commit 9cd83a2d266248a00400a845f8b3630634993887
parent ec19b8d3519c49d3407bbd91ec5e84d2d22afe41
Author: AndrewLockVI <andrewlaack1@gmail.com>
Date: Tue, 7 Jan 2025 10:06:27 -0600
Did lin-alg
Diffstat:
12 files changed, 185 insertions(+), 39 deletions(-)
diff --git a/Algorithms.md b/Algorithms.md
@@ -83,6 +83,11 @@ Ch 6 (Information Theory and Data Compression)
- RootedTree (ordered pair (T,r) where r is the root (arbitrary) and T is a graph (tree))
- Leaf - Exactly one neighbor
+Ch 7 (Game Strategy)
+ - FiniteTwoPlayerGameOfPureStrategy
+ - Minimax
+ - Negamax
+
#### Other Stuff To Look At
Operation types (operations done with n inputs)
diff --git a/ComputerSecurity.md b/ComputerSecurity.md
@@ -0,0 +1,12 @@
+:index: :security:
+# Computer Security
+
+Main index for notes related to CSCI 370, Computer Security
+
+## Links
+
+### 1.6 - Cryptography
+
+- [ ] Keyless.md
+- [ ] SingleKey.md
+- [ ] TwoKey.md
diff --git a/Coordinate.md b/Coordinate.md
@@ -0,0 +1,12 @@
+:linear-algebra:
+# Coordinate
+
+**Source:** Linear Algebra Done Right
+
+**Chapter:** 1
+
+## Notes
+
+**Definition:** A coordinate is a singular component of a vector or list.
+
+Consider v = (1, 4, 5). The third component of v is 5, the second component of v is 4, and the first component of v is 1.
diff --git a/DecisionTrees.md b/DecisionTrees.md
@@ -7,6 +7,12 @@ ML D4
**Definition:** Decision trees are a machine learning algorithm that does true/false comparison to go left and right until reaching a leaf node. This leaf node will then describe the output.
+### Associated Links
+
+Classification and Regression Trees by Leo Breiman
+
+
+
### Visualizing
You can use graphviz to visualize this graph. First, you train the model using sklearn.tree then you import export_graphviz from the same location. Using export_graphviz you can pass in the model, output file, feature names, class names , and some other information which will create a dotfile.
diff --git a/DiscreteMath.md b/DiscreteMath.md
@@ -215,3 +215,75 @@ Unit 10.3 (Representing Graphs and Isomorphisms)
- [AdjacencyMatrix](AdjacencyMatrix.md) (for dense)
- Isomorphic
- GraphInvariant
+
+Unit 10.4 (Connectivity)
+ - Path
+ - Cycle
+ - Closed Walk
+ - Trail
+ - SimplePath
+ - CutVertex (produces subgraph that is not connected)
+ - CutEdge - Bridge
+ - NonseparableGraph
+ - VertexCut - SeparationSet
+ - VertexConnectivity - Minimum verts in vertex cut or produce 1 vertex (fully connected graph)
+ - k-connected (vertex connectivity of graph >= k)
+ - EdgeCut
+ - EdgeConnectivity
+ - StronglyConnected (a->b and b->a for all b,a in digraph)
+ - WeaklyConnected (if path between the two assuming undirected graph)
+ - StronglyConnectedComponents / StrongComponents (maximal strongly connected subgraph)
+ - GiantStronglyConnectedComponent (GSCC - Connected component with significant amount of the graph's total vertices)
+
+Unit 10.5 (Euler and Hamilton Paths)
+ - Euler Circuit - Can traverse all edges (exactly once) back to self
+ - Euler Path - Same as above except a path with all edges instead of a circuit
+ - Hamilton Circuit - Can traverse all vertices (exactly once) back to self
+
+Unit 10.7 (Planar Graphs)
+ - Planar (can be drawn on a plane without edges crossing)
+ - Planar Representation (visual representation of planar graph without crossing edges)
+ - Regions
+ - Euler's Formula (r = e-v+2 where r is the number of regions in a planar representation)
+ - Homeomorphic
+ - Elementary Subdivision
+
+Unit 10.8 (Graph Coloring)
+ - Coloring
+ - DualGraph
+ - ChromaticNumber (minimum number of unique colors required to achieve a coloring denoted as \chi)
+ - FourColorTheorem - chromatic number of a planar graph is no greater than four.
