Modern algebra and the rise of mathematical structures(現代代數與數學結構的興起) pdf epub mobi txt 電子書 下載2025

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This book describes two stages in the historical development of the notion of mathematical structures: first, it traces its rise in the context of algebra from the mid-1800s to 1930, and then considers attempts to formulate elaborate theories after 1930 aimed at elucidating, from a purely mathematical perspective, the precise meaning of this idea.

I am a historian of mathematics working at Tel-Aviv University. You can see more about my work, here: http://www.tau.ac.il/~corry/

My research has focused on an attempt to understand the historical development of some of the main threads of twentieth-century mathematics. Among other things my research has dealt with the rise of modern algebra, the development of the idea of a mathematical structure, the rise of the modern axiomatic method, the introduction of digital computers into research in pure mathematics, and the works of some leading figures such as David Hilbert, Emmy Noether, Nicolas Bourbaki, and others. More recently I have also become interested in the Euclidean tradition of the middle ages and the renaissance, particularly around the question of the changing relationships between arithmetic and geometry.

As part of a more general academic interest in history and philosophy of science, in 1999-2009 I was editor of the journal Science in Context (Cambridge University Press), and in 2003-2009 I was director of the Cohn Institute for History and Philosophy of Science at Tel-Aviv University. In 2014-15, I was director of the Zvi Yavetz Graduate School of Historical Studies at TAU. Since November 2015 I am Dean of Humanities at Tel Aviv University.

I also have a keen interest in Latin American history, culture and literature. I wrote an introductory overview (in Hebrew) to the prose of Jorge Luis Borges, and also translated several books into Hebrew, including Mario Vargas Llosa's "La Casa Verde".

Introduction: Structures in Mathematics
One: Structures in the Images of Mathematics
1 Structures in Algebra: Changing Images
1.1 Jordan and Hölder: Two Versions of a Theorem
1.2 Heinrich Weber:Lehrbuch der Algebra
1.3 Bartel L. van der Waerden:Moderne Algebra
1.4 Other Textbooks of Algebra in the 1920s
2 Richard Dedekind: Numbers and Ideals
2.1 Lectures on Galois Theory
2.1 Algebraic Number Theory
2.2.1 Ideal Prime Numbers
2.2.2 Theory of Ideals: The First Version (1871)
2.2.3 Later Versions
2.2.4 The Last Version
2.2.5 Additional Contexts
2.3 Ideals andDualgruppen
2.4 Dedekind and the Structural Image of Algebra
3 David Hilbert: Algebra and Axiomatics
3.1 Algebraic Invariants
3.2 Algebraic Number Theory
3.2 Hilbert’s Axiomatic Approach
3.4 Hilbert and the Structural Image of Algebra
3.5 Postulational Analysis in the USA
4 Concrete and Abstract: Numbers, Polynomials, Rings
4.1 Kurt Hensel: Theory of p-adic Numbers
4.2 Ernst Steinitz:Algebraische Theorie der Körper
4.3 Alfred Loewy:Lehrbuch der Algebra
4.4 Abraham Fraenkel: Axioms forp-adicSystems
4.5 Abraham Fraenkel: Abstract Theory of Rings
4.6 Ideals and Abstract Rings after Fraenkel
4.7 Polynomials and their Decompositions
5 Emmy Noether: Ideals and Structures
5.1 Early Works
5,2 Idealtheorie in Ringbereichen
5.3 Abstrakter Aufbau der Idealtheorie
5.4 Later Works
5.5 Emmy Noether and the Structural Image of Algebra
Two: Structures in the Body of Mathematics
6 Oystein Ore: Algebraic Structures
6.1 Decomposition Theorems and Algebraic Structures
6.2 Non-Commutative Polynomials and Algebraic Structure
6.3 Structures and Lattices
6.4 Structures in Action
6.5 Universal Algebra, Model Theory, Boolean Algebras
6.6 Ore’s Structures and the Structural Image of Algebra
7 Nicolas Bourbaki: Theory of Structures
7.1 The Myth
7.2 Structures and Mathematics
7.3 Structures and the Body of Mathematics
7.3.1 Set Theory
7.3.2 Algebra
7.3.3 General Topology
7.3.4 Commutative Algebra
7.4 Structures and the Structural Image of Mathematics
8 Category Theory: Early Stages
8.1 Category Theory: Basic Concepts
8.2 Category Theory: A Theory of Structures
8.3 Category Theory: Early Works
8.4 Category Theory: Some Contributions
8.5 Category Theory and Bourbaki
9 Categories and Images of Mathematics
9.1 Categories and the Structural Image of Mathematics
9.2 Categories and the Essence of Mathematics
9.3 What is Algebra and what has it been in History?
Author Index
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