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Jacobian Matrix
|
Matrix Usages
|
Jun 2, 2023
|
Alan Jo
|
Alan Jo
|
Jun 2, 2023
|
ํ๋ ฌ์ ์์๋ค์ ๋ชจ๋ 1์ฐจ ๋ฏธ๋ถ ๊ณ์๋ก ๊ตฌ์ฑ ์ฆ ๋ฏธ์ ๋ณํ์ ๊ดํ ์ ํ ๋ณํ
๊ตญ์ ์์ญ์์ย **๋น์ ํ ๋ณํ์ ์ ํ ๋ณํ์ผ๋ก ๊ทผ์ฌ**
### Jacobian Matrix Usages
|Title|
|:-:|
> [Jacobian prerequisite knowledge (video) | Khan Academy](https://www.khanacademy.org/math/multivariable-calculus/multivariable-derivatives/jacobian/v/jacobian-prerequisite-knowledge)
> [์์ฝ๋น์(Jacobian) ํ๋ ฌ์ ๊ธฐํํ์ ์๋ฏธ - ๊ณต๋์ด์ ์ํ์ ๋ฆฌ๋
ธํธ (Angelo's Math Notes)](https://angeloyeo.github.io/2020/07/24/Jacobian.html)
> [Jacobian matrix and determinant](https://en.wikipedia.org/wiki/Jacobian_matrix_and_determinant)
|
3d36041b4bf64dcd96bd06ff680fe810
|
|
***Matrix Computation***
|
Matrix Usages
|
Jun 20, 2022
|
Alan Jo
|
Alan Jo
|
Apr 6, 2023
|
[AI Library](https://texonom.com/ai-library-30022d621bfd4843b908559bf1f6c1ac) [Machine Learning](https://texonom.com/machine-learning-96195e7f57d74bcf9e8719a53394e421)
|
### ***Matrix Computation Library***
|Title|
|:-:|
|[bolt dbalock](https://texonom.com/bolt-dbalock-2596f1659f5748009f1f41e5050d23ef)|
|
af84cd99a7d047caa70d3517e26f73e3
|
Matrix Derivative
|
Matrix Usages
|
Apr 17, 2023
|
Alan Jo
|
Alan Jo
|
Apr 17, 2023
|
[Transpose of Matrix](https://texonom.com/transpose-of-matrix-639bc5b5563c4c54b3e9ef0f37342bee)
|
ํ๋ ฌ ํฌ๊ธฐ ์ค์ด๋ ๋ฐฉํฅ์ผ๋ก, ์๋๋ฉด transpose
$$x^TB \rightarrow B \newlinex^Tb \rightarrow b \newlinex^Tx \rightarrow 2x \newlinex^TBx \rightarrow 2Bx \newliney^TBx \rightarrow B^Ty \newline$$
### Matrix Derivative Usages
|Title|
|:-:|
|[Hessian Matrix](https://texonom.com/hessian-matrix-e1ebbf5284284a1793233973648ef0b6)|
> [Untitled](https://atmos.washington.edu/~dennis/MatrixCalculus.pdf)
> [Untitled](http://www.gatsby.ucl.ac.uk/teaching/courses/sntn/sntn-2017/resources/Matrix_derivatives_cribsheet.pdf)
|
67e3bac465684331aa5205893b542749
|
Matrix Padding
|
Matrix Usages
|
Apr 6, 2023
|
Alan Jo
|
Alan Jo
|
Apr 6, 2023
|
### Normally Zero Padding which fills 0
์ฃผ์ด์ง ํ๋ ฌ์ ํฌ๊ธฐ๋ฅผ ์ผ์ ํ ํฌ๊ธฐ๋ก ๋ง์ถ๊ธฐ ์ํด ์ถ๊ฐ๋๋ ๊ฐ
|
0f44aaaee9d54bb3a6960130541ac90a
|
|
bolt dbalock
|
Matrix Computation Library
|
Jun 20, 2022
| null | null | null | null |
### 10x faster matrix and vector operations
[bolt](https://github.com/dblalock/bolt)
|
2596f1659f5748009f1f41e5050d23ef
|
**Hessian Matrix**
| null | null | null | null | null | null |
### Math
์ด๋ค ํจ์์ 2๊ณ ๋ํจ์๋ค์ ์ด์ฉํ์ฌ ํ๋ ฌ์ ๋ง๋ ๊ฒ ๊ทธ๋ฌ๋ฏ๋ก
**ํค์์ ํ๋ ฌ์ 2์ฐจ ๋ฏธ๋ถ๊ณ์์ ๋น์ทํ ์๋ฏธ๋ฅผ ๊ฐ๋๋ค**
$$H_{ij} = \frac{\partial^2l(\theta)}{\partial\theta_i\partial\theta_j}$$
### Geometry
ํค์์ ํ๋ ฌ์ ์ด์ฉํ๋ฉด ํน์ ํจ์์ ํน์ ์์น๊ฐ ์๋ก ๋ณผ๋กํ์ง, ์๋๋ก ๋ณผ๋กํ์ง, ์์ฅ์ ์ธ์ง๋ฅผ ํ๋จํ ์ ์๋ค๋ ์๋ฏธ
๊ธฐ๋ณธ bowl์ ํํ๋ฅผ ๋ ๋ณผ๋กํ๊ฑฐ๋ ์ค๋ชฉํ๊ฒ ๋ง๋๋ ๊ธฐํํ์ ์ธ ๋ณํ์ ์ํํด์ฃผ๋ ์ญํ
> [ํค์ธ ํ๋ ฌ(Hessian Matrix)์ ๊ธฐํํ์ ์๋ฏธ](https://angeloyeo.github.io/2020/06/17/Hessian.html)
|
e1ebbf5284284a1793233973648ef0b6
|
Anisotropic
|
Vector Notion
|
May 18, 2023
|
Alan Jo
|
Alan Jo
|
Jul 10, 2023
|
์ด๋ฐฉ์ฑ
์ฃผ์ด์ง ๊ณต๊ฐ์์ ํน์ ๋ฐฉํฅ์ผ๋ก๋ง ํฅํด ์์ด์ ์ผ์ข
์ cone ํํ๋ฅผ ์ด๋ฃจ๊ณ ์๋ ๊ฒ
> [Contextual Embedding - How Contextual are Contextualized Word Representations?](https://velog.io/@stapers/Contextual-Embedding-How-Contextual-are-Contextualized-Word-Representations)
|
56427ad6cfc84d46a0b46606b25bb7bd
|
|
Isotropic
|
Vector Notion
|
May 18, 2023
|
Alan Jo
|
Alan Jo
|
Jul 10, 2023
|
**๋ฑ๋ฐฉ์ฑ**
๋ฐฉํฅ๊ณผ ์๊ด์๋ ์ฑ์ง
๋ฒกํฐ๊ฐ ์ฃผ์ด์ง ๊ณต๊ฐ์์ ๋ชจ๋ ๋ฐฉํฅ์ผ๋ก ์กด์ฌํ๋ ์ํฉ
|
13d450b4d2d24ef18af47546f578c3e7
|
|
Linear Independent
|
Vector Notion
|
Nov 5, 2019
|
Alan Jo
|
Seong-lae Cho
|
Sep 13, 2023
|
[Linearity](https://texonom.com/linearity-53be0991221249d794ed8047fe36ecb5)
|
### Linear Independent notion
|Title|
|:-:|
|[Orthogonality](https://texonom.com/orthogonality-d694f04a603d46f18da03a4dc737ca51)|
|[Linear Dependent](https://texonom.com/linear-dependent-895c1bc53e2f48b494ef2e2837c16bbf)|
> [์ง๊ต์ฑ(orthogonality)์ ๊ณตํ์ ์๋ฏธ](https://satlab.tistory.com/37)
|
da490558cce24664be62d499d40b96a2
|
Unit Vector
|
Vector Notion
|
Oct 10, 2022
|
Alan Jo
|
Alan Jo
|
Apr 6, 2023
|
## Normalized Vector
**A unit vector**ย is often denoted by a lowercase letter with a circumflex, or "hat"
### Unit Vectors
|Title|
|:-:|
|[Orthonormal Vectors](https://texonom.com/orthonormal-vectors-6c05c455048d4d729c7a86ad3802b339)|
|
9d0e1e60888c4f338745830b40584981
|
|
Vector Operation
|
Vector Notion
|
Apr 6, 2023
