Numbers: Rational and Irrational

by Ivan Niven

If you desire to compete in mathematical competitions or have a leg up on your fellow student on your college science tests this is one of the best book to read. There are a great number of mathematical gems that once you learn and internalize them will save you a huge amount of time on competition style tests. For example, given that most tests don't allow calculators the roots of any polynomial you are given on a test must be relatively simple (and not irrational numbers which are difficult to compute with on timed tests). Given that, I ask what are the possible rational roots of the following equation x^5 - 3 x^3 + 2 x^2 + x - 1 = 0.

In the section of the text called ``Rational Roots of Polynomial Equations'' the book shows that there are only two possible rational values you need to check: plus and minus one. That knowledge gives rise to a huge savings in time.

I'm not the only one who has a very high view of this book. Readers can see what others have said here.

To make sure I understood this material as well as possible, as I read the book, I worked all the exercises at the end of each chapter.

Originally these notes and solutions were written in PDF (using the mathematical typesetting language LaTeX). I converted the PDF format to a format I thought more people would find easier to read. You can preview and buy a kindle version of the book here. If you are interested in purchasing the PDF version please contact me below.

As always, I am interested in hearing about any errors that might exist in this material.

John Weatherwax
Last modified: Tue Apr 15 07:08:47 EDT 2014