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fix: Proofread Part Foxtrot (optimization) - #83

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Jun 19, 2026
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Closes #60.

Proofread src/minmax.typ, src/regions.typ, src/opt.typ, src/mt2.typ (the files included under Part Foxtrot). Found and fixed:

  • src/minmax.typ: "draw in green" → "drawn in green", and "An critical inflection point" → "A critical inflection point", to match the parallel "drawn in ..." bullet list.
  • src/minmax.typ: broken punctuation in the "taking square roots of both sides, That is, ..." tip, joined into one sentence.
  • src/minmax.typ: in the critical-points sample for $f(x,y,z) = z(x-y)(y-z) - 2xz$, a sign flip in the substitution step "$x = 2(z+2) + z = z+4$" (should be "$- z$"); the final answer $z+4$ was already correct, only the intermediate algebra step was wrong.
  • src/regions.typ: stray $ placement in "$(1,0)$ and $(0,1$)." → "$(0,1)$".
  • src/regions.typ: subject-verb agreement, "the boundary ... are the four sides" → "is the four sides".
  • src/regions.typ: in the 3D regions table, the limit-cases entry for $x^2+y^2+z^2=1$, $x,y,z>0$ incorrectly listed boundary-style points "$(1,0)$ and $(0,1)$" (which aren't even valid 3-variable points); replaced with the correct limit cases "$x \to 0^+$ or $y \to 0^+$ or $z \to 0^+$", consistent with the analogous row in the 2D table.
  • src/opt.typ: missing "$g$" in "$ (x,y,z) = x+2y+3z=4$" (the constraint function), should be "$g(x,y,z) = ...$".
  • src/opt.typ: duplicated "The first expression" in a footnote where the second sentence should refer to "the second expression".
  • src/opt.typ: "doesn't like on the constraint" → "doesn't lie on the constraint".
  • src/opt.typ: in the $x^3+3y^3+4z^3$ Lagrange multiplier example, the total LM-critical point count was miscounted as 26; since the per-case sign choices are tied together by ratios like $z = 4x$ (not independent), the correct total is 14, not 26. This is also confirmed by the next sentence, which says the count "reduces ... to just 7" by halving via the ±-symmetry ($14/2 = 7$, but $26/2 = 13$ would be inconsistent).

No large mathematical errors were found beyond the miscounted LM-critical points above; src/mt2.typ (the practice midterm problem statements) had no issues.


Generated by Claude Code

Closes #60.

Proofread src/minmax.typ, src/regions.typ, src/opt.typ, src/mt2.typ
(the files included under Part Foxtrot). Found and fixed:

- src/minmax.typ: "draw in green" -> "drawn in green", and "An critical
  inflection point" -> "A critical inflection point", to match the
  parallel "drawn in ..." bullet list.
- src/minmax.typ: broken punctuation in the "taking square roots of both
  sides, That is, ..." tip, joined into one sentence.
- src/minmax.typ: in the critical-points sample for
  f(x,y,z) = z(x-y)(y-z) - 2xz, a sign flip in the substitution step
  "x = 2(z+2) + z = z+4" (should be "- z"); the final answer z+4 was
  already correct, only the intermediate algebra step was wrong.
- src/regions.typ: stray "$" placement in "(0,1$)" -> "(0,1)$".
- src/regions.typ: subject-verb agreement, "the boundary ... are the
  four sides" -> "is the four sides".
- src/regions.typ: in the 3D regions table, the limit-cases entry for
  x^2+y^2+z^2=1, x,y,z>0 incorrectly listed boundary-style points
  "(1,0) and (0,1)" (which aren't even valid 3-variable points);
  replaced with the correct limit cases "x -> 0+ or y -> 0+ or z -> 0+",
  consistent with the analogous row in the 2D table.
- src/opt.typ: missing "g" in "$ (x,y,z) = x+2y+3z=4$" (the constraint
  function), should be "$g(x,y,z) = ...$".
- src/opt.typ: duplicated "The first expression" in a footnote where the
  second sentence should refer to "the second expression".
- src/opt.typ: "doesn't like on the constraint" -> "doesn't lie on the
  constraint".
- src/opt.typ: in the x^3+3y^3+4z^3 Lagrange multiplier example, the
  total LM-critical point count was miscounted as 26; since the
  per-case sign choices are tied together by ratios like z = 4x (not
  independent), the correct total is 14, not 26. This is also confirmed
  by the next sentence, which says the count "reduces ... to just 7" by
  halving via the +/- symmetry (14/2 = 7, but 26/2 = 13 would be
  inconsistent).

No large mathematical errors were found beyond the miscounted LM-critical
points above; src/mt2.typ (the practice midterm problem statements) had
no issues.

Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01RnJnjJdFpjW9nJ1BfZGXo1
@vEnhance
vEnhance merged commit 2e2537f into main Jun 19, 2026
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@vEnhance vEnhance added the proofreading-campaign Systematically proofread the textbook label Jun 19, 2026
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Proofread Part Foxtrot

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