|
Alan Jo
|
Alan Jo
|
Apr 6, 2023
|
### Vector Operations
|Title|
|:-:|
|[Inner product](https://texonom.com/inner-product-0362165a5a3d490784d9c3ff41b2b19f)|
|[Outer Product](https://texonom.com/outer-product-4106750021e944d985d7fdb1b42570ae)|
|[Vector Addition](https://texonom.com/vector-addition-e75327dc94934cbb895656ca08112007)|
|[Vector Multiplication](https://texonom.com/vector-multiplication-aa46ebeebb3a4aa2bdd459a13dc655dd)|
|
61d2aa5fe6594af7a30b45309946b2d7
|
|
Vector Space
| null | null | null | null | null | null |
a module over a field, which also carries a multiplication operation that is compatible with the module structure
### Vector Space Notion
|Title|
|:-:|
|[Subspace](https://texonom.com/subspace-e559a723195a4ae5bda391c3332695d6)|
|[Basis Vector](https://texonom.com/basis-vector-374bc63669314745b4513e0ba77704d5)|
|[Inner Product space](https://texonom.com/inner-product-space-47e25eabbade4a0f923601f5f58255b2)|
|
7681a959944242619d201953076294f2
|
Orthonormal Vectors
| null | null | null | null | null | null |
๋ฐ๋์ย **ํย ์ ์ด์์ ๋ฒกํฐ๋ก๋ถํฐ ์ ์๋์ด์ผ**
> [[Linear Algebra] Lecture 17-(1) ์ง๊ตํ๋ ฌ(Orthogonal Matrices)๊ณผ ๊ทธ๋ ์๋ฏธํธ ๊ณผ์ (Gram-Schmidt Process)](https://twlab.tistory.com/37)
|
6c05c455048d4d729c7a86ad3802b339
|
Inner product
|
Vector Operations
|
Jan 23, 2022
|
Alan Jo
|
Alan Jo
|
Jun 11, 2023
|
## Dot Product
๋ด์ ์ ๋ ์ ํธ๊ฐ ์ผ๋ง๋ ๋ฎ์๋๋๋ฅผ ๊ณ์ฐํด์ฃผ๋ ์ผ์ด๊ธฐ๋ ํจ
[Commutative Property](https://texonom.com/commutative-property-216366d94b2d43fb87d11e87cc3a233a)
|
0362165a5a3d490784d9c3ff41b2b19f
|
|
Outer Product
|
Vector Operations
|
Jan 23, 2022
|
Alan Jo
|
Alan Jo
|
Apr 6, 2023
|
## Cross Product
- Anti [Commutative Property](https://texonom.com/commutative-property-216366d94b2d43fb87d11e87cc3a233a)
$$\vec{u} \times \vec{v} = - \vec{v} \times \vec{u}$$
|
4106750021e944d985d7fdb1b42570ae
|
|
Vector Addition
|
Vector Operations
|
Jan 23, 2022
|
Alan Jo
|
Alan Jo
|
Apr 6, 2023
|
move origin
|
e75327dc94934cbb895656ca08112007
|
|
Vector Multiplication
|
Vector Operations
|
Jan 23, 2022
|
Alan Jo
|
Alan Jo
|
Apr 6, 2023
|
### scaling scalars - change length
scaler can be [Commutative Property](https://texonom.com/commutative-property-216366d94b2d43fb87d11e87cc3a233a)
|
aa46ebeebb3a4aa2bdd459a13dc655dd
|
|
Basis Vector
|
Vector Space Notion
|
May 23, 2023
|
Alan Jo
|
Alan Jo
|
May 23, 2023
|
374bc63669314745b4513e0ba77704d5
|
||
Inner Product space
|
Vector Space Notion
|
Jun 6, 2023
|
Alan Jo
|
Alan Jo
|
Jun 6, 2023
|
47e25eabbade4a0f923601f5f58255b2
|
||
Subspace
|
Vector Space Notion
|
May 23, 2023
|
Alan Jo
|
Alan Jo
|
May 23, 2023
|
e559a723195a4ae5bda391c3332695d6
|
||
Vector Equation
|
Vector Usages
|
Oct 31, 2022
|
Alan Jo
|
Alan Jo
|
Oct 31, 2022
|
### Vector Equations
|Title|
|:-:|
|[Vector Equation of a Plane](https://texonom.com/vector-equation-of-a-plane-1f3a37a903984921bf16acf5bc138678)|
|[Vector Equation of a Line](https://texonom.com/vector-equation-of-a-line-40c9a0f52a944427a5c69456ca4b429c)|
|
122ad1c33c514ad3b2c9cee4aac00521
|
|
Vector Similarity
|
Vector Usages
|
Apr 28, 2023
|
Alan Jo
|
Alan Jo
|
Jun 5, 2023
|
[Latent Space](https://texonom.com/latent-space-d67b6bdef18b4058bfbc3d25f87ec087)
|
## Vectorized Pairwise Similarity
$$<a, b>$$
- [Inner product](https://texonom.com/inner-product-0362165a5a3d490784d9c3ff41b2b19f)
- [Euclidean Distance](https://texonom.com/euclidean-distance-0d3a8b5dc5e04ee595dc85365b2d3fd9)
### Pairwise similarity matrix
result value
### Vector Similarities
|Title|
|:-:|
|[Cosine Similarity](https://texonom.com/cosine-similarity-0686a915d71749b6aecbe611fd0f3efd)|
### Vector Similarity Algorithms
|Title|
|:-:|
|[HNSW Algorithm](https://texonom.com/hnsw-algorithm-2d387cef1103477f99d181e956f3d76d)|
|[KNN Algorithm](https://texonom.com/knn-algorithm-3b5f079c416349f5af4a54537c873d4b)|
|[Annoy Algorithm](https://texonom.com/annoy-algorithm-b91a06fdf7a64255a3f0452b28abd4df)|
### Vector Similarity Tools
|Title|
|:-:|
|[Faiss](https://texonom.com/faiss-445af9045d9c486995f31a2e75cff3ba)|
|
846675a408e74235acc836302110ab07
|
Vector Equation of a Line
|
Vector Equations
|
Oct 31, 2022
|
Alan Jo
|
Alan Jo
|
Oct 31, 2022
|
$$x = \vec{endpoint} + t \cdot\vec{direction}$$
if (t>0), it is ray
if t has a range, it is segment
### distance between one straight line and one point
$$D = \frac{\vec{AP} \times \vec{d}} {\vec{d}} = \overline{AP}sin{\theta} $$
