commit 90e19bfd85e880fa4f21f37751177b524bb7287f
parent eb2ca08e4fcb0fe61d51b4f9d753bf49d32c5f76
Author: Andrew <andrewlaack1@gmail.com>
Date: Tue, 27 Aug 2024 13:13:07 -0500
Took notes from yesterday's reading
Diffstat:
12 files changed, 95 insertions(+), 13 deletions(-)
diff --git a/Calculus.md b/Calculus.md
@@ -45,7 +45,7 @@ sec(x)tan(x) -> sec(x) + c
csc(x)cot(x) -> -csc(x) + c
-csc^2(x) -> cot(x) + c
+csc^2(x) -> -cot(x) + c
---
diff --git a/CompositeNumber.md b/CompositeNumber.md
@@ -0,0 +1,8 @@
+:discrete:
+# Composite Number
+
+U 2.4
+
+## Notes
+
+**Definition:** A composite number is a number that is not prime and thus is composed of two or more prime numbers.
diff --git a/DiscreteMath.md b/DiscreteMath.md
@@ -79,15 +79,14 @@ Unit 2.4 (sequence + other stuff):
- [[RecurrenceRelation.md]]
Unit 2.3 (paper book):
- - Tractable
- - Intractable
- - Unsolvable
- - NP Problems
- - P Problems
- - NP Complete
+ - [Tractable](Tractable.md)
+ - [Intractable](Intractable.md)
+ - [Unsolvable](Unsolvable.md)
+ - [NPProblem](NPProblem.md)
+ - [PProblem](PProblem.md)
+ - [NPComplete](NPComplete.md)
Unit 2.4 (integers and division):
- - Number Theory
- - Composite Number
- - Prime Number
- -
+ - [NumberTheory](NumberTheory.md)
+ - [CompositeNumber](CompositeNumber.md)
+ - [PrimeNumber](PrimeNumber.md)
diff --git a/Intractable.md b/Intractable.md
@@ -0,0 +1,10 @@
+:discrete: :algorithms:
+# Intractable
+
+U 2.3
+
+## Notes
+
+**Definition:** An intractable problem is one that can not be solved in polynomial time.
+
+These problems generally run in exonential, factorial, or some other time complexity that is higher than polynomial.
diff --git a/NPComplete.md b/NPComplete.md
@@ -0,0 +1,8 @@
+:discrete: :algorithms:
+# NP Complete Problem
+
+U 2.3
+
+## Notes
+
+**Definition:** NP complete problems are a set of problems of the NP family such that if any of them are found to be solvable in polynomial time then P=NP.
diff --git a/NPProblem.md b/NPProblem.md
@@ -0,0 +1,8 @@
+:discrete: :algorithms:
+# NP Problem
+
+U 2.3
+
+## Notes
+
+**Definition:** An NP problem (non-deterministic polynomial) is a problem that can be verified in polynomial time but is not (believed to be) solvable in polynomial time.
diff --git a/NumberTheory.md b/NumberTheory.md
@@ -0,0 +1,8 @@
+:discrete:
+# Number Theory
+
+U 2.4
+
+## Notes
+
+**Definition:** Number theory is a branch of mathematics that concerns itself with properties and functions on integers.
diff --git a/PProblem.md b/PProblem.md
@@ -0,0 +1,8 @@
+:discrete: :algorithms:
+# P Problem
+
+U 2.3
+
+## Notes
+
+**Definition:** A P problem is a problem that can be both solved and verified in polynomial time.
diff --git a/PrimeNumber.md b/PrimeNumber.md
@@ -0,0 +1,10 @@
+:discrete:
+# Prime Number
+
+U 2.4
+
+## Notes
+
+**Definition:** A prime number is a number greater than 1 such that its only divisors are itself and 1.
+
+A common way to prove the primality of a number is to show all numbers less than its square root do not divide it (a | b == False).
diff --git a/StatisticsAndProbability.md b/StatisticsAndProbability.md
@@ -26,8 +26,11 @@ Chapter 1.2:
- [[SetFunction.md]]
Chapter 1.3:
- - Permutation
- - Binomial Coefficient (denote \_nP\_r )
+ - Permutation (denote \_nP\_r permutations of n objects taken r at a time)
+ - When discussing subset based permutations we need bare in mind that binomial coefficients are discussing true subsets whereas permultations of the form nPr are descrbing permultations of r length of a set n long thus they are not ordered and thus are r! higher in count than the binomial coefficient (useful for deriving binomial coefficient formula).
+ - Binomial Coefficient (denote \_nC\_r )
+ - Ordered sample
+
---
diff --git a/Tractable.md b/Tractable.md
@@ -0,0 +1,10 @@
+:discrete: :algorithms:
+# Tractable
+
+U 2.3
+
+## Notes
+
+**Definition:** A tractable problem is a problem that can be solved in polynomial time (reasonable amount of time).
+
+See also [[Intractable.md]].
diff --git a/Unsolvable.md b/Unsolvable.md
@@ -0,0 +1,10 @@
+:discrete: :algorithms:
+# Unsolvable
+
+U 2.3
+
+## Notes
+
+**Definition:** Unsolvable problems are problems that can't be solved in even exponential time.
+
+A well known example of an unsolvable problem is the halting problem.
