diff --git a/documents/by-course/math-8/course-notes/main.typ b/documents/by-course/math-8/course-notes/main.typ
index ff1b9ad..c2c92e2 100644
--- a/documents/by-course/math-8/course-notes/main.typ
+++ b/documents/by-course/math-8/course-notes/main.typ
@@ -17,8 +17,18 @@
 
 #outline()
 
+= Introduction
+
+Math 8 is an introductory course on mathematical logic and the methods of
+proof. In general it will be quite trivial for anyone somewhat familiar with
+competition mathematics or proofs. If you are at UCSB, I highly recommend you
+take this course as soon as possible to unlock the rest of the higher
+mathematics offerings here (which are much more interesting).
+
 = Course Logistics
 
+Everything in this section is information only valid for the Winter 2025 quarter with Professor Porter.
+
 The textbook for the course is _Smith, Eggen, Andre. A Transition to Advanced
 Mathematics. 8th ed_. #smallcaps[isbn:] `978-1-285-46326-1`. Chapters 1-5 will
 be covered.
@@ -315,13 +325,15 @@ $ P => Q and Q => P $
   then showing that this fact leads to a contradiction.
 
   A proof by contradiction of $P => Q$ proceeds by assuming $P and not Q$, then
-  showing a contradiction, implying that $P$ indeed implies $Q$.
+  showing a contradiction, forcing that $P$ indeed implies $Q$.
 ]
 
 #definition[
   A real number $x in RR$ is called rational iff
   $ exists p,q in ZZ, x = p / q $
+]
 
+#definition[
   $x$ is irrational if it is not rational.
 ]