Ernst Schröder on algebra and logic / Stephen Pollard.

Format:

Book

Author/Creator:

Pollard, Stephen (Stephen Randall), translator.

Contributor:

Schröder, Ernst, 1841-1902.

ProQuest ebook central

Rosengarten Family Fund.

Series:

Synthese library ; v. 465.

Synthese Library ; v. 465

Language:

English

German

Subjects (All):

Algebraic logic.

Algebraic logic--Philosophy.

Physical Description:

1 online resource (355 pages)

Place of Publication:

Cham : Springer, 2022.

Contents:

Intro

Preface

Translator's Introduction

0.1 The Lehrbuch Project

0.2 Doing Algebra with Classes

0.3 From Boole to Boolean Algebra

References

Contents

1 Numbers

1.1 The Mathematical Sciences

1.2 Numbers in General

1.3 What Makes Counting Possible?

1.4 When Do We Count?

1.5 The Emergence or Construction of the Natural Numbers

1.6 The Appellation of a Number

1.7 The Concept of Multiplicity

1.8 Numbers as Measures of Numerousness

1.9 Numbers as Rules

1.10 The General Purpose of Numbers

1.11 Cardinal and Ordinal Numbers

1.12 Independence of Numbers from the Ordering Imposed by the Counting Process

1.13 A Single Axiom

1.14 A Fundamental Proposition

1.15 Calculation: Expressions

1.16 Relations: Equations and Inequalities

1.17 Propositions About Equations

1.18 More on Equations

1.19 Ambiguous Expressions

1.20 Logical Subordination

1.21 Substitution

1.22 Parentheses

1.23 Literal and Numerical Numbers

1.24 Use of Letters Justified: Principles of Nomenclature

1.25 Use of Letters: Motivations and Benefits

1.26 Analytic and Synthetic Equations

1.27 Theorems, Rules

1.28 Constant and Variable Numbers, Functions

1.29 Conclusion

2 The Three Direct Operations

2.1 Independent Treatment of Addition: Concepts and Terminology

2.2 First Law of Addition

2.3 Second Law of Addition

2.4 The Two Laws Combined

2.5 Addendum on Inequalities

2.6 Recursive Treatment of Addition: Number and Sum

2.7 The Associative Law for Trinomials

2.8 The Associative Law for Polynomials

2.9 The Commutative Law for Binomials

2.10 The Commutative Law for Polynomials

2.11 Independent Treatment of Multiplication: Basic Concepts

2.12 The Commutative Law of Multiplication

2.13 The Associative Law of Multiplication

2.14 Combination and Extension of the Two Laws

2.15 Expanded Definition of Product

Dirichlet's Proof of the Fundamental Theorem

2.16 The Distributive Laws

2.17 Extension of the Distributive Laws

Multiplying Out and Factoring

2.18 Fusion of the Distributive Laws in the Rule for Multiplying Polynomials

2.19 Toward an Alternative Treatment of the Foregoing

2.20 Additional Properties of Inequalities

2.21 Recursive Treatment of Multiplication: Concept and Laws

2.22 Another Proof of the Fundamental Theorem

2.23 Independent Treatment of Elevation: Potentiation and Exponentiation

2.24 Laws Governing These Operations

the Iteration Law

2.25 The Second Law

2.26 The Third Law

2.27 Addendum on Inequalities

2.28 Recursive Treatment of Elevation

2.29 Review

Iteration

3 The Four Inverse Operations

3.1 Introduction

Inversion

3.2 Inversion of Univocal Operations: Subtraction

3.3 Division

3.4 Roots and Logarithms

3.5 Overview of the Operations, Expressions, and Operands

3.6 The Transposition Rules

Notes:

3.7 Application to the Solution of Pure Equations

Includes index.

Electronic reproduction. Ann Arbor, MI Available via World Wide Web.

Online resource; title from PDF title page (SpringerLink, viewed August 8, 2022).

Local Notes:

Acquired for the Penn Libraries with assistance from the Rosengarten Family Fund.

Other Format:

Print version: Pollard, Stephen Ernst Schröder on Algebra and Logic

ISBN:

9783031056710

303105671X

Publisher Number:

99991462561

Access Restriction:

Restricted for use by site license.