From fb6e36545b56d93a4cbcded3151a2cb45a1022ea Mon Sep 17 00:00:00 2001
From: Trance-0 <60459821+Trance-0@users.noreply.github.com>
Date: Mon, 3 Mar 2025 19:45:05 -0600
Subject: [PATCH] update typo

---
 pages/Math4121/Math4121_L1.md            | 2 +-
 pages/Math4121/Math4121_L10.md           | 2 +-
 pages/Math4121/Math4121_L12.md           | 2 +-
 pages/Math4121/Math4121_L13.md           | 2 +-
 pages/Math4121/Math4121_L14.md           | 2 +-
 pages/Math4121/Math4121_L15.md           | 2 +-
 pages/Math4121/Math4121_L16.md           | 2 +-
 pages/Math4121/Math4121_L17.md           | 2 +-
 pages/Math4121/Math4121_L18.md           | 2 +-
 pages/Math4121/Math4121_L19.md           | 2 +-
 pages/Math4121/Math4121_L2.md            | 2 +-
 pages/Math4121/Math4121_L20.md           | 2 +-
 pages/Math4121/Math4121_L3.md            | 2 +-
 pages/Math4121/Math4121_L4.md            | 2 +-
 pages/Math4121/Math4121_L5.md            | 2 +-
 pages/Math4121/Math4121_L6.md            | 2 +-
 pages/Math4121/Math4121_L7.md            | 2 +-
 pages/Math4121/Math4121_L8.md            | 2 +-
 pages/Math4121/Math4121_L9.md            | 2 +-
 pages/Math4121/index.md                  | 2 +-
 pages/Math416/Exam_reviews/Math416_E1.md | 3 +++
 pages/Math416/Math416_L12.md             | 4 ++--
 pages/Math416/_meta.js                   | 1 +
 23 files changed, 26 insertions(+), 22 deletions(-)
 create mode 100644 pages/Math416/Exam_reviews/Math416_E1.md

diff --git a/pages/Math4121/Math4121_L1.md b/pages/Math4121/Math4121_L1.md
index b9b4878..e68fd8f 100644
--- a/pages/Math4121/Math4121_L1.md
+++ b/pages/Math4121/Math4121_L1.md
@@ -1,4 +1,4 @@
-# Math 4121 Lecture 1
+# Math4121 Lecture 1
 
 ## Chapter 5: Differentiation
 
diff --git a/pages/Math4121/Math4121_L10.md b/pages/Math4121/Math4121_L10.md
index 411af63..67e6dfd 100644
--- a/pages/Math4121/Math4121_L10.md
+++ b/pages/Math4121/Math4121_L10.md
@@ -1,4 +1,4 @@
-# Math 4121 Lecture 10
+# Math4121 Lecture 10
 
 ## Recap
 
diff --git a/pages/Math4121/Math4121_L12.md b/pages/Math4121/Math4121_L12.md
index 7c44821..d200007 100644
--- a/pages/Math4121/Math4121_L12.md
+++ b/pages/Math4121/Math4121_L12.md
@@ -1,4 +1,4 @@
-# Math 4121 Lecture 12
+# Math4121 Lecture 12
 
 ## Chapter 7: Uniform Convergence and Integrals
 
diff --git a/pages/Math4121/Math4121_L13.md b/pages/Math4121/Math4121_L13.md
index 4300e5d..1d18f9b 100644
--- a/pages/Math4121/Math4121_L13.md
+++ b/pages/Math4121/Math4121_L13.md
@@ -1,4 +1,4 @@
-# Math 4121 Lecture 13
+# Math4121 Lecture 13
 
 ## Hidden Chapter 1
 
diff --git a/pages/Math4121/Math4121_L14.md b/pages/Math4121/Math4121_L14.md
index 5232065..240d63f 100644
--- a/pages/Math4121/Math4121_L14.md
+++ b/pages/Math4121/Math4121_L14.md
@@ -1,4 +1,4 @@
-# Math 4121 Lecture 14
+# Math4121 Lecture 14
 