### Distance between two lines
$$\vec{a_1} + t\cdot\vec{b_1}\vec{a_2} + t\cdot\vec{b_2}d = |\frac{(\vec{a_2} - \vec{a_1}) \cdot (\vec{b_1}\times \vec{b_2}) } {|\vec{b_1} \times \vec{b_2}|}|$$
> [Lesson Explainer: The Perpendicular Distance between Points and Straight Lines in Space | Nagwa](https://www.nagwa.com/en/explainers/939127418581/)
> [Shortest Distance Between Two Lines in 3D](https://www.youtube.com/watch?v=6vpXM1dskmY)
|
40c9a0f52a944427a5c69456ca4b429c
|
|
Vector Equation of a Plane
|
Vector Equations
|
Oct 31, 2022
|
Alan Jo
|
Alan Jo
|
Oct 31, 2022
|
$$\vec{normal} \cdot(\vec{x} - \vec{point}) = 0$$
> [Lesson Explainer: Equation of a Plane: Vector, Scalar, and General Forms | Nagwa](https://www.nagwa.com/en/explainers/373101390857/)
|
1f3a37a903984921bf16acf5bc138678
|
|
Cosine Similarity
|
Vector Similarities
|
Mar 10, 2023
|
Alan Jo
|
Alan Jo
|
Jun 1, 2023
|
์ฐจ์์ด ๋์์ง์๋ก [Curse of dimensionality](https://texonom.com/curse-of-dimensionality-343455a61aa14779b6edf4c93464fac3) ๋๋ฌธ์ ๊ฑฐ๋ฆฌํ์
์ ์๋ฏธ๊ฐ ์ ์ด์ง๋ค
๊ทธ๋์ ์ ์ฌ๋ ๊ฐ๋๋ก ๊ณ์ฐ
|
0686a915d71749b6aecbe611fd0f3efd
|
|
Annoy Algorithm
|
Vector Similarity Algorithms
|
Jun 1, 2023
|
Alan Jo
|
Alan Jo
|
Jun 1, 2023
|
## Approximate Nearest Neighbors
[annoy](https://github.com/spotify/annoy)
- ๊ทผ์ฌํด์ ๊ฐ๊น์ด ๋ฒกํฐ ์ฐพ์
- ๋ฐ์ดํฐ ์ถ๊ฐ๊ฐ ์ด๋ ต๋ค
|
b91a06fdf7a64255a3f0452b28abd4df
|
|
HNSW Algorithm
|
Vector Similarity Algorithms
|
Jun 1, 2023
|
Alan Jo
|
Alan Jo
|
Jul 13, 2023
|
[Small worlds Network](https://texonom.com/small-worlds-network-b779baa02bc846b5970d67d561d755c0)
|
## Hierarchical Navigable Small words
### HNSW Algorithm Notion
|Title|
|:-:|
|[Probability Based Skip List](https://texonom.com/probability-based-skip-list-9111e1422511456bbfb7e7c3fa227860)|
### HNSW Algorithm Tools
|Title|
|:-:|
|[HNSWlib](https://texonom.com/hnswlib-11dcfb3c5e5d448da1b0c7be3998520e)|
|[](https://texonom.com/b47fdad5d11f4717974fc3aac3d667bd)|
> [๋์ถฉ? ๊ฑฐ์ ์ ํํ๋ค! ๋ฒกํฐ ๊ฒ์ ์์ง์ ANN HNSW ์๊ณ ๋ฆฌ์ฆ ๋์
๊ธฐ (feat. SWIG Golang)](https://forward.nhn.com/2022/sessions/42)
|
2d387cef1103477f99d181e956f3d76d
|
KNN Algorithm
|
Vector Similarity Algorithms
|
Jun 1, 2023
|
Alan Jo
|
Alan Jo
|
Jun 1, 2023
|
3b5f079c416349f5af4a54537c873d4b
|
||
Probability Based Skip List
|
HNSW Algorithm Notion
|
Jun 1, 2023
|
Alan Jo
|
Alan Jo
|
Jun 1, 2023
|
|
9111e1422511456bbfb7e7c3fa227860
|
|
[pg_embedding](https://github.com/neondatabase/pg_embedding)
|
HNSW Algorithm Tools
|
Jun 1, 2023
|
Alan Jo
|
Alan Jo
|
Jul 13, 2023
|
b47fdad5d11f4717974fc3aac3d667bd
|
||
HNSWlib
|
HNSW Algorithm Tools
|
Jun 1, 2023
|
Alan Jo
|
Alan Jo
|
Jun 1, 2023
|
### HNSWlib Usages
|Title|
|:-:|
|[](https://texonom.com/2ab069bd60b3423faa91c460afa92955)|
|[hnswlib python](https://texonom.com/hnswlib-python-8b119e7305e74014b4761b8c40404767)|
|
11dcfb3c5e5d448da1b0c7be3998520e
|
|
[hnswlib-node](https://github.com/yoshoku/hnswlib-node)
|
HNSWlib Usages
|
Jun 1, 2023
|
Alan Jo
|
Alan Jo
|
Jun 1, 2023
|
2ab069bd60b3423faa91c460afa92955
|
||
hnswlib python
|
HNSWlib Usages
|
Jun 6, 2023
|
Alan Jo
|
Alan Jo
|
Jun 6, 2023
|
[hnswlib](https://github.com/nmslib/hnswlib)
### Index space
> [How to use the hnswlib.Index function in hnswlib | Snyk](https://snyk.io/advisor/python/hnswlib/functions/hnswlib.Index)
|
8b119e7305e74014b4761b8c40404767
|
|
Faiss
|
Vector Similarity Tools
|
Mar 10, 2023
|
Alan Jo
|
Alan Jo
|
Apr 28, 2023
|
> [Faiss ์์ํ๊ธฐ](https://velog.io/@nawnoes/Faiss-์์ํ๊ธฐ)
|
445af9045d9c486995f31a2e75cff3ba
|
|
**BLAS**
|
Linear Algebra Usages
|
Feb 21, 2022
|
Alan Jo
|
Alan Jo
|
Jun 5, 2023
|
## Basic Linear Algebra Subprograms
[nblas](https://texonom.com/nblas-e7eb59d9195848f78ee8e73cd23e916c)
> [์ธ์์ ๋ฐ๊พผ 10๊ฐ์ ์ปดํจํฐ ์ฝ๋ - Sciencetimes](https://www.sciencetimes.co.kr/news/%ec%84%b8%ec%83%81%ec%9d%84-%eb%b0%94%ea%be%bc-10%ea%b0%9c%ec%9d%98-%ec%bb%b4%ed%93%a8%ed%84%b0-%ec%bd%94%eb%93%9c/)
|
17d8d7491b2147829b88426574733651
|
|
Vectorious
|
Linear Algebra Usages
|
Jun 5, 2023
|
Alan Jo
|
Alan Jo
|
Jun 5, 2023
|
[vectorious](https://github.com/mateogianolio/vectorious)
Node js [N-API](https://texonom.com/n-api-8f1b5ef6b76847deb6e7dd2c688b82fd)
[nblas](https://texonom.com/nblas-e7eb59d9195848f78ee8e73cd23e916c)
|
fd5a587523a9423089cf74ae0899b8ce
|
|
nblas
|
BLAS
| null | null | null | null | null |
e7eb59d9195848f78ee8e73cd23e916c
|
|
Arithmetic Precision
|
Arithmetic Notion
|
Dec 17, 2021
|
Alan Jo
|
Alan Jo
