diff --git a/kaplansky_direct_finite_char2_v2.txt b/kaplansky_direct_finite_char2_v2.txt
index 80c29aa..5da0b7e 100644
--- a/kaplansky_direct_finite_char2_v2.txt
+++ b/kaplansky_direct_finite_char2_v2.txt
@@ -751,14 +751,12 @@ Two things worth emphasizing from those conventions:
      transpose-times-X, not conjugate-transpose; the field K has no
      notion of conjugate-transpose in general.
 
-PART VI. WHAT A CURIOUS READER CAN ACTUALLY COMPUTE
+PART VI. EXPLICIT COMPUTATIONS
 ================================================================================
 
-The mathematics of the paper is genuinely beyond high school. But
-several SECTIONS OF IT are not: they are finite calculations you can
-do by hand with a pencil, or on a computer in a short script. Below
-are six small exercises, each roughly 30-60 minutes of careful work
-for a determined reader. Together they touch the "nerve" of the
+Several sections of the paper are finite calculations that can be
+done by hand with a pencil, or on a computer in a short script. Below
+are six small exercises. Together they touch the "nerve" of the
 argument.
 
 Exercise 1 (Direct finiteness of finite matrices). Let A, B be
@@ -996,7 +994,7 @@ requirement is not a matter of taste. Two scalar facts drive it:
   - Can the "nonsofic group" be simplified to a nicer presentation
     with fewer generators and relations?
 
-7. What a high school reader should take away.
+7. Summary.
 
   - Infinite-dimensional linear algebra really is different from
     finite-dimensional linear algebra. A one-sided inverse of a