Introduction to Set and Functions E-Book

Simone Malacrida

• Herausgeber: BookRix
• Kategorie: Wissenschaft und neue Technologien
• Sprache: Englisch

Veröffentlichungsjahr: 2023

Beschreibung

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.

Leseprobe

Simone Malacrida

Introduction to Set and Functions

BookRix GmbH & Co. KG81371 Munich

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.