Essays on the Theory of Numbers by Richard Dedekind
Essays on the Theory of Numbers - Table of Contents
Part I – Continuity and Irrational Numbers
1. Properties of Rational Numbers
2. Comparison of the Rational Numbers with the Points of a Straight Line
3. Continuity of the Straight Line
4. Creation of Irrational Numbers
5. Continuity of the Domain of Real Numbers
6. Operations with Real Numbers
7. Infinitesimal Analysis
Part II – The Nature and Meaning of Numbers
1. Systems of Elements
2. Transformation of a System
3. Similarity of a Transformation. Similar Systems
4. Transformation of a System in Itself
5. The Finite and Infinite
6. Simply Infinite Systems. Series of Natural Numbers
7. Greater and Less Numbers
8. Finite and Infinite Parts of the Number-Series
9. Definition of a Transformation of the Number-Series by Induction
10. The Class of Simply Infinite Systems
11. Addition of Numbers
12. Multiplication of Numbers
13. Involution of Numbers
14. Number of the Elements of a Finite System
What You Will Learn in Essays on the Theory of Numbers
"Essays on the Theory of Numbers" is a seminal work by the German mathematician "Richard Dedekind", a pioneer in modern "number theory" and abstract mathematics. Published posthumously, this collection brings together Dedekind’s most important essays, presenting his deep investigations into the nature of integers, divisibility, and arithmetic structure. His clear and rigorous style laid a foundation for generations of mathematicians, influencing algebra, analysis, and the formal understanding of number systems.
The book introduces fundamental concepts such as "Dedekind cuts", which provide a precise way to construct real numbers from rationals, and "ideal theory", which generalizes the notion of divisibility in rings of integers. Dedekind’s insights also explore the logical and structural aspects of numbers, emphasizing the relationships and patterns underlying arithmetic. These essays demonstrate his ability to combine abstract reasoning with concrete examples, making complex ideas accessible to dedicated readers of mathematics.
Widely regarded as historically and mathematically significant, "Essays on the Theory of Numbers" remains a key resource for students and researchers interested in the foundations of mathematics. It not only reflects Dedekind’s originality but also shows how his work connects with later developments in "abstract algebra", set theory, and mathematical logic. This collection is essential for anyone seeking a deep understanding of the theoretical underpinnings of modern number theory.
Book Details & Specifications
Title:
Essays on the Theory of Numbers by Richard Dedekind
Publisher:
Dover
Year:
2007
Pages:
78
Type:
PDF
Language:
English
ISBN-10 #:
0486210103
ISBN-13 #:
978-0486210100
License:
Public Domain Work
Amazon:
Amazon
About the Author: Richard Dedekind
The author
Richard Dedekind
was a German mathematician and professor at the "University of Göttingen", renowned for his contributions to "number theory" and abstract algebra. Born in 1831, he introduced fundamental concepts such as "ideals" and provided rigorous foundations for the real numbers, influencing modern mathematics and generations of mathematicians. His work, "Essays on the Theory of Numbers", compiles his seminal work on "algebraic number theory", integers, and the structure of number systems.
Read or Downloadable Essays on the Theory of Numbers
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