This book encourages efficient and active self-study in mathematics learners. It contains over 200 challenging exercises, most of which are developed specifically for this book. The exercises help readers to internalize what is taught in the text, refine and expand select issues, and prepare the ground for continued learning.  The book’s structure engages with the reader actively, leading to more profound understanding, satisfaction and deep insights in learning mathematics. The book also includes many definitions and formulas.The book starts off with elementary mathematics and takes the readers on a tour de force that enables them to better grasp advanced topics in mathematics, as well as the spirit of mathematical research. It demonstrates and instils values of mathematical research observation, conjecture, proof, implementation, generalization and raising new questions. weiterlesen