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Mathematical Methods for Engineers and Geoscientists

We start with a fun puzzle in mathematics and mathematical methods. How many corners does a four-dimensional cube have? Does such a thing exist, you ask? You may be a geoscientist or a philosopher. If your answer is: there are surely more than the eight corners there are for a three-dimensional cube, you are an engineer. If you know without hesitation that there are exactly sixteen corners and you can prove why, you are a mathematician. To explain the goal of this book, I refer to Hersh (1997): The United States suffers from “innumeracy” in its general population, “math avoidance” amonghigh-schoolstudents,and50percentfailureamongcollegecalculusstudents.Causes include starvation budgets in the school, mental attrition by television, parents who don’t like math. There’s another, unrecognized cause of failure: misconception of the nature of mathematics. I think the speci c reference to the United States may be omitted. It is really a worldwide problem. Moreover, there is one more consequence of “math avoidance” and “misconception”: good mathematical approaches are sometimes applied inc- rectly. Particularly, the methods of statistics are often misused for different goals. Applying mathematical methods is similar to using nuclear power: the nal results depend on the competence of the user. I try to convince my readers to apply the “energy” of mathematics with consideration.

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