commit 7310b0d1029adee2d45f135cf222888e54b82d0c
parent 39e0e8880493033dc3349d28343170e4ab31b3c3
Author: Andrew <andrewlaack1@gmail.com>
Date: Wed, 21 Aug 2024 14:38:16 -0500
Took some more notes (stats+discrete
Diffstat:
8 files changed, 77 insertions(+), 10 deletions(-)
diff --git a/Complement.md b/Complement.md
@@ -1,4 +1,4 @@
-:prob:
+:prob: :discrete:
# Complement
L1
diff --git a/DiscreteMath.md b/DiscreteMath.md
@@ -7,7 +7,7 @@ Discrete math related links.
#### Discrete Mathematics and Its Applications
-Unit 1.1:
+Unit 1.1 (logic):
- [[Proposition.md]]
- [[Negation.md]]
- [[Connectives.md]]
@@ -16,11 +16,11 @@ Unit 1.1:
- [[Contrapositive.md]] - Swap then inverse
- [[Biconditional.md]] - IFF
-Unit 1.2:
+Unit 1.2 (logic):
- [[Proposition.md]]
- [[Connectives.md]]
-Unit 1.3:
+Unit 1.3 (logic):
- [[Tautology.md]] - Always true - use the symbol t
- [[Contradiction.md]] - Always false
- [[Contingency.md]] - Must be evaluated
@@ -31,7 +31,7 @@ Unit 1.3:
- [[Commutative.md]]
- [[Satisfiable.md]]
-Unit 1.4:
+Unit 1.4 (proof):
- [[Predicate.md]]
- [[PropositionalFunction.md]]
- [[Quantifiers.md]]
@@ -39,13 +39,13 @@ Unit 1.4:
- [[Preconditions.md]]
- [[Postcondition.md]]
-Unit 1.5:
+Unit 1.5 (proof):
- [[NestedQuantifier.md]]
-Unit 1.6:
+Unit 1.6 (proof):
- [[LawOfDetachment.md]]
-Unit 1.7:
+Unit 1.7 (proof):
- [[DirectProof.md]]
- [[Contrapositive.md]] - Also known as contraposition
- [[Contradiction.md]]
@@ -53,5 +53,18 @@ Unit 1.7:
- [[VacuousProof.md]]
- [[ExhaustiveProof.md]]
-Unit 2.1:
+Unit 2.1 (sets):
- [[Set.md]]
+ - [[Subset.md]]
+ - [[PowerSet.md]]
+ - [[CartesianProduct.md]]
+ - [[TruthSet.md]]
+ - [[Complement.md]]
+
+Unit 2.3 (functions):
+ - [[Range.md]]
+ - [[Image.md]]
+ - [[Preimage.md]]
+ - [[Codomain.md]]
+ - [[Injective.md]] - one-to-one
+ - [[Surjective.md]] - onto
diff --git a/Inference.md b/Inference.md
@@ -0,0 +1,10 @@
+:ml:
+# Inference
+
+Ch2
+
+## Notes
+
+**Definition:** Inference is the statistical process of finding relationships between data.
+
+This is not to be confused with [[Prediction.md]] which is the process of guessing an output.
diff --git a/MachineLearning.md b/MachineLearning.md
@@ -30,6 +30,12 @@ h(x) = this is the function with an input of x this should be about the correct
## Main Links
+Introduction to Statistical Learning (Python):
+
+Ch 2:
+ - [[Inference.md]]
+ - [[Prediction.md]]
+
ML Categories:
[[SupervisedLearning.md]]
diff --git a/PowerSet.md b/PowerSet.md
@@ -1,4 +1,4 @@
-:sets: :math310:
+:sets: :math310: :discrete:
# Power Set
AM Ch1
@@ -10,3 +10,13 @@ AM Ch1
Example:
P(A) = {X : X $\in$ A}
+
+B = {0, 1}
+
+P(B) = {{}, {0}, {1}, {0,1}}
+
+Notice that {0,1} and {1,0} are not both included as sets are unordered and unique.
+
+#### Cardinality
+
+The cardinality of a powerset is equal to 2^n where n is the number of elements in the original set.
diff --git a/Prediction.md b/Prediction.md
@@ -0,0 +1,10 @@
+:ml:
+# Prediction
+
+Ch2
+
+## Notes
+
+**Definition:** Prediction is the process of predicting an output given a sample.
+
+This is different than [[Inference.md]] which is focused on understanding relationshipts between variables.
diff --git a/Subset.md b/Subset.md
@@ -0,0 +1,10 @@
+:discrete: :logic:
+# Subset
+
+U 2.1.2
+
+## Notes
+
+**Definition:** The set A is a subset of B which means all elements of A are in B.
+
+A **proper** subset is a subset where the two sets are not equivalent ($A \neq B$). This is described using $\sub$ instead of $\subseteq$ which included non-proper subsets.
diff --git a/TruthSet.md b/TruthSet.md
@@ -0,0 +1,8 @@
+:discrete: :logic:
+# Truth Set
+
+U 2.1.2
+
+## Notes
+
+**Definition:** The truth set of a function P(x) is the set of all elements of the domain such that P(x) is true.
