mathematics

Mathematics: From the Birth of Numbers
$50.00
This summer I am tutoring a 9th grader in mathematics. Periodically we take a break from doing problems and simply talk about math and algebra in a general sense. As we talk and work through some concepts, we come up with all kinds of questions, like where did "0" come from and which set (the set of integers or the set of even numbers), both infinite in size, is larger. Also, if kilo- means a thousand and milli- means thousand where did the two prefixes come from.

It turns out that by bringing just one book (albeit a very big book) to his house, we have been able to answer all his questions.

This is a phenomenal book. I think adult armchair mathematicians will get a big kick out of it, but more importantly, it is very likely to pique the interest of middle school and high school students when they see it lying around the family library.

I doubt most students will leave their video games to look at a book like this, but one never knows. Even if it is just one student out of a thousand, it is worth it. That student might be your daughter or your son.

The Princeton Companion to Mathematics
$99.00
This book is a great companion with which to navigate higher mathematics. It allows you to quickly intuit the stunning abstract concepts of higher mathematics, that you often cannot easily see when following the traditional approach of deriving concepts rigorously, from a well-defined foundation. This companion guide gives you a top-down perspective to complement the necessary rigorous bottom-up perspective that you get elsewhere. Mathematical encyclopedias and wikipedia topics don't do this as effectively, so I heartily recommend this book.

What Is Mathematics? An Elementary Approach to Ideas and Methods
$24.95
Basic Math Quick Reference Handbook
This thorough coverage of so many aspects of mathematics forms a threshold that separates the interested enthusiast from the professional mathematician.
Couldn't be better.

Concepts of Modern Mathematics
$12.95
I think this book is poorly titled. It describes itself as a book about concepts in "modern" mathematics. However, the concepts in the book are actually mostly quite old. Nearly all of the topics and problems discussed are those I learned way back when I was in school (longer ago than I care to imagine) and are mostly of an elementary nature.

Although the book seems well written for a short survey of basic mathematics topics, it in no way discusses much in the way of "modern" mathematics concepts, which I would consider to be those sorts of mathematical topics and problems that face mathematicians today and that pertain to modern applications.

I was very disappointed in the book and felt it was a waste of the $10 I spent on it.