|
Jun 6, 2023
|
์ ๋ฐ๋ ์ฐ์
### Highest-order operand
|
baffc5389f06430eb20806e985685c9b
|
|
Elementary arithmetic
| null | null | null | null | null | null |
57a9f00b3f30433299816f32b4d49fbd
|
|
**Fixed-point arithmetic**
|
Arithmetic Notion
|
Dec 17, 2021
|
Alan Jo
|
Alan Jo
|
Jun 6, 2023
|
> [Fixed-point arithmetic - Wikipedia](https://en.wikipedia.org/wiki/Fixed-point_arithmetic)
|
c46e0722c58c4e2fbc1d2f7027bf6fbe
|
|
The Tower Function
|
Calculus Examples
|
Aug 23, 2020
|
Alan Jo
|
Alan Jo
|
Aug 29, 2021
|
> [๋ฐ์ด ๋ฌดํํ ๊ณ์ ์๊ธฐ๋ ํจ์ 2ํ | The Power Tower Function](https://www.youtube.com/watch?v=doItxhmZavo)
> [์ญ์ฌ์ ์ต๊ณ ์ ์ํ์๋ ์ ์ ์์๋ ํจ์ #Shorts](https://www.youtube.com/watch?v=GPe9Lt8OAdM)
|
7a63cab2617a402782fbf88c9055d43c
|
|
Concave Point
|
Calculus Notion
|
Mar 9, 2023
|
Alan Jo
|
Alan Jo
|
Mar 9, 2023
|
c3f6835eb9ef4378830d3b916da3f074
|
||
Convex Point
|
Calculus Notion
|
Mar 9, 2023
|
Alan Jo
|
Alan Jo
|
Mar 9, 2023
|
160b14cc61114a8a9be9797578e11c7a
|
||
Derivation
|
Calculus Notion
|
Aug 29, 2021
|
Alan Jo
|
Alan Jo
|
Jun 11, 2023
|
[Vector Field](https://texonom.com/vector-field-ff7ea488edb74510a51e844eee7a222f) [Scalar Field](https://texonom.com/scalar-field-a0e05a5b310c4a6283bc214ec02383e0)
|
## Differentiation
### Derivation Notion
|Title|
|:-:|
|[Differential Equation](https://texonom.com/differential-equation-419a4e3d42924ec79afc700734b88996)|
|[Derivative](https://texonom.com/derivative-67f45809e7a84277be4fca74a3b86ceb)|
|[Gradient](https://texonom.com/gradient-685dfab242a4421da9f5bd89ae5975ed)|
|[Divergence](https://texonom.com/divergence-d8b434d51ae549db839bf075fa2452bb)|
|[Curl](https://texonom.com/curl-5472397a80234ddeb5d8dca28b9ccae2)|
|[Del](https://texonom.com/del-f6d1cdf554914c98a06c1180179bf401)|
|[Antiderivative](https://texonom.com/antiderivative-7e0e92c4cdcb4bc48c323100aa512c81)|
> [Gradient, Divergence, Curl์ ๋ํ์ฌ.](https://sillurian.tistory.com/10)
|
79d0547aee0d45ce93cdae0f26bc3ce6
|
Explicit Function
|
Calculus Notion
|
Nov 14, 2022
|
Alan Jo
|
Alan Jo
|
Mar 9, 2023
|
### ์ํจ์
์ข
์๋ณ์์ ๋
๋ฆฝ๋ณ์๋ค์ด ๋ถ๋ฆฌ๋ ํจ์
|
df8104e2876c42e9b112f6308718e3bc
|
|
Implicit Function
|
Calculus Notion
|
Nov 14, 2022
|
Alan Jo
|
Alan Jo
|
Dec 5, 2022
|
[Normal Vector](https://texonom.com/normal-vector-84412bdb0b8c43e3a206cd54bc9901f7)
|
### ์ํจ์
์ข
์๋ณ์๊ฐ ๋
๋ฆฝ๋ณ์์ ๋ถ๋ฆฌ๋์ง ์์ ํ๋์ ๊ด๊ณ์
### Implicit Function Notion
|Title|
|:-:|
|[Implicit Function Theorem](https://texonom.com/implicit-function-theorem-37a2205114464b178be0937046505686)|
|
1e383ff61a8b4831abca72e4c37649bd
|
I**nflection point**
|
Calculus Notion
|
Jan 11, 2022
|
Alan Jo
|
Alan Jo
|
Jan 11, 2022
|
๋ณ๊ณก์
|
6448287d912942cea85ee85a981505d6
|
|
Integral
|
Calculus Notion
|
Apr 5, 2022
|
Alan Jo
|
Alan Jo
|
Apr 5, 2022
|
### Integral Notion
|Title|
|:-:|
|[Lebesgue integral](https://texonom.com/lebesgue-integral-df7652d80314427db614b002c7a74de0)|
|[Riemann integral](https://texonom.com/riemann-integral-47f26748e1174265ae26d8a12b04fdca)|
|
ed91b8e9d33d49bfa6a32e93f7bfdfca
|
|
Local extremum point
| null | null | null | null | null | null |
f7a7579a29474436b2a8670a28fed921
|
|
Vector Calculus
|
Calculus Notion
|
Oct 30, 2022
|
Alan Jo
|
Alan Jo
|
Oct 30, 2022
|
[Vector](https://texonom.com/vector-9ed4d1c8519c496dbfadb1f6b3522255)
|
### Vector Calculus Notion
|Title|
|:-:|
|[Vector Differential Operator](https://texonom.com/vector-differential-operator-4f2b33fb3ea348ba978e3d117c8246a4)|
|[Vector Integral Theorem](https://texonom.com/vector-integral-theorem-2295053d5673460a927e2479d83070b8)|
> [Vector calculus - Wikipedia](https://en.wikipedia.org/wiki/Vector_calculus)
|
77976c6127ad49c9a6611e16a40f337f
|
Curl
|
Derivation Notion
|
Jun 11, 2023
|
Alan Jo
|
Alan Jo
|
Jun 11, 2023
|
[Outer Product](https://texonom.com/outer-product-4106750021e944d985d7fdb1b42570ae)
|
Derivative which map Vector field to Vector field
### describes theย infinitesimal circulation of a vector field
### Curl Notion
|Title|
|:-:|
|[Stokes' theorem](https://texonom.com/stokes-theorem-d3b508adeddc45c98a0f27d792b17999)|
> [Curl (mathematics)](https://en.wikipedia.org/wiki/Curl_(mathematics))
|
5472397a80234ddeb5d8dca28b9ccae2
|
Del
|
Derivation Notion
|
May 6, 2023
|
Alan Jo
|
Alan Jo
|
Jun 11, 2023
|
Del operator
nabla symbol
$$\nabla$$
|
f6d1cdf554914c98a06c1180179bf401
|
|
Derivative
|
Derivation Notion
|
Oct 30, 2022
|
Alan Jo
|
Alan Jo
|
May 6, 2023
|
