diff --git a/content/Math401/Math401_T6.md b/content/Math401/Math401_T6.md
index 4059db0..13cde28 100644
--- a/content/Math401/Math401_T6.md
+++ b/content/Math401/Math401_T6.md
@@ -49,12 +49,26 @@ A state $|\psi\rangle$ is entangled if it cannot be expressed as a product state
 Example: the Bell state $|\psi^+\rangle=\frac{1}{\sqrt{2}}(|00\rangle+|11\rangle)$ is entangled.
 
 Assume it can be written as $|\psi\rangle=|\psi_1\rangle\otimes|\psi_2\rangle$ where $|\psi_1\rangle=a|0\rangle+b|1\rangle$ and $|\psi_2\rangle=c|0\rangle+d|1\rangle$. Then:
-$$|\psi\rangle=a|00\rangle+b|01\rangle+c|10\rangle+d|11\rangle$$
+
+$$
+|\psi\rangle=a|00\rangle+b|01\rangle+c|10\rangle+d|11\rangle
+$$
+
 Setting this equal to $|\psi^+\rangle=\frac{1}{\sqrt{2}}(|00\rangle+|11\rangle)$ gives:
-$$ac|00\rangle+ad|01\rangle+bc|10\rangle+bd|11\rangle=\frac{1}{\sqrt{2}}(|00\rangle+|11\rangle)$$
+
+$$
+ac|00\rangle+ad|01\rangle+bc|10\rangle+bd|11\rangle=\frac{1}{\sqrt{2}}(|00\rangle+|11\rangle)
+$$
+
 This requires:
-$$ac=bd=\frac{1}{2}$$
-$$ad=bc=0$$
+
+$$
+ac=bd=\frac{1}{2}
+$$
+
+$$
+ad=bc=0
+$$
 
 This is a contradiction, so $|\psi^+\rangle$ is entangled.
 
diff --git a/content/Math401/_meta.js b/content/Math401/_meta.js
index c64f3b0..0df50d8 100644
--- a/content/Math401/_meta.js
+++ b/content/Math401/_meta.js
@@ -21,4 +21,6 @@ export default {
     },
     Math401_P1: "Math 401, Paper 1: Concentration of measure effects in quantum information (Patrick Hayden)",
     Math401_P1_1: "Math 401, Paper 1, Side note 1: Quantum information theory and Measure concentration",
+    Math401_P1_2: "Math 401, Paper 1, Side note 2: Page's lemma",
+    Math401_P1_3: "Math 401, Paper 1, Side note 3: Levy's concentration theorem",
 }
\ No newline at end of file
diff --git a/favicon.ico b/favicon.ico
new file mode 100644
index 0000000..1552bc4
Binary files /dev/null and b/favicon.ico differ
diff --git a/next.config.mjs b/next.config.mjs
index b3e5e44..96bf57a 100644
--- a/next.config.mjs
+++ b/next.config.mjs
@@ -2,13 +2,7 @@ import nextra from 'nextra'
 import withBundleAnalyzer from '@next/bundle-analyzer'
 
 const withNextra = nextra({
-  latex: {
-    renderer: 'katex',
-    options: {
-      // suppress warnings from katex for `\\`
-      strict: false,
-    }
-  },
+  latex: true,
   mdxOptions: {
     format: 'detect'
   },
diff --git a/package.json b/package.json
index 7d2c101..8f0fe3a 100644
--- a/package.json
+++ b/package.json
@@ -1,10 +1,10 @@
 {
   "scripts": {
-    "dev": "next dev",
-    "build": "cross-env NODE_OPTIONS='--max-old-space-size=16384' next build && npm run postbuild",
+    "dev": "next --turbopack",
+    "build": "cross-env VERCEL_FORCE_NO_BUILD_CACHE=1 NODE_OPTIONS='--max-old-space-size=16384' next build && npm run postbuild",
     "build:test": "cross-env ANALYZE=true NODE_OPTIONS='--inspect --max-old-space-size=4096' next build",
     "build:analyze": "cross-env ANALYZE=true NODE_OPTIONS='--max-old-space-size=16384' next build",
-    "postbuild": "pagefind --site .next/server/app --output-path public/_pagefind",
+    "postbuild": "next-sitemap && pagefind --site .next/server/app --output-path public/_pagefind && cp -r ./public/_pagefind ./out",
     "start": "next start"
   },
   "dependencies": {