This book on mathematics discusses the innovative theories and applications of the field. This book elucidates the concepts and innovative models around prospective developments with respect to mathematics. Principles and theorems that are developed in this field are of great importance to various allied fields. The various advancements in this field are glanced at and their applications as well as ramifications are looked at in detail. The chapters covered in this extensive book deal with the core subject of mathematics. For someone with an interest and eye for detail, this book covers the most significant topics in the field of mathematics.