​The book records the essential discoveries of mathematical and computational scientists in chronological order, following the birth of ideas on the basis of prior ideas ad infinitum. The authors document the winding path of mathematical scholarship throughout history, and most importantly, the thought process of each individual that resulted in the mastery of their subject. The book implicitly addresses the nature and character of every scientist as one tries to understand their visible actions in both adverse and congenial environments. The authors hope that this will enable the reader to understand their mode of thinking, and perhaps even to emulate their virtues in life.

This volume documents the contributions presented at The ICRTMPCS II International Conference on Advances in Mathematical and Computational Sciences. Entries focus on modern trends and techniques in branches of pure and applied mathematics, statistics, and computer science. Highlighting applications in coding theory, cryptography, graph theory, fuzzy theory, variance analysis, data analysis, and sampling theory.

Johann Bode developed a so-called law of planetary distances best known as Bode’s Law. The story of the discovery of Juno in 1804 by Karl Harding tells how Juno fit into that scheme and is examined as it relates to the philosopher Georg Hegel’s 1801 thesis that there could be no planets between Mars and Jupiter. By 1804 that gap was not only filled but had three residents: Ceres, Pallas and Juno! When Juno was discovered no one could have imagined its study would call into question Newton’s law of gravity, or be the impetus for developing the mathematics of the fast Fourier transform by Carl Gauss. Clifford Cunningham, a dedicated scholar, opens to scrutiny this critical moment of astronomical discovery, continuing the story of asteroid begun in earlier volumes of this series. The fascinating issues raised by the discovery of Juno take us on an extraordinary journey. The revelation of the existence of this new class of celestial bodies transformed our understanding of the Solar System, the implications of which are thoroughly discussed in terms of Romantic Era science, philosophy, poetry, mathematics and astronomy. The account given here is based on both English and foreign correspondence and scientific papers, most of which are translated for the first time.

This book presents interesting, important unsolved problems in the mathematical and computational sciences. The contributing authors are leading researchers in their fields and they explain outstanding challenges in their domains, first by offering basic definitions, explaining the context, and summarizing related algorithms, theorems, and proofs, and then by suggesting creative solutions. The authors feel a strong motivation to excite deep research and discussion in the mathematical and computational sciences community, and the book will be of value to postgraduate students and researchers in the areas of theoretical computer science, discrete mathematics, engineering, and cryptology.