notes

commit a2936e1937d4b8f59bec9f5df6a3f1b9e3561c4f
parent de27ee3e73ef92d66873624de68748665513fe86
Author: Andrew <andrewlaack1@gmail.com>
Date:   Sat,  2 Nov 2024 14:28:11 -0500

Took notes on discrete math

Diffstat:
M
DiscreteMath.md
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6
+++---
A
HasseDiagram.md
 | 
10
++++++++++
A
LexicographicOrdering.md
 | 
12
++++++++++++
A
PartiallyOrderedSet.md
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10
++++++++++
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ReinforcementLearning.md
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4
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5 files changed, 39 insertions(+), 3 deletions(-)
diff --git a/DiscreteMath.md b/DiscreteMath.md
@@ -181,6 +181,6 @@ Unit 9.5 (Equivalence Relations)
 	- [Partition](Partition.md)
 
 Unit 9.6 (Partial Orderings)
-	- PartialOrdering (reflexive, antisymmetric, transitive)
-	- PartiallyOrdered (poset)
-	- TotalOrdering (chain)
+	- [PartiallyOrderedSet](PartiallyOrderedSet.md)
+	- [HasseDiagram](HasseDiagram.md)
+	- [LexicographicOrdering](LexicographicOrdering.md)
diff --git a/HasseDiagram.md b/HasseDiagram.md
@@ -0,0 +1,10 @@
+:discrete: 
+# Hasse Diagram
+
+Ch 9.6
+
+## Notes
+
+**Definition:** A hasse diagram is a way to show a (finite) poset in a graphical way. 
+
+To create a hasse diagram first we create a digraph of a relation. We then remove all loops and finally we remove directionallity s.t. all elements below the current that are directly connected must also be comparable.
diff --git a/LexicographicOrdering.md b/LexicographicOrdering.md
@@ -0,0 +1,12 @@
+:discrete:
+# Lexicographic Ordering
+
+Ch 9.6
+
+## Notes
+
+**Definition:** Lexicographic ordering is the same as alphabetic ordering.
+
+Consider the case of (1, 1, 100), (1,4), (2,1), (2,2), (2,0)
+
+In lexicographic order we see that (1,1,100) (1,4) < (2,0) < (2,1) < (2,2).
diff --git a/PartiallyOrderedSet.md b/PartiallyOrderedSet.md
@@ -0,0 +1,10 @@
+:discrete:
+# Partially Ordered Set (Poset)
+
+Ch 9.6
+
+## Notes
+
+**Definition:** (S,R) is a partial ordered set (poset) if the relation R is reflexive, antisymmetrice, and transitive with respect to the set S.
+
+Basically, we can define R as {(1,1), (2,2), (3,3), (3,2)} and since this is a partial ordering (reflexive, antisymmetric, and transitive), if we define S as {1,2,3} we see (S,R) is a poset.
diff --git a/ReinforcementLearning.md b/ReinforcementLearning.md
@@ -27,3 +27,7 @@ L1
 * Bandits
 * Evaluation
 * Control
+
+L2
+* DiscountFactor (MRP gamma)
+* MarkovRewardProcess