Appendix D: Corrections and Changes
This book is revised in place rather than reprinted, so a copy downloaded a year ago is not the copy on the site today. This appendix is the difference. It is kept current at abdulqabiz.com/mathematics-refresher-book/corrections.html, where anything found after this printing will appear first.
Corrections are places the book said something untrue; if your copy predates them, mark it up. Changes are places it said something true but unhelpfully; nothing there needs correcting in an older copy.
Every correction below came from a re-verification of the manuscript against independent computation — every worked example, all 117 exercises with their answers, the 161 drills of Appendix B, the four Checkpoint Reviews, and every cross-reference. Nothing in that pass turned up a wrong answer, and everything it did turn up is listed here in full.
That is a statement about the effort, not a guarantee. A book of this size will still be hiding mistakes, and the ones that matter are exactly the ones a careful reader trips over rather than the ones a check like this catches. If you find one — a wrong answer, a step that does not follow, a figure that misleads — please report it at the address in the Preface. It will be fixed and it will appear here.
Corrections since version 1.0
Chapter 2, the zero-product principle. Was: “It works because zero is the only number with this property — which is also why dividing by zero is forbidden.” Now: the clause after the dash was wrong. Having no zero divisors and having no reciprocal are different facts about zero, and neither causes the other. Division by zero is undefined because nothing multiplied by zero can give one.
Chapter 4, “In the wild”. Was: “least squares (1805, Legendre and Gauss).” Now: “least squares (Legendre 1805; Gauss 1809).” Legendre published first; Gauss published in 1809, claiming use from 1795.
Preface, the retention protocol. Was: “four cumulative Checkpoint Reviews are placed in the text where Parts end.” Now: they sit after Chapters 2, 8, 14 and 20. Only three of those are part boundaries — Checkpoint II falls inside Part II — and Part IV has no checkpoint.
Was: “do the five main Exercises.” Now: “the chapter’s main Exercises.” Most chapters have five; Chapters 2 and 6 have six.
Appendix A, answer to Exercise 2.3. Was: “x < -2 or x \ge 1 (excluding x = -2).” Now: the stated solution set never contained -2. It is barred because the expression is undefined there, not because of a sign change.
Changes since version 1.0
The Preface now describes Part IV. “How to read it” walked Parts I to III and stopped, so a reader deciding whether the book was for them was never told the chapters on artificial intelligence existed.
Eight exercises are now labelled as memory exercises. Exercises 3.3, 7.1, 7.3, 10.1, 10.2, 11.1, 12.1 and 15.3(b) ask for something the same chapter has already worked with the same numbers. The questions and answers are unchanged — they were never wrong — but each now says so, and asks you to close the book and work it from memory before comparing. That is the retention protocol’s fourth step applied where it fits best: a worked example redone from a blank page is worth more than a fresh problem solved with the method still on screen.
If you find an error this appendix does not list, please report it at the address in the Preface so it can join the next revision.