[Gradient](https://texonom.com/gradient-685dfab242a4421da9f5bd89ae5975ed)
|
### Derivative Notion
|Title|
|:-:|
|[Partial Derivative](https://texonom.com/partial-derivative-e9c7ff432f1c43af8669ef0addd78cd9)|
|[Chain Rule](https://texonom.com/chain-rule-cdc4287f5b2a4bcda97886907836d5d0)|
|[Quotient Rule](https://texonom.com/quotient-rule-283d6806817f4684838f842865de0397)|
|
67f45809e7a84277be4fca74a3b86ceb
|
Differential Equation
|
Derivation Notion
|
Aug 29, 2021
|
Alan Jo
|
Alan Jo
|
Jun 15, 2022
|
### Differential Equation Notion
|Title|
|:-:|
### Differential Equation Methods
|Title|
|:-:|
|[Laplace Transform](https://texonom.com/laplace-transform-155ade7fe1bc4712b183339c25d68fda)|
|
419a4e3d42924ec79afc700734b88996
|
|
**Divergence**
|
Derivation Notion
|
Jun 11, 2023
|
Alan Jo
|
Alan Jo
|
Jun 11, 2023
|
[Inner product](https://texonom.com/inner-product-0362165a5a3d490784d9c3ff41b2b19f)
|
## Vector field to multi variable scalar function
### **Divergence Notion**
|Title|
|:-:|
|[Gauss Divergence Theorem](https://texonom.com/gauss-divergence-theorem-6b5f20e56c78488997efddf7f1fd2ebf)|
> [Divergence](https://en.wikipedia.org/wiki/Divergence)
|
d8b434d51ae549db839bf075fa2452bb
|
Gradient
|
Derivation Notion
|
Mar 16, 2023
|
Alan Jo
|
Alan Jo
|
Jun 11, 2023
|
### Derivate multi variable scalar function to vector field using [Partial Derivative](https://texonom.com/partial-derivative-e9c7ff432f1c43af8669ef0addd78cd9)
2์ฐจ์ผ ๋ ๋ฑ๊ณ ์ ๊ฐ๋
์ผ๋ก ์ดํดํ๋ฉด ์ฝ๋ค. ๊ทธ๋๋์ธํธ์ ํฌ๊ธฐ๋ ๊ฒฝ์ฌ๋
> [Gradient, Divergence, Curl์ ๋ํ์ฌ.](https://sillurian.tistory.com/10)
> [์ํ - Divergence ,Gradient, Curl[๋ฏธ์]](https://m.blog.naver.com/ptm0228/221676279348)
> [Gradient](https://en.wikipedia.org/wiki/Gradient)
|
685dfab242a4421da9f5bd89ae5975ed
|
|
**Stokes' theorem**
|
Curl Notion
|
Jun 11, 2023
|
Alan Jo
|
Alan Jo
|
Jun 11, 2023
|
d3b508adeddc45c98a0f27d792b17999
|
||
Chain Rule
| null | null | null | null | null | null |
> [Chain rule](https://en.wikipedia.org/wiki/Chain_rule)
|
cdc4287f5b2a4bcda97886907836d5d0
|
Partial Derivative
|
Derivative Notion
|
Oct 30, 2022
|
Alan Jo
|
Alan Jo
|
May 6, 2023
|
[Gradient](https://texonom.com/gradient-685dfab242a4421da9f5bd89ae5975ed)
|
๋ค๋ณ์ ํจ์์ ํน์ ๋ณ์๋ฅผ ์ ์ธํ ๋๋จธ์ง ๋ณ์๋ฅผ ์์๋ก ๊ฐ์ฃผํ์ฌ ๋ฏธ๋ถํ๋ ๊ฒ
Nabla์ ํผ์ฉํ์ง ์๊ธฐ
### partial f partial x
$$\frac{\partial f}{\partial x}$$
$$\lim_{h\rightarrow 0}\frac{f(x +h,y) - f(x,y)} {x + h - x}$$
### Partial Derivative Notion
|Title|
|:-:|
|
e9c7ff432f1c43af8669ef0addd78cd9
|
Quotient Rule
|
Derivative Notion
|
Jun 6, 2023
|
Alan Jo
|
Alan Jo
|
Jun 6, 2023
|
283d6806817f4684838f842865de0397
|
||
Laplace Transform
|
Differential Equation Methods
|
Jun 15, 2022
|
Alan Jo
|
Alan Jo
|
Sep 13, 2023
|
[Pierre-Simonย Laplace](https://texonom.com/pierre-simonlaplace-9a48a934756544579f8398d8a349029b)
|
ln์ผ๋ก ์ฒ๋ฆฌํ๊ณ ๋ฏธ๋ถ๋ฐฉ์ ์ ์ฒ๋ฆฌ์ ์ฉ์ดํ๋ค
๋ฐ์ฐํ๋ ํจ์์ ๋ํ [Fourier Transform](https://texonom.com/fourier-transform-5ee1f9063a9743dd9846ddc600286d5a)์ ์ ์ฉํ๊ธฐ ์ํ ๋ฐฉ๋ฒ
### Laplace Transform Notion
|Title|
|:-:|
> [7๋ถ๋ง์ ์ดํดํด๋ณด๋ ๋ผํ๋ผ์ค ๋ณํ](https://www.youtube.com/watch?v=4ONICadjLBY)
|
155ade7fe1bc4712b183339c25d68fda
|
****Gauss Divergence Theorem****
|
Divergence Notion
|
Jun 11, 2023
|
Alan Jo
|
Alan Jo
|
Jun 11, 2023
|
[Surface Integral](https://texonom.com/surface-integral-29bad5fdca49449bb4a96603905b160f) [Volume integral](https://texonom.com/volume-integral-41bc72e8ff194d54b11f16135b751348)
|
> [Divergence theorem](https://en.wikipedia.org/wiki/Divergence_theorem)
> [Gauss Divergence Theorem. Get the DEEPEST Intuition.](https://www.youtube.com/watch?v=zZqxbwl3Dno)
|
6b5f20e56c78488997efddf7f1fd2ebf
|
Implicit Function Theorem
|
Implicit Function Notion
|
Nov 14, 2022
|
Alan Jo
|
Alan Jo
|
Nov 14, 2022
|
> [Implicit function theorem - Wikipedia](https://en.wikipedia.org/wiki/Implicit_function_theorem)
|
37a2205114464b178be0937046505686
|
|
Lebesgue integral
|
Integral Notion
|
Apr 5, 2022
|
Alan Jo
|
Alan Jo
|
Jun 11, 2023
|
[Measure Theory](https://texonom.com/measure-theory-4fb6210801ea4d7abcb937cd068ba461) [Riemann integral](https://texonom.com/riemann-integral-47f26748e1174265ae26d8a12b04fdca)
|
### ๋ฅด๋ฒ ๊ทธ ์ ๋ถ
์ผ๋ฐ์ ์ธ ์ธก๋ ๊ณต๊ฐ ์์ ์ ์๋ ์ ์๋ ์ ๋ถ
์ค์์ ์์์์ ๋ฅด๋ฒ ๊ทธ ์ ๋ถ์ ๋ฆฌ๋ง ์ ๋ถ๋ณด๋ค ๋ ์ผ๋ฐ์
๋ฆฌ๋ง ์ ๋ถ์ด ์ ์๋์ง ์์๋ ๋ฅด๋ฒ ๊ทธ ์ ๋ถ์ด ์ ์๋๋ ํจ์๋ค์ด ์กด์ฌ
### Lebesgue integrals
|Title|
|:-:|
|[Surface Integral](https://texonom.com/surface-integral-29bad5fdca49449bb4a96603905b160f)|
