I am usually disappointed with American math text books. I have had an underwhelming experience with them. Often I open a book and in the next 15 minutes, I find a mistake, a typo, a misguided explanation, sloppiness, a misconception or some other annoyance.
I was pleasantly surprised when I opened the book Introduction to Algebra by Richard Rusczyk. I didn’t find any flaws in it — not in the first 15 minutes, and not even in the first hour. In fact, having used the book many times I have never found any mistakes. Not even a typo. This was disturbing. Is Richard Rusczyk human? It was such an unusual experience with an American math book, that I decided to deliberately look for a typo or a mistake. After half a year of light usage, I finally found something.
Look at problem 7.3.1.
Five chickens can lay 10 eggs in 20 days. How long does it take 18 chickens to lay 100 eggs?
There is nothing wrong with this problem. But the book is accompanied by the Introduction to Algebra Solutions Manual in which I found the following solution, that I’ve shortened for you:
The number of eggs is jointly proportional to the number of chickens and the amount of time. One chicken lays one egg in 10 days. Hence, 18 chickens will lay 100 eggs in 1000/18 days, which is slightly more than 55 and a half days.
What is wrong with this solution? Richard Rusczyk is human after all.
I like this book for its amazing accuracy and clean explanations. There are also a lot of diverse problems in terms of difficulty and ideas. Richard Rusczyk has good taste. Many of the problems are from different competitions and require inventiveness. I like that there are a lot of challenge problems that go beyond the boring parts of algebra. Also, I like that important points of algebra are chosen wisely and are emphasized.
This book might not be for everyone. It doesn’t have pretty pictures. It doesn’t have color at all. This is not a flaw for a math book. The book concentrates on ideas and problems, not entertainment. So if you’re looking for math entertainment, you’ll find it on my blog. For solid study, try Richard Rusczyk’s books.