From 3f78015c6dba6b4686d9e9cdf800a57218a4cac0 Mon Sep 17 00:00:00 2001
From: Zheyuan Wu <60459821+Trance-0@users.noreply.github.com>
Date: Wed, 20 Nov 2024 13:28:03 -0600
Subject: [PATCH] update page structures

---
 pages/CSE347/Exam_reviews/CSE347_E2.md | 54 ++++++++++++++++++++++++++
 pages/CSE347/_meta.js                  |  5 ++-
 pages/CSE442T/_meta.js                 |  5 ++-
 pages/Math4111/Math4111_L1.md          |  4 +-
 pages/Math4111/_meta.js                |  5 ++-
 pages/Math4111/{index.mdx => index.md} |  0
 pages/Math429/_meta.js                 |  5 ++-
 7 files changed, 68 insertions(+), 10 deletions(-)
 create mode 100644 pages/CSE347/Exam_reviews/CSE347_E2.md
 rename pages/Math4111/{index.mdx => index.md} (100%)

diff --git a/pages/CSE347/Exam_reviews/CSE347_E2.md b/pages/CSE347/Exam_reviews/CSE347_E2.md
new file mode 100644
index 0000000..ba4d7d2
--- /dev/null
+++ b/pages/CSE347/Exam_reviews/CSE347_E2.md
@@ -0,0 +1,54 @@
+# Exam 2 Review
+
+## Reductions
+
+We say that a problem $A$ reduces to a problem $B$ if there is a **polynomial time** reduction function $f$ such that for all $x$, $x \in A \iff f(x) \in B$.
+
+To prove a reduction, we need to show that the reduction function $f$:
+
+1. runs in polynomial time
+2. $x \in A \iff f(x) \in B$.
+
+### Useful results from reductions
+
+1. $B$ is at least as hard as $A$ if $A \leq B$.
+2. If we can solve $B$ in polynomial time, then we can solve $A$ in polynomial time.
+3. If we want to solve problem $A$, and we already know an efficient algorithm for $B$, then we can use the reduction $A \leq B$ to solve $A$ efficiently.
+4. If we want to show that $B$ is NP-hard, we can do this by showing that $A \leq B$ for some known NP-hard problem $A$.
+
+$P$ is the class of problems that can be solved in polynomial time. $NP$ is the class of problems that can be verified in polynomial time.
+
+We know that $P \subseteq NP$.
+
+### NP-complete problems
+
+A problem is NP-complete if it is in $NP$ and it is also NP-hard.
+
+#### NP
+
+A problem is in $NP$ if 
+
+1. there is a polynomial size certificate for the problem, and
+2. there is a polynomial time verifier for the problem that takes the certificate and checks whether it is a valid solution.
+
+#### NP-hard
+
+A problem is NP-hard if every instance of $NP$ hard problem can be reduced to it in polynomial time.
+
+List of known NP-hard problems:
+
+1. 3-SAT (or SAT)
+2. Independent Set
+3. Vertex Cover
+4. 3-coloring
+5. Hamiltonian Cycle
+6. Hamiltonian Path
+
+## Approximation Algorithms
+
+## Randomized Algorithms
+
+## Online Algorithms
+
+
+
diff --git a/pages/CSE347/_meta.js b/pages/CSE347/_meta.js
index ef2ee9d..cf64ff0 100644
--- a/pages/CSE347/_meta.js
+++ b/pages/CSE347/_meta.js
@@ -1,6 +1,7 @@
 export default {
-    index: {
-        display: 'hidden'
+    index: "Course Description",
+    "---":{
+        type: 'separator'
     },
     Exam_reviews: "Exam reviews",
     CSE347_L1: "Lecture 1",
diff --git a/pages/CSE442T/_meta.js b/pages/CSE442T/_meta.js
index 3b0c90a..8bab2a3 100644
--- a/pages/CSE442T/_meta.js
+++ b/pages/CSE442T/_meta.js
@@ -1,6 +1,7 @@
 export default {
-    index: {
-        display: 'hidden'
+    index: "Course Description",
+    "---":{
+        type: 'separator'
     },
     Exam_reviews: "Exam reviews",
     CSE442T_L1: "Lecture 1",
diff --git a/pages/Math4111/Math4111_L1.md b/pages/Math4111/Math4111_L1.md
index 552cba6..c5c24a5 100644
--- a/pages/Math4111/Math4111_L1.md
+++ b/pages/Math4111/Math4111_L1.md
@@ -1,8 +1,8 @@
 # Lecture 1
 
-## Introduction 
+## Introduction
 
-Reading is not recommended before class, it;s hard.
+Reading is not recommended before class, it's hard.
 
 ## Chapter 1: The real number and complex number systems
 
diff --git a/pages/Math4111/_meta.js b/pages/Math4111/_meta.js
index bc371f6..0924e21 100644
--- a/pages/Math4111/_meta.js
+++ b/pages/Math4111/_meta.js
@@ -1,6 +1,7 @@
 export default {
-    index: {
-        display: 'hidden'
+    index: "Course Description",
+    "---":{
+        type: 'separator'
     },
     Exam_reviews: "Exam reviews",
     Math4111_L1: "Lecture 1",
diff --git a/pages/Math4111/index.mdx b/pages/Math4111/index.md
similarity index 100%
rename from pages/Math4111/index.mdx
rename to pages/Math4111/index.md
diff --git a/pages/Math429/_meta.js b/pages/Math429/_meta.js
index ebe89c4..b988539 100644
--- a/pages/Math429/_meta.js
+++ b/pages/Math429/_meta.js
@@ -1,6 +1,7 @@
 export default {
-    index: {
-        display: 'hidden'
+    index: "Course Description",
+    "---":{
+        type: 'separator'
     },
     Math429_L1: "Lecture 1",
     Math429_L2: "Lecture 2",