This book is aimed at every fellow mathematician, but primarily at every new colleague who is about to participate in the A.S.E.P. competition. It is also directed at students with high goals.

It contains those theoretical elements that are not mentioned in high school textbooks and which we consider essential knowledge for a prospective mathematics teacher. These theoretical elements are accompanied by appropriate examples and applications.

We deemed it necessary to propose solutions for representative original exercises, for which a brief solution is provided at the end of each chapter. The chapters that are developed are:

• Algebra
• Analysis
• Statistics
• Probabilities
• Euclidean Geometry
• Analytical Geometry

At the end of the book, there are appendices with multiple-choice questions from all chapters along with their answers. A second appendix contains representative lesson plans from the taught material in high school.