|[Volume integral](https://texonom.com/volume-integral-41bc72e8ff194d54b11f16135b751348)|
> [๋ฅด๋ฒ ๊ทธ ์ ๋ถ - ์ํค๋ฐฑ๊ณผ, ์ฐ๋ฆฌ ๋ชจ๋์ ๋ฐฑ๊ณผ์ฌ์ ](https://ko.wikipedia.org/wiki/%EB%A5%B4%EB%B2%A0%EA%B7%B8_%EC%A0%81%EB%B6%84)
|
df7652d80314427db614b002c7a74de0
|
**Riemann integral**
|
Integral Notion
|
Apr 5, 2022
|
Alan Jo
|
Alan Jo
|
Apr 15, 2023
|
[Bernhard Riemann](https://texonom.com/bernhard-riemann-166d61214be5439ca5f7ba1090063a3e) [Lebesgue integral](https://texonom.com/lebesgue-integral-df7652d80314427db614b002c7a74de0)
|
๋ซํ๊ตฌ๊ฐ์ ์ ์๋ ์ค์ซ๊ฐ ํจ์์ ์ ๋ถ์ ์ข
๋ฅ
์ ์์ญ ๊ตฌ๊ฐ์ ์๊ฒ ๋๋ , ๊ฐ๊ฐ์ ์์ ๊ตฌ๊ฐ ์์ ๋์ด๋ฅผ ์ง์ฌ๊ฐํ์ ๋์ด๋ฅผ ํตํด ๊ทผ์ฌ
|
47f26748e1174265ae26d8a12b04fdca
|
Surface Integral
|
Lebesgue integrals
|
Jun 11, 2023
|
Alan Jo
|
Alan Jo
|
Jun 11, 2023
|
29bad5fdca49449bb4a96603905b160f
|
||
****Volume integral****
|
Lebesgue integrals
|
Jun 11, 2023
|
Alan Jo
|
Alan Jo
|
Jun 11, 2023
|
41bc72e8ff194d54b11f16135b751348
|
||
Vector Differential Operator
|
Vector Calculus Notion
|
Oct 30, 2022
|
Alan Jo
|
Alan Jo
|
Oct 30, 2022
|
[Derivation](https://texonom.com/derivation-79d0547aee0d45ce93cdae0f26bc3ce6)
|
### Vector Differential Operators
|Title|
|:-:|
|[Vector Curl](https://texonom.com/vector-curl-17571a486321485e80a305ac4bb93e19)|
|[Gradient Vector](https://texonom.com/gradient-vector-d3940976683946f89bd512d0bbf45672)|
|[Vector Divergence](https://texonom.com/vector-divergence-0ee28e695ecd48a68665f8a30cb7c864)|
> [Vector calculus - Wikipedia](https://en.wikipedia.org/wiki/Vector_calculus)
|
4f2b33fb3ea348ba978e3d117c8246a4
|
Vector Integral Theorem
|
Vector Calculus Notion
|
Oct 30, 2022
|
Alan Jo
|
Alan Jo
|
Oct 30, 2022
|
### Vector Integral Theorems
|Title|
|:-:|
> [Vector calculus - Wikipedia](https://en.wikipedia.org/wiki/Vector_calculus)
|
2295053d5673460a927e2479d83070b8
|
|
Gradient Vector
|
Vector Differential Operators
|
Oct 30, 2022
|
Alan Jo
|
Alan Jo
|
Oct 7, 2022
|
[Derivative](https://texonom.com/derivative-67f45809e7a84277be4fca74a3b86ceb) [Partial Derivative](https://texonom.com/partial-derivative-e9c7ff432f1c43af8669ef0addd78cd9)
|
$$\vec{z}, \vec{x} \text{ } is \text{ } \text{ on the surface } f(\vec{x}) = 0$$
$$\vec{z} = \vec{x} + \epsilon\vec{u} $$
$$f(z) = f(x + \epsilon u) - f(x_1 + \epsilon u_1, x_2 + \epsilon u_2, x_3 + \epsilon u_3)$$
$$h(x, y, z) = 0$$
$$\nabla h = (\frac{dh}{dx}, \frac{dh}{dy}, \frac{dh}{dz})$$
์ฌํํ๊ฒ ํธ๋ฏธ๋ถ์ผ๋ก ๊ตฌํด๋ ๋๊ณ
$$\nabla h = \frac{d\vec{h}}{dx} \times \frac{d\vec{h}}{dy}$$
xy ์๋๋๋ผ๋ ๊ณก๋ฉด์ ํด๋น ์ ํ๋ฉด์์์ ์์ง์ด๋ ๊ฑฐ๋ผ yz๋ xz ๋ ๊ฐ๋ฅ
> [Untitled](https://www.cs.ucr.edu/~craigs/courses/2022-fall-cs-130/lectures/normals.pdf)
|
d3940976683946f89bd512d0bbf45672
|
Vector Curl
|
Vector Differential Operators
|
Oct 30, 2022
|
Alan Jo
|
Alan Jo
|
Oct 30, 2022
|
**ํ์ Operator**
3์ฐจ์ ๋ฒกํฐ์ฅ์ ๋ค๋ฅธ 3์ฐจ์ ๋ฒกํฐ์ฅ์ผ๋ก ๋์์ํค๋ 1์ฐจ ๋ฏธ๋ถ ์ฐ์ฐ์์ ํ๋
|
17571a486321485e80a305ac4bb93e19
|
|
Vector Divergence
|
Vector Differential Operators
|
Oct 30, 2022
|
Alan Jo
|
Alan Jo
|
Oct 30, 2022
|
0ee28e695ecd48a68665f8a30cb7c864
|
||
Butterfly Effect
|
Chaos Theory Notion
|
Jun 22, 2021
| null | null | null |
62e1b65850da4b3ab2d429292473f8a1
|
||
Complex System
|
Chaos Theory Notion
|
May 16, 2022
| null | null | null |
> [Complex system - Wikipedia](https://en.wikipedia.org/wiki/Complex_system)
|
b2457d8f6fcc4fe2abffd71828908a1f
|
|
Lorenz Attractor
|
Chaos Theory Notion
|
Jun 22, 2021
| null | null | null |
b3249a819200420797f82e204cc9d58c
|
||
Combinatorics
|
Discrete Math Topics
|
May 13, 2023
|
Alan Jo
|
Alan Jo
|
May 13, 2023
|
887b47c6bb1c46388a8387d89bd304cf
|
||
Order Theory
|
Discrete Math Topics
|
May 13, 2023
|
Alan Jo
|
Alan Jo
|
May 13, 2023
|
8c7e8fb9638f41b19b6829d686fc6f9b
|
||
**Pigeonhole principle**
|
Discrete Math Topics
|
Nov 5, 2019
|
Alan Jo
|
Seong-lae Cho
|
May 13, 2023
|
๋น๋๊ธฐ์ง ์๋ฆฌ
|
998c7a67c04e43d28b132eaa02d5f0d8
|
|
Graph Signal Processing
|
Graph Theory Fields
|
Apr 28, 2023
|
Alan Jo
|
Alan Jo
|
Apr 28, 2023
|
## GSP
> [Untitled](https://web.media.mit.edu/~xdong/talk/BDI_GSP.pdf)
|
a6551be225984e4cad9bdd244d6a58b5
|
|
Dynamical System
|
Ergodic theory Notion
|
Apr 3, 2022
|
Alan Jo
|
Alan Jo
|
Aug 28, 2023
|
### Dynamical System Notion
|Title|
|:-:|
|[Dynamical systems theory](https://texonom.com/dynamical-systems-theory-b693764c797945f1b330d386a85ad936)|
