters, xiv + 991 pages).*Handbook of Discrete and Computational Geometry, Second Edition*

J.E. Goodman and J. O’Rourke, editors,

CRC Press LLC, Boca Raton, FL, 2004.

ISBN 978-1584883012 (65 chapters, xvii + 1539 pages).

# Notes on the Nash embedding theorem

Terence Tao notes on embedding theorem.

Throughout this post we shall always work in the smooth category, thus all manifolds, maps, coordinate charts, and functions are assumed to be smooth unless explicitly stated otherwise.

A (real) manifold $latex {M}&fg=000000$ can be defined in at least two ways. On one hand, one can define the manifold *extrinsically*, as a subset of some standard space such as a Euclidean space $latex {{bf R}^d}&fg=000000$. On the other hand, one can define the manifold *intrinsically*, as a topological space equipped with an atlas of coordinate charts. The fundamental *embedding theorems* show that, under reasonable assumptions, the intrinsic and extrinsic approaches give the same classes of manifolds (up to isomorphism in various categories). For instance, we have the following (special case of) the Whitney embedding theorem:

Theorem 1 (Whitney embedding theorem)Let $latex {M}&fg=000000$ be a compact manifold. Then there exists an embedding $latex {u: M rightarrow {bf…

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# Seizure Prediction Challenge Intro.

## About challenge

Current challenge:

Previous challenges:

- American Epilepsy Society Seizure Prediction Challenge (Aug. 2014)
- UPenn and Mayo Clinic’s Seizure Detection Challenge (May 2014)