Table of Contents
Table of Contents
“Introductions to Set and Functions"
INTRODUCTION
MATHEMATICAL LOGIC
SET THEORY
FUNCTIONS
LITERAL CALCULATION
POWERS AND RADICALS
MONOMIAL AND POLYNOMIAL CALCULATION
“Introductions to Set and Functions"
“Introductions to Set and Functions"
SIMONE MALACRIDA
The theoretical assumptions of the following mathematical topics are presented in this book:
mathematical logic
set theory
function theory
literal calculus
properties of powers and radicals
monomial and polynomial calculus
Each topic is covered 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.
ANALYTICAL INDEX
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INTRODUCTION
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I – MATHEMATICAL LOGIC
Introduction
Symbology
Principles
Property
Boolean logic
Applications of logic: proof of theorems
Applications of Boolean logic: electronic calculators
Exercises
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II – THEORY OF INS I EMI
Introduction
Operations
Numerical sets
Exercises
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III –WORK OR NOT
Definitions
Property
Applications
Exercises
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IV – CALCULATION OF LETTER L E
Operations
Exercises
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V – POWERS AND RADS
Power operations
Operations on radicals
Conditions of existence
Exercises uncles _
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VI – MONOMIAL AND PO LINOMIAL CALCULATION
Monomial
Polynomials
Notable products
Exercises
INTRODUCTION
INTRODUCTION
This short manual presents the introductory topics for the study of mathematics at the high school level.
Mathematical logic is the basic tool for understanding any subsequent scientific knowledge and, as such, is presented in the first chapter.
Set theory and function theory are cornerstones for the development of concepts such as geometry and analysis.
The literal calculus, declined in properties of powers, of radicals, in monomial and polynomial calculus is the basis of algebra, as well as the necessary prerequisite for the resolution of equations.
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 coincides, broadly, with what was taught in the first year of high school.
I
MATHEMATICAL LOGIC
MATHEMATICAL LOGIC
Introduction
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Mathematical logic deals with the coding, in mathematical terms, of intuitive concepts related to human reasoning.
It is the starting point for any mathematical learning process and, therefore, it makes complete sense to expose the elementary rules of this logic at the beginning of the whole discourse.
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We define an axiom as a statement assumed to be true because it is considered self-evident or because it is the starting point of a theory.
Logical axioms are satisfied by any logical structure and are divided into tautologies (true statements by definition devoid of new informative value) or axioms considered true regardless, unable to demonstrate their universal validity.
Non-logical axioms are never tautologies and are called postulates .
Both axioms and postulates are unprovable.
Generally, the axioms that found and start a theory are called principles .
A theorem , on the other hand, is a proposition which, starting from initial conditions (called hypotheses ) reaches conclusions (called theses ) through a logical procedure called demonstration .
Theorems are, therefore, provable by definition.
Other provable statements are the lemmas which usually precede and give the basis of a theorem and the corollaries which, instead, are consequent to the demonstration of a given theorem.
A conjecture , on the other hand, is a proposition believed to be true thanks to general considerations, intuition and common sense, but not yet demonstrated in the form of a theorem.
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Symbology
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Mathematical logic causes symbols to intervene which will then return in all the individual fields of mathematics. These symbols are varied and belong to different categories.
The equality between two mathematical elements is indicated with the symbol of 
, if instead these elements are different from each other the symbol of inequality is given by 
.
In the geometric field it is also useful to introduce the concept of congruence , indicated in this way 
and of similarity 
.
proportionality can also be defined , denoted by 
.
In many cases mathematical and geometric concepts must be defined, the definition symbol is this 
.
Finally, the negation is given by a bar above the logical concept.
Then there are quantitative logical symbols which correspond to linguistic concepts. The existence of an element is indicated thus
Impressum
Verlag: BookRix GmbH & Co. KG
Tag der Veröffentlichung: 19.04.2023
ISBN: 978-3-7554-3938-7
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