Working Through Hill Algebra Textbook
I picked up the Hill Algebra Textbook back when I was still grinding through discrete math at a community college, mostly because the library had three copies sitting on a cart and none of the other textbooks in the stack had answers in the back. The book itself is a slim volume, roughly 180 pages, covering basic algebraic manipulation with an emphasis on factoring, quadratic forms, and introductory matrix operations that bleed into linear algebra territory. It is not a comprehensive algebra text. It is a bridge text. The way it structures problems is what makes it worth using or not worth using, depending on your tolerance for worked examples. Each chapter opens with a dense theory section—sometimes fewer than ten pages—then moves into problem sets where the difficulty jumps from trivial to slightly questionable without much transition. I remember working through chapter four on factoring trinomials where the author assumes you already know how to complete the square, which is something taught two chapters later. That ordering issue tripped up a lot of people in my study group. We ended up making a shared Google Doc with cross-references so nobody wasted two hours trying to factor something they hadn't learned how to handle yet.
Where Hill Algebra Textbook Falls Short
The book has a genuine gap in its coverage of polynomial long division. There is one example, and it is wrong in the second step. I caught it because the remainder didn't match the expected value, which you can verify by multiplying the quotient back out and adding the remainder. The errata for this edition was never published. What I did was just skip that example and use the method from my pre-calculus book instead, which covers the same ground with actual checking steps. If you are self-studying and run into this, do not assume the book is misleading you on purpose. It is just a one-off typo that propagates if you follow along blindly. Another thing nobody mentions in reviews: the matrix section assumes familiarity with determinants before introducing them. You will see a cofactor expansion problem on page 142 without any definition of what a determinant actually is. The index points to page eight, which covers order of operations for algebraic expressions. This is not a minor navigation error. It is a structural gap that breaks the flow for anyone not already comfortable with the material. I spent about twenty minutes flipping through my old linear algebra notes to find a proper definition before I could even attempt the problem set. If you are using this book as a primary resource, keep a supplemental text nearby. Otherwise you will hit that wall and either stall out or guess your way through.
What the Book Does Well
The problem sets on systems of equations are genuinely useful. They cover substitution, elimination, and graphing methods in roughly equal measure, which is more balanced than most texts in this price range. The worked examples walk through the mechanics without skipping algebraic steps, which is rare. Most books assume you can handle the arithmetic mentally. This one writes out the intermediate lines, which saves time when you are checking your work. The answer key is another point in its favor. Not every chapter has full solutions, but the odd-numbered problems in the back include final answers. That is enough to verify your approach without giving away the method. I used the answer key to quickly check whether my setup was correct before redoing the work, which cut my practice time roughly in half compared to going through a text with no answers at all.
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How I Actually Used It
I treated it as a supplement, not a standalone course. My main text was Larson's College Algebra, and I used Hill Algebra Textbook for targeted practice on factoring and matrix operations. When I needed extra problems on completing the square, I went to the relevant chapter here. When I needed more depth on logarithms, I switched to the main text. This split worked because the book is narrow in scope but solid in the areas it covers. If you are buying this used, check the printing date. Earlier editions had different page orders for the polynomial section, and some libraries have copies with marginalia from students who wrote over the examples. That can make the book harder to follow. I found a clean copy at a campus surplus sale for four dollars, and it was in better condition than the library's three-copy set. Used copies tend to vary in quality, so inspecting the problem sets before committing is worth the five minutes. The book does not cover rational expressions, conic sections, or sequences and series. If you need those, you are looking at a different text entirely. Knowing the scope upfront saves you from expecting coverage that is not there. I almost returned my copy after hitting the end of the matrix chapter and realizing there was no discussion of eigenvalues, but that was never going to be in a book this size. The subtitle says Algebra and Matrices, which is accurate if you read it literally rather than hoping it means everything algebraic related to matrices.
Practical Takeaways
Use it for factoring practice and basic matrix operations. Pair it with a full algebra text for anything beyond those topics. Check the answer key to validate your approach. Expect one wrong example in the polynomial long division section and work around it. Keep a second resource nearby for determinant definitions and related topics. At this price point, it is adequate for what it attempts, which is not very much, but it handles those limited areas without major errors aside from the one typo I mentioned.
