diff --git a/src/usage/indexing.md b/src/usage/indexing.md
index 872ddfd..f9ac692 100644
--- a/src/usage/indexing.md
+++ b/src/usage/indexing.md
@@ -5,8 +5,8 @@ Indexing is the process of building a data structure that allows for efficient s
 To construct an index for vectors, first create a table named `items` with a column named `embedding` of type `vector(n)`. Then, populate the table with generated data.
 
 ```sql
-CREATE TABLE items (val vector(3));
-INSERT INTO items (val) SELECT ARRAY[random(), random(), random()]::real[] FROM generate_series(1, 1000);
+CREATE TABLE items (embedding vector(3));
+INSERT INTO items (embedding) SELECT ARRAY[random(), random(), random()]::real[] FROM generate_series(1, 1000);
 ```
 
 ::: tip
diff --git a/src/use-case/sparse-vector.md b/src/use-case/sparse-vector.md
index 9de306d..13029e5 100644
--- a/src/use-case/sparse-vector.md
+++ b/src/use-case/sparse-vector.md
@@ -200,7 +200,7 @@ D_{L2} = \Sigma (x_i - y_i) ^ 2
 $$
 For sparse vectors, `vector_dot_ops` calculates the dot product, which is a more efficient method.
 $$
-D_{dot} = - \Sigma x_iy_i
+D_{dot} = - \Sigma x_i y_i
 $$
 
 
@@ -266,4 +266,4 @@ scores = reranker.compute_score([["The text you want to search...", candidate] f
 reranked_text = [t for _, t in sorted(zip(scores, mix_text))]
 ```
 
-Congratulations! We have now completed our first step into the world of sparse vector search.
\ No newline at end of file
+Congratulations! We have now completed our first step into the world of sparse vector search.
diff --git a/typos.toml b/typos.toml
new file mode 100644
index 0000000..10d3da7
--- /dev/null
+++ b/typos.toml
@@ -0,0 +1,3 @@
+[default]
+extend-ignore-re = ['\$.+\$']
+extend-ignore-identifiers-re = ['\$.+\$']