Equations and Inequalities

Rating:
Summary: Unusual math here
Review: This book contains just 4 chapters:
(1) Algebraic Identities and Equations
(2) Algebraic Inequalities
(3) Number Theory
(4) Hints and Answers
The material is not readily available in any book I have seen. The 1st chapter covers finite sums, polynomials, and irrational equations. The 2nd chapter covers how to prove many inequalities and the 3rd chapter uses congruences and other principles to derive many interesting number theory results.
For example in chapter 3 I encountered the following "Show that among 50 arbitrarily chosen distinct prime numbers one can always find 13 primes such that the difference between any two of them is divisible by 5". Sounds difficult but is really trivial using methods in the book. There are lots of worked examples and exercises after each topic. The methods are understandable but not trivial ! Chapter 4 is the jewel as it gives the solutions to the exercises, I hate it when I don't know how to do a problem and have no way to find out. Also, sometimes one solves a problem incorrectly or there is a better way. Most math students today do not do anywhere near enough calculations and so are weak in standard manipulation and this will correct that if the exercises are attempted. I really like this book and so will you !

Rating:
Summary: Great First course in Problem Solving
Review: This is a great book for high school students and undergrads who don't have much experience with solving problems. Sums, inequalities, systems of equations, and number theory are the core of the book. The author provides worked examples and then a set of exercises and some challenging problems are included at the end of each chapter(almost all of the solutions are given). Very readable and a great addition to any mathematics library. Highly recommend.