+
+Unit 11.1 (Introduction to Trees)
+ - Tree (connected, undirected, with no simple circuits)
+ - Forest (disconnected, undirected, no simple circuits)
+ - Root
+ - RootedTree
+ - InternalVertices (vertices that have children in a tree (~opposite of leaf))
+ - mAryTree (m-ary trees are trees where each vertex has no more than m children)
+ - FullmAryTree (m-ary tree if every internal vertex has m children )
+ - OrderedRootedTree (rbt where children are ordered. this terminology allows us to say left and right children, but generally we leave out ordered part)
+ - Balanced (all leaves at either h or h-1 level (remember height starts at 0 for root))
+
+Unit 11.3 (Tree Traversals)
+ - UniversalAddressSystem (x_1.x_2.x_3...x_n for the current node where x_1... is the path from root to current. Notice we don't include x_0 := 0)
+ - TraversalAlgorithms (Way to traverse every vertex in ordered rooted tree)
+ - PreorderTraversal (Traverse right subtree first, adding current item at each step, thus first element is root)
+ - InorderTraversal (Leftmost then parent then right then leftmost then partent... final element is the rightmost leaf)
+ - PostorderTraversal (all child nodes starting from left, then parent, then right, so on)
+ - InfixForm
+ - PrefixForm
+ - PolishNotation
+ - PostfixForm
+ - ReversePolishNotation
+
+Unit 11.4 (Spanning Trees)
+ - SpanningTree - Subgraph of simple graph G s.t. it contains every vertex in G.
+ - DepthFirstSearch - Go deep then wide.
+ - BreadthFirstSearch - Start somewhere, go out.
+
+Unit 11.5 (Minimum Spanning Trees)
+ - MinimumSpanningTree - Spanning tree with weighted graph that minimizes sum of weights.
+ - PrimsAlgorithm - Select minimum weighted edge, select minimum edge incident without creating loop, repeart until n-1 edges have been selected
+ - KruskalsAlgorithm - Choose edge with minimum weight, choose next with min weight, continue until selecting n-1 edges, ensure not creating simple circuits
+ -
diff --git a/LinearAlgebra.md b/LinearAlgebra.md
@@ -12,11 +12,12 @@ Linear Algebra Done Right:
Chapter 1:
- [VectorSpace](VectorSpace.md)
- [Tuple](Tuple.md)
- - [RealVectorSpace](RealVectorSpace.md)
- [ComplexVectorSpace](ComplexVectorSpace.md)
- [Subspace](Subspace.md)
- [SumOfVectorSpaces](SumOfVectorSpaces.md)
- [DirectSum](DirectSum.md)
+ - [RealVectorSpace.md](RealVectorSpace.md)
+ - [Coordinate](Coordinate.md)
Khan Academy:
diff --git a/MachineLearning.md b/MachineLearning.md
@@ -69,7 +69,7 @@ Ch 2 (Maths behind DL):
* BatchGradientDescent
* Backpropagation
* AutomaticDifferentiation
-*
+* Mutable
ISL Python:
diff --git a/RealVectorSpace.md b/RealVectorSpace.md
@@ -1,8 +1,16 @@
-:lin-alg:
+:linear-algebra:
# Real Vector Space
-Ch 1
+**Source:** Linear Algebra Done Right
+
+**Chapter:** 1
## Notes
-**Definition:** A real vector space is a vector space on the real numbers.
+**Definition:** A real vector space is a [VectorSpace](VectorSpace.md) on $R$ where $R$ is the set of real numbers.
+
+## Importance
+
+The importance of this distinction lies in the fact that vector spaces are defined on a set $F$ which is often the set of complex numbers or real numbers, but if we define a set {2,3}, we notice normal vector spaces cease to be so because there is no longer a multiplicative identity.
+
+In line with this, we also define a complex vector space as a vector space over the set of complex numbers.
diff --git a/StatisticsAndProbability.md b/StatisticsAndProbability.md
@@ -51,7 +51,8 @@ Chapter 2.1:
- [ProbabilityMassFunction](ProbabilityMassFunction.md)
- [DiscreteRandomVariable](DiscreteRandomVariable.md)
- Support (space of X)
- - HypergeometricDistribution ()
+ - HypergeometricDistribution
+
---
diff --git a/Subspace.md b/Subspace.md
@@ -1,16 +1,24 @@
:ml: :lin-alg:
# Subspace
-ML D5
+**Source:** Linear Algebra Done Right
+
+**Chapter:** 1
## Notes
+### Linear Algebra Context
-#### ML Context
-**Definition:** A subspace is a lower dimensional space.
+**Definition:** A subspace is a subset of a vector space.
