Inequalities are a boon to various derivative valuation problems that arise in real life. One can use inequalities to get around problems for which closed form solutions are difficult. The other day I was struggling with an inequality . So, took my friend’s help who worked on it in a jiffy and produced a bound. He also happened to suggest this book to me so that , I can quickly refresh basic inequalities and probably stop bothering him with trivial questions –:) . This book is a remarkable little gem that quickly got me up to speed .
First three chapters of the book can be speed read as they introduce the inequalities from an axiomatic point of view. Chapter 4 is probably the best in this book as it states and proves arithmetic-mean-geometric-mean inequality, Cauchy inequality, Holder inequality, Triangle inequality, Minkowski’s inequality using algebra and geometry proofs.
Chapter 5 talks about various applications of the inequalities. Most of the applications use the Arithmetic mean Geometric mean inequality except one example where equation of a tangent is derived using Cauchy’s inequality( I liked this example as it was a very simple and cool application of Cauchy’s inequality). Chapter 6 is extremely relevant from a metric space perspective, where various inequalities are applied to prove that a metric has the relevant properties of distance metric. For a person looking to brush up his/her knowledge on inequalities, this book is apt. It can be easily read within a couple of hours.