This site is NOT about making mathematics easy because it isn't. It is about making it make sense because it does.
M4T Library
My collection of books with very good reviews
Inequalities – The Math Olympiad Approach
1. This book can be used to introduce proofs in a way that’s beautiful (symmetry is aesthetically pleasing to most people) and simple (there are a lot of easy two or three line proofs which proves something non-obvious and yet still pretty). I also think that inequalities are more on the “practical”/applied side of math (optimizing anything is all about finding bounds and inequalities), just in case anyone thinks that this type of math is too non-practical for a student to care about. But honestly, I think that beauty and simplicity will attract students to math more than practicality, and the problems in this book are organized in a way that allows students to explore inequalities, starting from very basic claims to progressively more challenging problems (even ones coming from math competitions).
How round is your circle
2. What this book shows you is that you can really understand Mathematics, when you try to build things, even something simple, like cutting a good circle from wood. Many areas of mathematics are discussed that people instinctively feel they understand, such as the roundness of a curve or circle, dividing an angle into 3 equal parts and other interesting Objects De Mathematica. You will find fascinating ways to really model the pythagorean theorem, or gather the sectors of a circle to make an equivalent triangle. There is much to discover between these pages, and Mathematics becomes concrete, objectified, and deeply understood. As another example: “what would a 3 dimensional object that has constant width throughout (based on the tetrahedron) Look like? You can see what this object looks like, when you read the work, and see the model. To add to your understanding, the Authors have constucted Models of the various mathematical principles and ideas, that you can see with your own eyes: such as “two-tip” polyhedrons, and summing the squares of numbers from 1 to n. Reading this book will improve your grasp of mathematics, as well as inspire you to study Engineering, if you havent already. Future Engineers, will be much smarter for having read this great book. Richard H. Pratt, Ph.D.
