eBook - ePub

Proofs 101

Name: Proofs 101
Author: Joseph Kirtland

An Introduction to Formal Mathematics

Joseph Kirtland,

176 pages
English
ePUB (mobile friendly)
Available on iOS & Android

eBook - ePub

Proofs 101

An Introduction to Formal Mathematics

Joseph Kirtland,

About this book

Proofs 101: An Introduction to Formal Mathematics serves as an introduction to proofs for mathematics majors who have completed the calculus sequence (at least Calculus I and II) and a first course in linear algebra.

The book prepares students for the proofs they will need to analyze and write the axiomatic nature of mathematics and the rigors of upper-level mathematics courses. Basic number theory, relations, functions, cardinality, and set theory will provide the material for the proofs and lay the foundation for a deeper understanding of mathematics, which students will need to carry with them throughout their future studies.

Features

Designed to be teachable across a single semester
Suitable as an undergraduate textbook for Introduction to Proofs or Transition to Advanced Mathematics courses
Offers a balanced variety of easy, moderate, and difficult exercises

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Yes, you can access Proofs 101 by Joseph Kirtland in PDF and/or ePUB format, as well as other popular books in Mathematics & Applied Mathematics. We have over one million books available in our catalogue for you to explore.

Information

Publisher

Chapman and Hall/CRC

Year

2020

eBook ISBN

9781000227383

Edition

Topic

Mathematics

Subtopic

Applied Mathematics

Index

Mathematics

CHAPTER 1 Logic

1.1 INTRODUCTION

Logic is at the foundation of everything we do in mathematics. It provides a formal language that is used to state and process results and a system of deductive reasoning used to justify or prove them. With the goal of this book in mind, the tools learned from logic are essential for crafting, writing, and analyzing proofs.

This chapter introduces a few of the basic concepts in logic. While this is not an in-depth study, it does provide all of the tools we will need in subsequent chapters. However, once you finish reading this chapter and are interested in learning more about logic, I suggest [O'L16] and [GU89].

1.2 STATEMENTS AND LOGICAL CONNECTIVES

Statements are the basic elements of logic.

Definition 1.2.1. A statement is a declarative sentence that is either true or false, but not both.

To simplify the calculus of logic, the letters

P, Q, R, S, \dots

are used to denote statements. The following sentences are all statements.

$P :$	$7 + 4 = 12.$
$Q :$	The Empire State Building is in New York City.
$R :$	The $2^{100}$ digit of $π$ is 3.

The statement

P

is false,

Q

is true, and

R

, while we may not know the

2^{100}

digit of

π

, is definitely either true or false.

Sentences such as, Are you tired,

x + 3 = 11

, and The Empire State Building is tall, are not statements. The first is not a statement as it ...

Cover
Half Title
Title Page
Copyright Page
Dedication
Contents
Preface
Acknowledgments
Symbol Description
Chapter 1 ▪ Logic
Chapter 2 ▪ Proof Techniques
Chapter 3 ▪ Sets
Chapter 4 ▪ Proof by Mathematical Induction
Chapter 5 ▪ Relations
Chapter 6 ▪ Functions
Chapter 7 ▪ Cardinality of Sets
Chapter 8 ▪ Conclusion
Chapter 9 ▪ Hints and Solutions
Bibliography
Index

About this book

Frequently asked questions

Information

CHAPTER 1

Logic

1.1 INTRODUCTION

1.2 STATEMENTS AND LOGICAL CONNECTIVES

Table of contents