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- Herausgeber: Simone Malacrida
- Kategorie: Wissenschaft und neue Technologien
- Sprache: Englisch
The theoretical assumptions of the following mathematical topics are presented in this book:
numerical successions
numerical series
combinatorial calculus
elementary statistics
Each topic is treated by emphasizing practical applications and solving some significant exercises.
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Veröffentlichungsjahr: 2022
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Table of Contents
“Introduction to Series and Basic Statistics"
INTRODUCTION
SUCCESSION AND SERIES
COMBINATORY CALCULATION
ELEMENTARY STATISTICS
“Introduction to Series and Basic Statistics"
SIMONE MALACRIDA
The theoretical assumptions of the following mathematical topics are presented in this book:
numerical successions
numerical series
combinatorial calculus
elementary statistics
Each topic is treated by emphasizing practical applications and solving some significant exercises.
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Simone Malacrida (1977)
Engineer and writer, has worked on research, finance, energy policy and industrial plants.
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ANALYTICAL INDEX
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INTRODUCTION
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I – SUCCESSION AND SERIES
Successions
Series: Definitions
Notable series
Applications
Exercises
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II – COMBINATORY CALCULATION
Definitions
Operations
Applications
Exercises
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III – ELEMENTARY STATISTICS
Chance
Conditional probability and Bayes' theorem
Elementary statistics
Applications
Exercises
INTRODUCTION
This book focuses on two distinct topics.
On the one hand, numerical sequences and series are presented, as a fundamental basis for understanding developments related to mathematical analysis (such as function series and power series).
On the other hand, combinatorial calculus with elements of elementary statistics is introduced.
This second part is the prerequisite for understanding statistics, stochastic laws and probability distributions, topics that require academic analytical knowledge and which, therefore, are not part of the scope of this manual.
Each chapter will be accompanied by some final exercise. This manual is not a workbook and, precisely for this reason, you will not find hundreds of exercises.
The questions proposed were considered significant for understanding the main rules and for their application.
In addition, particular emphasis has been given to the method of solving them since the real leap in quality between the study of a rule and its application is given precisely by the method, i.e. by the quality of the reasoning, and not by the quantity of calculations.
The program presented in this manual expands what is taught at technical institutes and high schools, coinciding with what is present in the first university mathematics and statistics courses.
I
SUCCESSION AND SERIES
Successions
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A mathematical sequence of elements of a given set A is a function from the set of natural numbers N in A.
The nth element of the sequence is the image of the number n according to the sequence f:
The sequence is an ordered list consisting of a countable infinity of items.
Unlike countable sets, the order of the elements is relevant for a sequence.
A sequence is called recursive when starting from the value of a particular element it is possible to calculate the next one through a function that is the same for all the following elements:
A sequence whose terms are only numbers is called a numerical sequence .
A numerical sequence is said to be positive if for each n the image assumes only positive values, while it is said to be definitively positive if the image assumes positive values only from a given element onwards.
Analogous definitions apply for negative signs.
A sequence is bounded if there exists a number M such that:
