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The text is designed for students who intend to enroll in science-based degree programs, in particular Mathematics, Physics and Engineering. Usually, the various faculty prepare students for these entrance test, in which occurs the adequacy of the basic mathematical tools in their possession. In order to fill any gaps, each faculty is organizing the preliminary courses to be held in September (pre-courses, courses or zero), after which it is expected the test. The objective of this volume is to provide a useful support for such introductory courses: in it describes the mathematical tools, from the most basic (proportions, linear equations) to those more challenging (complex numbers, logic and set theory), passing through the higher degree equations, trigonometry, logarithms and exponentials. Each chapter is accompanied by a large quantity of examples: some of these simply show the techniques work for the topics, while others tend to stimulate the interest of the student by presenting less obvious problems, for which it must be a minimum of reflection before locate the tool or the suitable method. This is to put the emphasis on the fact that, especially at the university level, figure out a formula or theorem does not mean repeating learn to perfection the statement or demonstration, but knowing when and how to use them properly. For this reason we have omitted the proofs of several theorems and formulas of numerous, especially in the section of trigonometry: no shortage of textbooks in which they are listed exhaustively. With a similar philosophy at the end of the various chapters different exercises are offered, the student is invited to settle with his forces, before going to refer to the section of the solutions.
Domenico Candeloro, Professor of Mathematics since 1994, currently teaches Mathematical Analysis and Applied Mathematics at the Faculty of Engineering in the Terni branch, over the course of Stochastic Processes with a degree in Mathematics. He has held the Probability Analysis and Calculation courses Funzionale.Gli topics of his research can frame in Measure Theory and its applications in the field of probability. In particular it worked on finitely additive measures, integration and convergence issues and, more recently, stochastic processes and stochastic calculus in abstract functional spaces.
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