Forecasting in Mathematics - Recent Advances, New Perspectives and Applications

What is it about?

This book is titled Forecasting in Mathematics – Recent Advances, New Perspectives and Applications. Additionally, each time I work on the field of mathematical probability and statistics I find the pleasure to tackle the knowledge, the theorems, the proofs, and the applications of the theory. In fact, each problem is like a riddle to be solved, a conquest to be won, and I become relieved and extremely happy when I reach the end of the solution. This verily proves two important facts: firstly, the power of mathematics and its models to deal with such kind of problems and secondly the power of the human mind that is able to understand such class of problems and to tame such a wild concept that is randomness, probability, stochasticity, uncertainty, chaos, chance, nondeterminism. Mathematical probability and statistics are an attractive, thriving, and respectable part of mathematics. Some mathematicians and philosophers of science say the gateway to mathematics deepest mysteries. Moreover, mathematical probability and statistics denotes an accumulation of mathematical discussions connected with the efforts to most efficiently collect and use numerical data subject to random or deterministic variations. In the twentieth century and present time, the concept of probability and mathematical statistics has become one of the fundamental notions of modern science and philosophy of nature. This was accomplished after a long history of efforts done by prominent and distinguished mathematicians and philosophers like the famous French Blaise Pascal and Pierre de Fermat, the Dutch Christiaan Huyghens, the Swiss Jakob Bernoulli, the German Carl Friedrich Gauss, the French Siméon-Denis Poisson, the English Thomas Bayes, the French Joseph Louis Lagrange and Pierre-Simon de Laplace, the English Karl Pearson and Ronald Aylmer Fisher, the Russian Andrey Nikolaevich Kolmogorov, the American John von Neumann, etc… As a matter of fact, each time I read or meditate these outstanding giants I feel the respect, the admiration, and the esteem to these magnificent men and giants of science who most of them were mathematicians, physicists, astronomers, statisticians, philosophers, etc... at the same time. They were, as we call them today: Universalists. Moreover, the book develops methods for simulating simple or complicated processes or phenomena. If the computer can be made to imitate an experiment or a process, then by repeating the computer simulation with different data, we can draw statistical conclusions. Thus, a simulation of a spectrum of mathematical processes on computers was done. The result and accuracy of all the algorithms are truly amazing and delightful; hence, this confirms two complementary accomplishments: first the triumphs of the theoretical calculations already established using different theorems and second the power and success of modern computers to verify them. To conclude, due to its universality, mathematics is the most positive and certain branch of science. It is successfully called by philosophers the Esperanto of all sciences since it is the common, the logical, and the exact language of understanding, capable of expressing accurately all scientific endeavor. Although Probability and Statistics are approximate sciences that deal with rough guesses, hypotheses tests, estimated computations, expected calculations, and uncertain results, they still keep in them the spirit of “exact” sciences through their numbers, proofs, figures, and graphs, since they remain to be a branch of mathematics. Surely, the pleasure of working and doing mathematics is everlasting. I hope that the reader will benefit from it and share the pleasure of examining the present book. Sincerely, I am truly astonished by the power of probability and statistics to deal with deterministic or random data and phenomena, and this feeling and impression never left me from the first time I was introduced to this branch of science and mathematics. I hope that in the present book I will convey and share this feeling with the reader. I hope also that he will discover and learn about the concepts and applications of the probability and statistics paradigm.

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Why is it important?

Mathematical probability and statistics are an attractive, thriving, and respectable part of mathematics. Some mathematicians and philosophers of science say the gateway to mathematics deepest mysteries. Moreover, mathematical statistics denotes an accumulation of mathematical discussions connected with the efforts to most efficiently collect and use numerical data subject to random or deterministic variations. In the twentieth century and present time, the concept of probability and mathematical statistics has become one of the fundamental notions of modern science and philosophy of nature. This was accomplished after a long history of efforts done by prominent and distinguished mathematicians and philosophers. This book is an illustration of the use of mathematics when applied to solve specific problems in engineering, statistics, or science in general.

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