 ## Recap
 
diff --git a/pages/Math4121/Math4121_L15.md b/pages/Math4121/Math4121_L15.md
index c489afb..fd27196 100644
--- a/pages/Math4121/Math4121_L15.md
+++ b/pages/Math4121/Math4121_L15.md
@@ -1,4 +1,4 @@
-# Math 4121 Lecture 15
+# Math4121 Lecture 15
 
 ## Continue on patches for Riemann integral
 
diff --git a/pages/Math4121/Math4121_L16.md b/pages/Math4121/Math4121_L16.md
index fedee98..8701b88 100644
--- a/pages/Math4121/Math4121_L16.md
+++ b/pages/Math4121/Math4121_L16.md
@@ -1,4 +1,4 @@
-# Math 4121 Lecture 16
+# Math4121 Lecture 16
 
 ## Continue on Patches for Riemann Integrals
 
diff --git a/pages/Math4121/Math4121_L17.md b/pages/Math4121/Math4121_L17.md
index d0e2454..836af8a 100644
--- a/pages/Math4121/Math4121_L17.md
+++ b/pages/Math4121/Math4121_L17.md
@@ -1,4 +1,4 @@
-# Math 4121 Lecture 17
+# Math4121 Lecture 17
 
 ## Continue on Last lecture
 
diff --git a/pages/Math4121/Math4121_L18.md b/pages/Math4121/Math4121_L18.md
index 887baec..7c18629 100644
--- a/pages/Math4121/Math4121_L18.md
+++ b/pages/Math4121/Math4121_L18.md
@@ -1,4 +1,4 @@
-# Math 4121 Lecture 18
+# Math4121 Lecture 18
 
 ## Continue
 
diff --git a/pages/Math4121/Math4121_L19.md b/pages/Math4121/Math4121_L19.md
index 6998058..f7004c5 100644
--- a/pages/Math4121/Math4121_L19.md
+++ b/pages/Math4121/Math4121_L19.md
@@ -1,4 +1,4 @@
-# Math 4121 Lecture 19
+# Math4121 Lecture 19
 
 ## Continue on the "small set"
 
diff --git a/pages/Math4121/Math4121_L2.md b/pages/Math4121/Math4121_L2.md
index 6b8556c..33fc200 100644
--- a/pages/Math4121/Math4121_L2.md
+++ b/pages/Math4121/Math4121_L2.md
@@ -1,4 +1,4 @@
-# Math 4121 Lecture 2
+# Math4121 Lecture 2
 
 ## Chapter 5: Differentiation
 
diff --git a/pages/Math4121/Math4121_L20.md b/pages/Math4121/Math4121_L20.md
index 3a5db79..b78b287 100644
--- a/pages/Math4121/Math4121_L20.md
+++ b/pages/Math4121/Math4121_L20.md
@@ -1,4 +1,4 @@
-# Math 4121 Lecture 20
+# Math4121 Lecture 20
 
 ## Continue on Chapter 4
 
diff --git a/pages/Math4121/Math4121_L3.md b/pages/Math4121/Math4121_L3.md
index bf7af18..c60eb25 100644
--- a/pages/Math4121/Math4121_L3.md
+++ b/pages/Math4121/Math4121_L3.md
@@ -1,4 +1,4 @@
-# Math 4121 Lecture 3
+# Math4121 Lecture 3
 
 ## Continue on Differentiation
 
diff --git a/pages/Math4121/Math4121_L4.md b/pages/Math4121/Math4121_L4.md
index 3e64cd8..e02fe9e 100644
--- a/pages/Math4121/Math4121_L4.md
+++ b/pages/Math4121/Math4121_L4.md
@@ -1,4 +1,4 @@
-# Math 4121 Lecture 4
+# Math4121 Lecture 4
 
 ## Chapter 5. Differentiation
 
diff --git a/pages/Math4121/Math4121_L5.md b/pages/Math4121/Math4121_L5.md
index 98dd913..bde8258 100644
--- a/pages/Math4121/Math4121_L5.md
+++ b/pages/Math4121/Math4121_L5.md
@@ -1,4 +1,4 @@
-# Math 4121 Lecture 5
+# Math4121 Lecture 5
 
