Isodimensional Discrete Mathematics (IDM)
The IDM is a different kind of mathematics, thanks to the discrete nature of its foundations. The definition of basic mathematical concepts (numbers, number systems, real line, etc.) is simpler and more intuitive, without diminishing mathematical rigor. In addition, the discrete foundation usually simplifies deductions and proofs and, in general, facilitates mathematical abstraction. Another quality to highlight of the IMD is that it does not interfere at all with the principles, criteria and/or approaches of traditional mathematics because, simply, they are two different ways of doing mathematics, but sharing the same mathematical concepts, so the conclusions obtained in one, can also be valid in the other, and vice versa. The foundations of the IDM can be found in the book Nuevos Fundamentos de la Recta Numérica, which can be downloaded freely, although it is also possible to acquire it in paper (soft cover), both in Spanish and in English (Discrete Foundations of Real Numbers). This book, although it is self-sufficient in its content, is an extract of another much more voluminous one entitled Fundamentos Discretos de una Nueva Matemática, devoted to the study of basic concepts of different types (arithmetic, algebraic, geometric, etc.), from the perspective of discrete foundations. This analysis has allowed us to solve some pending questions in traditional mathematics, such as unifying circular and hyperbolic complex numbers, or providing working methods that are not viable (in a general form) in continuous mathematics, such as the differentiation and integration of discrete functions. Other topics of interest are also dealt with, for example, finding out the reasons for some basic theorems, knowing the nature of the main mathematical constants, or thoroughly analyzing complex and hyper-complex algebras (which exceed one million, so only statistical results on its properties are provided), or studying basic physical concepts (randomness, time, entropy, etc.) from the point of view of the IDM. More details about this book can be found in the table of contents.