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Exercises at the end of each chapter are designed to highlight and reinforce material in the chapter and encourage the reader to develop a deeper understanding of the material. It is especially useful for geoscientists and mechanical, electrical, environmental, and chemical engineers who would like to learn more about the engineering technology needed to produce oil and gas. Our colleagues in industry and academia and students in multidisciplinary classes helped us identify material that should be understood by people with a range of technical backgrounds. We thank Helge Alsleben, Bill Eustes, Jim Gilman, Pradeep Kaul, Don Mims, Wayne Pennington, and Rob Sutton for comments on specific chapters and Kathy Fanchi for helping prepare this manuscript.
Do you like this book? How to Read and Open File Type for PC ? This article is about the study of topics such as quantity and structure. When mathematical structures are good models of real phenomena, then mathematical reasoning can provide insight or predictions about nature. The research required to solve mathematical problems can take years or even centuries of sustained inquiry. The universe cannot be read until we have learned the language and become familiar with the characters in which it is written. It is written in mathematical language, and the letters are triangles, circles and other geometrical figures, without which means it is humanly impossible to comprehend a single word.
Without these, one is wandering about in a dark labyrinth. David Hilbert said of mathematics: “We are not speaking here of arbitrariness in any sense. Mathematics is not like a game whose tasks are determined by arbitrarily stipulated rules. Rather, it is a conceptual system possessing internal necessity that can only be so and by no means otherwise. There is no clear line separating pure and applied mathematics, and practical applications for what began as pure mathematics are often discovered.
Mathematics has since been greatly extended, and there has been a fruitful interaction between mathematics and science, to the benefit of both. Mathematical discoveries continue to be made today. 9 million, and more than 75 thousand items are added to the database each year. In Greece, the word for “mathematics” came to have the narrower and more technical meaning “mathematical study” even in Classical times. Some of these definitions emphasize the deductive character of much of mathematics, some emphasize its abstractness, some emphasize certain topics within mathematics. Today, no consensus on the definition of mathematics prevails, even among professionals. There is not even consensus on whether mathematics is an art or a science.
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