 ## Continue on differentiation
 
diff --git a/pages/Math4121/Math4121_L6.md b/pages/Math4121/Math4121_L6.md
index 7becfd2..6767b7b 100644
--- a/pages/Math4121/Math4121_L6.md
+++ b/pages/Math4121/Math4121_L6.md
@@ -1,4 +1,4 @@
-# Math 4121 Lecture 6
+# Math4121 Lecture 6
 
 ## Chapter 6: Riemann-Stieltjes Integral
 
diff --git a/pages/Math4121/Math4121_L7.md b/pages/Math4121/Math4121_L7.md
index bc04ae9..998b50f 100644
--- a/pages/Math4121/Math4121_L7.md
+++ b/pages/Math4121/Math4121_L7.md
@@ -1,4 +1,4 @@
-# Math 4121 Lecture 7
+# Math4121 Lecture 7
 
 ## Continue on Chapter 6
 
diff --git a/pages/Math4121/Math4121_L8.md b/pages/Math4121/Math4121_L8.md
index e192470..c918c63 100644
--- a/pages/Math4121/Math4121_L8.md
+++ b/pages/Math4121/Math4121_L8.md
@@ -1,4 +1,4 @@
-# Math 4121 Lecture 8
+# Math4121 Lecture 8
 
 ## Continue on Riemann-Stieltjes Integral
 
diff --git a/pages/Math4121/Math4121_L9.md b/pages/Math4121/Math4121_L9.md
index 5155f59..1fd0e6f 100644
--- a/pages/Math4121/Math4121_L9.md
+++ b/pages/Math4121/Math4121_L9.md
@@ -1,4 +1,4 @@
-# Math 4121 Lecture 9
+# Math4121 Lecture 9
 
 Exam next week.
 
diff --git a/pages/Math4121/index.md b/pages/Math4121/index.md
index 5ec3ae3..fa62fda 100644
--- a/pages/Math4121/index.md
+++ b/pages/Math4121/index.md
@@ -1,4 +1,4 @@
-# Math 4121
+# Math4121
 
 Riemann integration; measurable functions; Measures; the Lebesgue integral; integrable functions; $L^p$ spaces.
 
diff --git a/pages/Math416/Exam_reviews/Math416_E1.md b/pages/Math416/Exam_reviews/Math416_E1.md
new file mode 100644
index 0000000..e83e4a5
--- /dev/null
+++ b/pages/Math416/Exam_reviews/Math416_E1.md
@@ -0,0 +1,3 @@
+# Math 416 Midterm 1 Review
+
+
diff --git a/pages/Math416/Math416_L12.md b/pages/Math416/Math416_L12.md
index 0c5b0ab..a8b340a 100644
--- a/pages/Math416/Math416_L12.md
+++ b/pages/Math416/Math416_L12.md
@@ -61,7 +61,7 @@ $$
 \end{aligned}
 $$
 
-Use the fact that $f$ is holomorphic on $U$, then $f$ is continuous on $U$, so $\lim_{z\toz_1}f(z)=f(z_1)$.
+Use the fact that $f$ is holomorphic on $U$, then $f$ is continuous on $U$, so $\lim_{z\to z_1}f(z)=f(z_1)$.
 
 There exists a $\delta>0$ such that $|z-z_1|<\delta$ implies $|f(z)-f(z_1)|<\epsilon$.
 
@@ -71,7 +71,7 @@ $$
 |I|\leq\frac{1}{z_1-z_0}\int_{z}^{z_1}|f(\xi)-f(z_1)|d\xi<\frac{\epsilon}{z_1-z_0}\int_{z}^{z_1}d\xi=\epsilon
 $$
 
-So $I\to 0$ as $z_1\toz$.
+So $I\to 0$ as $z_1\to z$.
 
 Therefore, $g'(z_1)=f(z_1)$ for all $z_1\in U$.
 
diff --git a/pages/Math416/_meta.js b/pages/Math416/_meta.js
index 2d5e369..683a868 100644
--- a/pages/Math416/_meta.js
+++ b/pages/Math416/_meta.js
@@ -3,6 +3,7 @@ export default {
     "---": {
         type: 'separator'
     },
+    Exam_reviews: "Exam reviews",
     Math416_L1: "Complex Variables (Lecture 1)",
     Math416_L2: "Complex Variables (Lecture 2)",
     Math416_L3: "Complex Variables (Lecture 3)",