This book is intended as a teacher's manual & as an independent-study handbook for students & mathematical competitors Based on a traditional teaching philosophy & a non-traditional writing approach (the stair-step method) this book consists of new problems with solutions created by the authors The main idea of this approach is to start from relatively easy problems & "step-by-step" increase the level of difficulty toward effectively maximizing students' learning potential In addition to providing solutions a separate table of answers is also given at the end of the book A broad view of mathematics is covered well beyond the typical elementary level by providing more in depth treatment of Geometry & Trigonometry Number Theory Algebra Calculus & Combinatorics