|[Logistic Map](https://texonom.com/logistic-map-d968681610c749e9983e28f97ee5c50b)|
> [Dynamical system - Wikipedia](https://en.wikipedia.org/wiki/Dynamical_system)
|
a4e33185067b49b28e8f62454028f7b1
|
|
Poincare R**ecurrence **Theorem
|
Ergodic theory Notion
|
Nov 13, 2019
|
Alan Jo
|
Alan Jo
|
Jul 12, 2023
|
[Grigori Perelman](https://texonom.com/grigori-perelman-c53487e421c94fceb6a83431c7cc1149) [Henri Poincare](https://texonom.com/henri-poincare-1382da083d864065972f27c140c4aa64)
|
### ํธ์ต์นด๋ ์ฌ๊ท ์ ๋ฆฌ
ํน์ ํ ๊ณ๋ ์ถฉ๋ถํ ์๊ฐ์ด ์ง๋ ํ์๋ ์ด๊ธฐ์ํ์ ์์ฃผ ๊ฐ๊น์ด ์ํ๋ก ํ๊ทํ๋ค๋ ๋ด์ฉ์ ์ ๋ฆฌ
์๋์ง ์ค์๊ฐ ์ด์ฐ์ ์ธ ์์์ญํ์ ๊ณ์ ๋ํด์๋ ๋น์ทํ ์ ๋ฆฌ๊ฐ ์ฑ๋ฆฝ
> [Poincarรฉ recurrence theorem - Wikipedia](https://en.wikipedia.org/wiki/Poincar%C3%A9_recurrence_theorem)
|
1aca4c4a3d2446c1892de56b1071953c
|
**Dynamical systems theory**
|
Dynamical System Notion
|
Apr 3, 2022
|
Alan Jo
|
Alan Jo
|
Apr 3, 2022
|
> [Dynamical systems theory - Wikipedia](https://en.wikipedia.org/wiki/Dynamical_systems_theory)
|
b693764c797945f1b330d386a85ad936
|
|
Category Theory
| null | null | null | null | null | null |
์งํฉ๋ก ์ ๋ฐ๋์ ํด๋นํ๋ ๊ฐ๋
์์ ๋์ ์์๋ค ๊ฐ์ ๊ด๊ณ์ ์ฃผ๋ชฉํ์ฌ ์ถ์์ ์ธ ๊ฐ๋
๋ค์ ๋ค๋ฃจ๊ณ ์ ํ๋ ์ํ ์ด๋ก
### Category Theory Notion
|Title|
|:-:|
|[Topos Theroy](https://texonom.com/topos-theroy-cd8c3fed6bb14e8cbda9294ed472a4df)|
> [Category theory](https://en.wikipedia.org/wiki/Category_theory)
|
1b6594b7d4ce4c128ec2f9aed95d9f3c
|
Gรถdelโs incompleteness theorem
|
Foundations of Mathematics Notion
|
May 30, 2021
|
Alan Jo
|
Alan Jo
|
Sep 17, 2023
|
1์ฐจ ๋
ผ๋ฆฌ์์ ์ฆ๋ช
๊ฐ๋ฅํ ๋ช
์ ์ ์งํฉ์ ๋ชจํ์ ๊ฐ๋๋ค๋ ์ ๋ฆฌ
์๋ฆฌ๋
ผ๋ฆฌํ
์ฆ, ์ฆ๋ช
์ด๋ก ์ผ๋ก ์ ์ํ ์ง๋ฆฌ์ ๋ชจํ ์ด๋ก ์ผ๋ก ์ ์ํ ์ง๋ฆฌ๊ฐ ์๋ก ์ผ์น
์ ํผํ๊ธฐ ์ํด ์๋ฌด๋ฆฌ ์ธ์ฌํ๊ฒ ๊ณต๋ฆฌ๊ณ๋ฅผ ์ค๊ณํด๋ ๊ทธ๊ฒ์ ํผํ ์๋ ์๋ค๋ ๊ฒ์ ์ฆ๋ช
ํ์์ผ๋ฉฐ, ์ด๊ฒ์ด ๋ถ์์ ์ฑ ์ ๋ฆฌ
[2nd Gรถdelโs incompleteness theorem](https://texonom.com/2nd-gdels-incompleteness-theorem-173d1bd5bdac42448e637253f602a763)
> [Zarathu Blog: ๊ดด๋ธ์ ๋ถ์์ ์ฑ ์ ๋ฆฌ](https://blog.zarathu.com/posts/2019-05-20-godelincompleteness/)
> [๊ดด๋ธ์ ๋ถ์์ ์ฑ ์ ๋ฆฌ](https://jinseob2kim.github.io/godel.html)
> [๊ดด๋ธ์ ์์ ์ฑ ์ ๋ฆฌ - ์ํค๋ฐฑ๊ณผ, ์ฐ๋ฆฌ ๋ชจ๋์ ๋ฐฑ๊ณผ์ฌ์ ](https://ko.wikipedia.org/wiki/%EA%B4%B4%EB%8D%B8%EC%9D%98_%EC%99%84%EC%A0%84%EC%84%B1_%EC%A0%95%EB%A6%AC)
> [๋น์ ์ด ์ํ์ ๋ชจ๋ฅด๋ ์ด์ . (feat. ๋ถ์์ ์ฑ์ ์ ๋ฆฌ)](https://www.youtube.com/watch?v=oippSXvxUlw)
|
820d082fd9bf424f8125dda3bf9e859b
|
|
**Langlands program**
|
Foundations of Mathematics Notion
|
Aug 25, 2022
|
Alan Jo
|
Alan Jo
|
Aug 25, 2022
|
[Number Theory](https://texonom.com/number-theory-0bf9f82f550d43d382ba1c67ebb7dae2) [Harmonic Analysis](https://texonom.com/harmonic-analysis-e1e54ebeffd0407088bebab57acbfd53)
|
๋์์ ์ ์ด๋ก ์์ ๊ฐ๋ฃจ์ ๊ตฐ๋ค์ ๋ณดํ ํ์์ ๊ด๋ จ์ํค๊ณ ๊ตญ์์ฒด์ ์๋ธ ํ์ ๋ํ ๋์์ ๊ทธ๋ฃน์ ํํ ์ด๋ก ์ ์๋ก ์ฐ๊ด์ง๋ ๊ด๋ฒ์ํ ์ํฅ๋ ฅ ์๋ ์ถ์ธก์ ๋ง
๋ก๋ฒํธ ๋ญ๊ธ๋์ฆ์ ์ํด ์ ์
> [The Biggest Project in Modern Mathematics](https://youtu.be/_bJeKUosqoY)
|
629d720ec59b4bf4a42c0b066675b220
|
Set Theory
| null | null | null | null | null | null |
### Set Theory Notion
|Title|
|:-:|
|[Russell'sย paradox](https://texonom.com/russellsparadox-7ecbb574edd24c5ab9066b8a5fcc6dea)|
|[Infinite Set](https://texonom.com/infinite-set-971d3736190a4752a1ee3d1e2fea7028)|
|[Cantor's theorem](https://texonom.com/cantors-theorem-3057f62f2b4947448aaf1c7a0fd8904d)|
|[Power Set](https://texonom.com/power-set-58038c26c9ef49e1bf59cae859c90394)|
|[Continuum Hypothesis](https://texonom.com/continuum-hypothesis-8792f326812a41d0b546db08fbd82a52)|
|[Diagonal Argument](https://texonom.com/diagonal-argument-8a8921d2ba3745a199517d8650d50395)|
|[Countable Set](https://texonom.com/countable-set-94c63f44bb5c4334857afe94d13cad59)|
|[Uncountable Set](https://texonom.com/uncountable-set-287e751cba3c466e92f123ca2f04e13f)|
|[Infinite Set](https://texonom.com/infinite-set-93755bd42acf41e2ac688467ad687885)|
|[Finite Set](https://texonom.com/finite-set-63ed2bdb689946429effb738e5422255)|
|[Cantorโs paradox](https://texonom.com/cantors-paradox-c84022d0e5e344889da73daf136602ce)|
|[Naive set theory](https://texonom.com/naive-set-theory-67e68d75439f41bb8eb032834706044d)|
|[Equinumerosity](https://texonom.com/equinumerosity-907dd17f4fab4b9b8212011bc680e5bf)|
|[Cantor set](https://texonom.com/cantor-set-9cfdfcff7f82497eaca09074d723a722)|
|[Complement Set](https://texonom.com/complement-set-2ed91c78263a44a18c5a65ab86be77db)|
|[Symmetric difference](https://texonom.com/symmetric-difference-07bdea8546c04dabb5cd4ec7fd61b67b)|
