Has anyone ever seen with their own eyes that the Earth goes around the sun? Even to this day, no one has. However, 500 and even 2000 years ago, some astronomers managed to point out that this is the case. At that time, people's range of activities was strictly confined, the technology and tools used were extremely primitive, and many of the mathematical methods used today had not been developed. How did those astronomers make and verify this discovery? This book explains this exciting demonstration process. It enables anyone with a basic junior-high-school knowledge of geometry and a certain degree of spatial imagination to understand this and other interesting discoveries in the solar system. By demonstrating this interesting process, the book not only satisfies readers' curiosity using the simplest mathematics, but also inspires them to explore the new and unknown world.

Has anyone ever seen with their own eyes that the Earth goes around the sun? Even to this day, no one has. However, 500 and even 2000 years ago, some astronomers managed to point out that this is the case. At that time, people's range of activities was strictly confined, the technology and tools used were extremely primitive, and many of the mathematical methods used today had not been developed. How did those astronomers make and verify this discovery? This book explains this exciting demonstration process. It enables anyone with a basic junior-high-school knowledge of geometry and a certain degree of spatial imagination to understand this and other interesting discoveries in the solar system. By demonstrating this interesting process, the book not only satisfies readers' curiosity using the simplest mathematics, but also inspires them to explore the new and unknown world.

This book provides an introduction to the analysis of stochastic dynamic models in biology and medicine. The main aim is to offer a coherent set of probabilistic techniques and mathematical tools which can be used for the simulation and analysis of various biological phenomena. These tools are illustrated on a number of examples. For each example, the biological background is described, and mathematical models are developed following a unified set of principles. These models are then analyzed and, finally, the biological implications of the mathematical results are interpreted. The biological topics covered include gene expression, biochemistry, cellular regulation, and cancer biology. The book will be accessible to graduate students who have a strong background in differential equations, the theory of nonlinear dynamical systems, Markovian stochastic processes, and both discrete and continuous state spaces, and who are familiar with the basic concepts of probability theory.