Solutions for the Problems in Numbers: Rational and Irrational by Ivan Niven by John Weatherwax (PDF)

Description

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 equationx^5 – 3 x^3 + 2 x^2 + x – 1 = 0In 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. Don’t waste your time checking the values 1/2 or 1/3 (which might be considered good test answers) since they can’t be roots!Another great area that this book excels in is in the approximation of irrational numbers by rational numbers. We all learned in high school that pi is approximately 22/7 but did we learn how to get approximations like this? Whatare similar rational approximations to e, sqrt(2), sqrt(3), etc. These are another set of nice tools to have in your toolbox. In addition, once understood they are really easy to generate and you look smart saying: “I got my answer using the approximation e = 30/11″.What you’ll find in this text are my solutions to the end of section problems as I worked through this excellent book.

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