commit f62b8dc5520abe3d55bf3d01a24a16259abd7280
parent ec6143d8dd2255580da4ad609adab157781ce0ad
Author: Andrew <andrewlaack1@gmail.com>
Date: Wed, 14 Aug 2024 18:35:23 -0500
Took notes
Diffstat:
7 files changed, 70 insertions(+), 1 deletion(-)
diff --git a/CentralLimitTheroem.md b/CentralLimitTheroem.md
@@ -0,0 +1,8 @@
+:prob:
+# Central Limit Theroem (CLT)
+
+L20
+
+## Notes
+
+**Definition:** The CLT states that as the number of trials increases distributions tend towards a normal distribution.
diff --git a/Contingency.md b/Contingency.md
@@ -0,0 +1,10 @@
+:discrete:
+# Contingency
+
+1.3.1
+
+## Notes
+
+**Definition:** A contingency is a proposition that is neither always true nor always false.
+
+An example of a contingency is simply $p$.
diff --git a/Contradiction.md b/Contradiction.md
@@ -1,4 +1,4 @@
-:proofs: :math310:
+:proofs: :math310: :discrete:
# Contradiction
Throughout textbook
@@ -6,3 +6,5 @@ Throughout textbook
## Notes
**Definition:** Contradiction is used to prove if then statements. This is done by assuming the then is true and the if is not true which would imply the statement is false. From here, you then show this causes a contradiction thus if the if is true then the then is true.
+
+A contradiction is a proposition that is always false such as $p \wedge \neg p$.
diff --git a/DiscreteMath.md b/DiscreteMath.md
@@ -15,3 +15,12 @@ Unit 1.1:
- [[Inverse.md]] - Negate both
- [[Contrapositive.md]] - Swap then inverse
- [[Biconditional.md]] - IFF
+
+Unit 1.2:
+ - [[Proposition.md]]
+ - [[Connectives.md]]
+
+Unit 1.3:
+ - [[Tautology.md]] - Always true - use the symbol t
+ - [[Contradiction.md]] - Always false
+ - [[Contingency.md]] - Must be evaluated
diff --git a/StatisticsAndProbability.md b/StatisticsAndProbability.md
@@ -108,3 +108,5 @@ L19:
- [[LawOfLargeNumbers.md]]
- [[RegressionToTheMean.md]]
- [[MarkovInequality.md]]
+L20:
+ - [[CentralLimitTheroem.md]]
diff --git a/Tautology.md b/Tautology.md
@@ -0,0 +1,10 @@
+:discrete:
+# Tautology
+
+1.3.1
+
+## Notes
+
+**Definition:** A tautology is a statement that is always true.
+
+An example of a tautology is $p \vee \neg p$.
diff --git a/Transpose.md b/Transpose.md
@@ -64,3 +64,31 @@ B^T = [1 3]
(AB)^T = B^T A^T
Note: This can be scaled up with an arbitrarily large list of matricies.
+
+#### Sum of transpose
+
+Where C = A + B
+
+C^T = (A+B)^T = A^T + B^T
+
+This builds upon our knowledge of matrix addition and product of transpose knowledge.
+
+#### Inverse
+
+AA^-1 = I_n
+
+(AA^-1)^T = I_n^T = I_n = (A^-1)^T A^T
+
+Thus (A^-1)^T is the inverse of A^T.
+
+Note: the transpose of the identity matrix is still itself as the diagonal does not change.
+
+#### Vector
+
+The transpose of a vector is a 1xn matrix where the original vector can be thought of as a nx1 matrix.
+
+A = [a_1]
+ [a_2]
+ [a_3]
+
+A^T = [a_1 a_2 a_3]