-Often we find that many higher dimensional points all reside in or near a similar lower dimensional subspace which is the basis for [[Projection.md]]
+To verify a subset U of a vector space V is a subspace of V we only need to verify:
-#### Lin Alg Context
+1. Closed under addition
+2. Closed under scalar multiplication
+3. Additive Identity
-**Definition:** A subspace is a subset of a vector space.
+### ML Context
+
+**Definition:** A subspace is a lower dimensional space.
+
+Often we find that many higher dimensional points all reside in or near a similar lower dimensional subspace which is the basis for [[Projection.md]]
diff --git a/VectorSpace.md b/VectorSpace.md
@@ -1,12 +1,31 @@
:math310: :linear-algebra:
-# Vector Space
+# Vector Space
-AM Ch8
+**Source:** Linear Algebra Done Right
+
+**Chapter:** 1
## Notes
-**Definition:** A vector space is a set of elements that obey certain properties.
+**Definition:** A vector space is a space where we find a closure under vector addition and scalar multiplication.
+
+Along with this, the following must be true:
+
+1. Commutative, a + b = b + a
+2. Associative, a(b * c) = b * (a * c) and a + (b + c) = b + (a + c)
+3. Additive Identity, a + 0 = a
+4. Additive Inverse, a + -a = 0
+5. Multiplicative Identity, 1a = a
+6. Distributive, a(u + v) = au + av and (a + b)u = au + bu
+
+## Related Information
+
+When defining a vector space we define it as a set $V$ along with an addition and scalar multiplication on $V$ that satisfies the prior properties.
+
+We define addition and scalar multiplication as functions.
-An interesting thing about vector spaces is the union of two vector spaces is itself a vector space.
+The addition function can be:
+a : (V)^2 -> B : f(n,m) = n+m for all n,m in V.
-Vector spaces must include an identity vector (under multiplication and addition) as well as be closed under multiplication and addition. Additionally, they must include additive inverses, respect distributivity, and associativity.
+The multiplication function can be:
+m : (V,F) -> V : m(v,f) = vf for all v in V and c in F.
diff --git a/index.md b/index.md
@@ -1,9 +1,11 @@
:index:
+
# Index
-This is the index for my main note classifications. I will maintain this as a home page.
+This is the index for my main note classifications. I will maintain this as a home page.
[[ModelNotes.md]]
+[[TexRef.md]]
## Formal Schooling
@@ -12,9 +14,12 @@ This is the index for my main note classifications. I will maintain this as a ho
[[BIOL115.md]]
[[HHP102.md]]
[[Math310.md]]
-[[TexRef.md]]
+[[Algorithms.md]]
+[[DiscreteMath.md]]
+[[Assembly.md]]
+[[ComputerSecurity.md]]
-## Other Focuses
+## Other Focuses
[[ComputerArchitecture.md]]
[[MachineLearning.md]]
@@ -22,34 +27,31 @@ This is the index for my main note classifications. I will maintain this as a ho
[[StatisticsAndProbability.md]]
[[LinuxStuff.md]]
[[LinearAlgebra.md]]
-[[DiscreteMath.md]]
[[Calculus.md]]
-[[Algorithms.md]]
[[Physics.md]]
-[[Assembly.md]]
[[Vocabulary.md]]
[[ReinforcementLearning.md]]
## Things to Learn More About
Stats + Prob
- - [ ] ECDF (sort of like cdf)
- - [ ] Convolution (not NN)
- - [ ] https://en.wikipedia.org/wiki/Primality_test
- - [ ] https://en.wikipedia.org/wiki/Continuous-time_Markov_chain
+- [ ] ECDF (sort of like cdf)
+- [ ] Convolution (not NN)
+- [ ] https://en.wikipedia.org/wiki/Primality_test
+- [ ] https://en.wikipedia.org/wiki/Continuous-time_Markov_chain
Lin-alg
- - [ ] Cofactor (define)
- - [ ] Minors
- - [ ] SVD
- - [ ] PCA
- - [ ] Norms (for regression)
+- [ ] Cofactor (define)
+- [ ] Minors
+- [ ] SVD
+- [ ] PCA
+- [ ] Norms (for regression)
ML
- - [ ] RNN
- - [ ] LSTM
- - [ ] Mamba
- - [ ] Transformer
- - [ ] KAN
- - [ ] Linear Regression statistical approach
- - [ ] Boosting (XGBoost, AdaBoost, LightGBM, etc.)
+- [ ] RNN
+- [ ] LSTM
+- [ ] Mamba
+- [ ] Transformer
+- [ ] KAN
+- [ ] Linear Regression statistical approach
+- [ ] Boosting (XGBoost, AdaBoost, LightGBM, etc.)