|[Poset](https://texonom.com/poset-9a126737d3414bfc9225fe391603b9ad)|
|[Borel set](https://texonom.com/borel-set-76ba23edebd64061af05154588ab2870)|
|[ZFC](https://texonom.com/zfc-f844451d3f134288a92febc7b8e8257b)|
> [Untitled](https://www.math.snu.ac.kr/~kye/lecture/02_1_set_theory/%BE%E7%C0%BA%C7%FD.htm)
### Set
> [MySQL ํฉ์งํฉ, ๊ต์งํฉ, ์ฐจ์งํฉ, ๋์นญ์ฐจ](https://zetawiki.com/wiki/MySQL_%ED%95%A9%EC%A7%91%ED%95%A9,_%EA%B5%90%EC%A7%91%ED%95%A9,_%EC%B0%A8%EC%A7%91%ED%95%A9,_%EB%8C%80%EC%B9%AD%EC%B0%A8)
|
a74b3919af5e4e6e885862f6f76103f9
|
Type Theory
|
Foundations of Mathematics Notion
|
May 13, 2023
|
Alan Jo
|
Alan Jo
|
May 13, 2023
|
a6967220456b47498b951f11598381f7
|
||
Topos Theroy
|
Category Theory Notion
|
Jul 12, 2023
|
Alan Jo
|
Alan Jo
|
Jul 12, 2023
|
### Topos Theroy Notion
|Title|
|:-:|
|[Topos](https://texonom.com/topos-6d05bbca3e3d4051bc512027cb7543ef)|
|[Elementary Topoi](https://texonom.com/elementary-topoi-99bdc34b5e4a47e3b3597391ceb5ea7a)|
|[Grothendieck tp[po](https://texonom.com/grothendieck-tppo-76ca3dfbb8b644648d81fd583eefbf28)|
> [Topos](https://en.wikipedia.org/wiki/Topos)
|
cd8c3fed6bb14e8cbda9294ed472a4df
|
|
E**lementary Topoi**
|
Topos Theroy Notion
|
Jul 12, 2023
|
Alan Jo
|
Alan Jo
|
Jul 12, 2023
|
[Logic](https://texonom.com/logic-e562053ace984677a72cb9eaf5c6f91e)
|
99bdc34b5e4a47e3b3597391ceb5ea7a
|
|
Grothendieck tp[po
|
Topos Theroy Notion
|
Jul 12, 2023
|
Alan Jo
|
Alan Jo
|
Jul 12, 2023
|
[Algebraic Geometry](https://texonom.com/algebraic-geometry-4dc98f1cbfff43e1b969e0b660c484c2)
|
76ca3dfbb8b644648d81fd583eefbf28
|
|
Topos
|
Topos Theroy Notion
|
Jul 12, 2023
|
Alan Jo
|
Alan Jo
|
Jul 12, 2023
|
[Sheaf](https://texonom.com/sheaf-c1aa0624425d40ab86351c509a86b389)
|
### ์ผ๋ฐํ๋ ๊ณต๊ฐ
๊ฐ๋
๋ค์ ์ผ๋ฐํ์์ผ์ ๋ค๋ฃจ๋ ๊ฒ
|
6d05bbca3e3d4051bc512027cb7543ef
|
2nd Gรถdelโs incompleteness theorem
|
Gรถdelโs incompleteness theorem
| null | null | null | null | null |
> [๋น์ ์ด ์ํ์ ๋ชจ๋ฅด๋ ์ด์ . (feat. ๋ถ์์ ์ฑ์ ์ ๋ฆฌ)](https://www.youtube.com/watch?v=oippSXvxUlw)
|
173d1bd5bdac42448e637253f602a763
|
**Borel set**
|
Set Theory Notion
|
Mar 27, 2023
|
Alan Jo
|
Alan Jo
|
Mar 27, 2023
|
76ba23edebd64061af05154588ab2870
|
||
**Cantor set**
|
Set Theory Notion
|
Apr 5, 2022
|
Alan Jo
|
Alan Jo
|
Apr 15, 2023
|
### ๋น๊ฐ์ฐ ๋ฌดํ์งํฉ
์ค์์์ ๋ซํ ๊ตฌ๊ฐย \left[0, 1 \right] [0,1]๋ฅผ 3๋ฑ๋ถํด๋๊ฐ๋ฉด์ ๊ฐ์ด๋ฐ ๊ฒ์ ์ ๊ฑฐํ๋ ์์
์ ๋ฐ๋ณตํ์ฌ ์ป๋ ์งํฉ
๋น๊ฐ์ฐ ์งํฉ์์๋ ์ธก๋๊ฐ 0์ธ ์งํฉ ์ฆ ๊ธธ์ด๊ฐ 0์ด๋ค
ํ๋ํธ์ ์ผ์ข
0๊ณผ 1์ฌ์ด์ ์ค๋ฃจ๋ก ์ด๋ฃจ์ด์ง ์งํฉ์ด๊ณ 3๋ฑ๋ถํด์ ๊ฐ์ด๋ฐ ๊ตฌ๊ฐ์ ๋ฐ๋ณต์ ์ผ๋ก ์ ์ธํ๋ ๋ฐฉ์์ผ๋ก ๋ง๋ ๋ค
์กฐ๋ฐํ ๊ณณ์ด ์๋ ์์ ์งํฉ
[Cantor function](https://texonom.com/cantor-function-bab4b944c0cb44bdb0089d40ec6b1542)
> [Cantor set - Wikipedia](https://en.wikipedia.org/wiki/Cantor_set)
|
9cfdfcff7f82497eaca09074d723a722
|
|
Cantorโs paradox
|
Set Theory Notion
|
Apr 5, 2022
|
Alan Jo
|
Alan Jo
|
Apr 5, 2022
|
[Russell'sย paradox](https://texonom.com/russellsparadox-7ecbb574edd24c5ab9066b8a5fcc6dea)
|
๋ชจ๋ ์งํฉ๋ค์ ๋ชจ์์ด ์งํฉ์ ์ด๋ฃฐ ์ ์๋ค
|
c84022d0e5e344889da73daf136602ce
|
Cantor's theorem
|
Set Theory Notion
|
Apr 5, 2022
|
Alan Jo
|
Alan Jo
|
Apr 5, 2022
|
๋ฉฑ์งํฉ์ ํฌ๊ธฐ๊ฐ ํญ์ ์๋์ ์งํฉ์ ํฌ๊ธฐ๋ณด๋ค ํฌ๋ค๋ ์ ๋ฆฌ
์ฆ ์งํฉ๊ณผ ๋ฉฑ์งํฉ์ ์์๋ ์ผ๋์ผ ๋์ํ ์ ์๋ค
> [์นธํ ์ด์ ์ ๋ฆฌ - ์ํค๋ฐฑ๊ณผ, ์ฐ๋ฆฌ ๋ชจ๋์ ๋ฐฑ๊ณผ์ฌ์ ](https://ko.wikipedia.org/wiki/%EC%B9%B8%ED%86%A0%EC%96%B4%EC%9D%98_%EC%A0%95%EB%A6%AC)
|
3057f62f2b4947448aaf1c7a0fd8904d
|
|
Complement Set
|
Set Theory Notion
|
Oct 31, 2022
|
Alan Jo
|
Alan Jo
|
Oct 31, 2022
|
2ed91c78263a44a18c5a65ab86be77db
|
||
Continuum Hypothesis
|
Set Theory Notion
|
Apr 5, 2022
|
Alan Jo
|
Alan Jo
|
Apr 5, 2022
|
**์ฐ์์ฒด ๊ฐ์ค**
ํ์ค์ ๊ณต๋ฆฌ๊ณ๋ก๋ ์ฆ๋ช
ํ ์๋, ๋ฐ์ฆํ ์๋ ์๋ค
์ค์ ์งํฉ์ ๋ชจ๋ ๋ถ๋ถ ์งํฉ์ ๊ฐ์ฐ์งํฉ์ด๊ฑฐ๋ ์๋๋ฉด ์ค์ ์งํฉ๊ณผ ํฌ๊ธฐ๊ฐ ๊ฐ๋ค๋ ๋ช
์
ํ๋ฒ ๋ฅดํธ ๋ฌธ์ ์ 1๋ฒ
|
8792f326812a41d0b546db08fbd82a52
|
|
Countable Set
|
Set Theory Notion
|
Apr 5, 2022
|
Alan Jo
|
Alan Jo
|
Apr 15, 2023
|
### ๊ฐ์ฐ์งํฉ
์์ฐ์ ์ ์๋ ๊ฐ์ฐ์ด๊ณ
์ ๋ฆฌ์๋ ๊ฐ์ฐ์ธ๋ฐ ์ค์๋ ๋น๊ฐ์ฐ
|
94c63f44bb5c4334857afe94d13cad59
|
|
Diagonal Argument
|
Set Theory Notion
|
Apr 5, 2022
|
Alan Jo
|
Alan Jo
|
Apr 5, 2022
|
์นธํ ์ด๊ฐ ์ค์๊ฐ ์์ฐ์๋ณด๋ค ๋ง์์ ์ฆ๋ช
ํ๋ ๋ฐ ์ฌ์ฉํ ๋ฐฉ๋ฒ
์ค์ ์งํฉ์ด ๋น๊ฐ์ฐ์งํฉ์์ ๋ณด์ด๋ ๋ฐ ์ฌ์ฉ๋๋ค
> [๋๊ฐ์ ๋
ผ๋ฒ - ์ํค๋ฐฑ๊ณผ, ์ฐ๋ฆฌ ๋ชจ๋์ ๋ฐฑ๊ณผ์ฌ์ ](https://ko.wikipedia.org/wiki/%EB%8C%80%EA%B0%81%EC%84%A0_%EB%85%BC%EB%B2%95)
|
8a8921d2ba3745a199517d8650d50395
|
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