語系:
繁體中文
English
說明(常見問題)
回圖書館首頁
手機版館藏查詢
登入
回首頁
切換:
標籤
|
MARC模式
|
ISBD
The continuous, the discrete and the...
~
Bell, John L.
FindBook
Google Book
Amazon
博客來
The continuous, the discrete and the infinitesimal in philosophy and mathematics
紀錄類型:
書目-電子資源 : Monograph/item
正題名/作者:
The continuous, the discrete and the infinitesimal in philosophy and mathematics/ by John L. Bell.
作者:
Bell, John L.
出版者:
Cham :Springer International Publishing : : 2019.,
面頁冊數:
xvii, 313 p. :ill., digital ;24 cm.
內容註:
Part I: The Continuous, the Discrete, and the Infinitesimal in the History of Thought -- Chapter 1. The Continuous and the Discrete in Ancient Greece, the Orient, and the European Middle Ages -- Chapter 2. The 16th and 17th Centuries: The Founding of the Infinitesimal Calculus -- Chapter 3. The 18th and Early 19th Centuries: The Age of Continuity -- Chapter 4. The Reduction of the Continuous to the Discrete in the 19th and early 20th Centuries -- Chapter 5. Dissenting Voices: Divergent Conceptions of the Continuum in the 19th and Early 20th Centuries -- Part II: Continuity and Infinitesimals in Today's Mathematics -- Chapter 6. Topology -- Chapter 7. Category/Topos Theory -- Chapter 8. Nonstandard Analysis -- Chapter 9. The Constructive and Intuitionistic Continua -- Chapter 10. Smooth Infiniteimal Analysis/Synthetic Geometry.
Contained By:
Springer eBooks
標題:
Mathematics - Philosophy. -
電子資源:
https://doi.org/10.1007/978-3-030-18707-1
ISBN:
9783030187071
The continuous, the discrete and the infinitesimal in philosophy and mathematics
Bell, John L.
The continuous, the discrete and the infinitesimal in philosophy and mathematics
[electronic resource] /by John L. Bell. - Cham :Springer International Publishing :2019. - xvii, 313 p. :ill., digital ;24 cm. - The Western Ontario series in philosophy of science ;v.82. - Western Ontario series in philosophy of science ;v.82..
Part I: The Continuous, the Discrete, and the Infinitesimal in the History of Thought -- Chapter 1. The Continuous and the Discrete in Ancient Greece, the Orient, and the European Middle Ages -- Chapter 2. The 16th and 17th Centuries: The Founding of the Infinitesimal Calculus -- Chapter 3. The 18th and Early 19th Centuries: The Age of Continuity -- Chapter 4. The Reduction of the Continuous to the Discrete in the 19th and early 20th Centuries -- Chapter 5. Dissenting Voices: Divergent Conceptions of the Continuum in the 19th and Early 20th Centuries -- Part II: Continuity and Infinitesimals in Today's Mathematics -- Chapter 6. Topology -- Chapter 7. Category/Topos Theory -- Chapter 8. Nonstandard Analysis -- Chapter 9. The Constructive and Intuitionistic Continua -- Chapter 10. Smooth Infiniteimal Analysis/Synthetic Geometry.
This book explores and articulates the concepts of the continuous and the infinitesimal from two points of view: the philosophical and the mathematical. The first section covers the history of these ideas in philosophy. Chapter one, entitled 'The continuous and the discrete in Ancient Greece, the Orient and the European Middle Ages,' reviews the work of Plato, Aristotle, Epicurus, and other Ancient Greeks; the elements of early Chinese, Indian and Islamic thought; and early Europeans including Henry of Harclay, Nicholas of Autrecourt, Duns Scotus, William of Ockham, Thomas Bradwardine and Nicolas Oreme. The second chapter of the book covers European thinkers of the sixteenth and seventeenth centuries: Galileo, Newton, Leibniz, Descartes, Arnauld, Fermat, and more. Chapter three, 'The age of continuity,' discusses eighteenth century mathematicians including Euler and Carnot, and philosophers, among them Hume, Kant and Hegel. Examining the nineteenth and early twentieth centuries, the fourth chapter describes the reduction of the continuous to the discrete, citing the contributions of Bolzano, Cauchy and Reimann. Part one of the book concludes with a chapter on divergent conceptions of the continuum, with the work of nineteenth and early twentieth century philosophers and mathematicians, including Veronese, Poincare, Brouwer, and Weyl. Part two of this book covers contemporary mathematics, discussing topology and manifolds, categories, and functors, Grothendieck topologies, sheaves, and elementary topoi. Among the theories presented in detail are non-standard analysis, constructive and intuitionist analysis, and smooth infinitesimal analysis/synthetic differential geometry. No other book so thoroughly covers the history and development of the concepts of the continuous and the infinitesimal.
ISBN: 9783030187071
Standard No.: 10.1007/978-3-030-18707-1doiSubjects--Topical Terms:
523930
Mathematics
--Philosophy.
LC Class. No.: QA8.4 / .B455 2019
Dewey Class. No.: 510.1
The continuous, the discrete and the infinitesimal in philosophy and mathematics
LDR
:03723nmm a2200337 a 4500
001
2193412
003
DE-He213
005
20191225095256.0
006
m d
007
cr nn 008maaau
008
200514s2019 gw s 0 eng d
020
$a
9783030187071
$q
(electronic bk.)
020
$a
9783030187064
$q
(paper)
024
7
$a
10.1007/978-3-030-18707-1
$2
doi
035
$a
978-3-030-18707-1
040
$a
GP
$c
GP
041
0
$a
eng
050
4
$a
QA8.4
$b
.B455 2019
072
7
$a
PBB
$2
bicssc
072
7
$a
MAT015000
$2
bisacsh
072
7
$a
PBB
$2
thema
082
0 4
$a
510.1
$2
23
090
$a
QA8.4
$b
.B433 2019
100
1
$a
Bell, John L.
$3
887441
245
1 4
$a
The continuous, the discrete and the infinitesimal in philosophy and mathematics
$h
[electronic resource] /
$c
by John L. Bell.
260
$a
Cham :
$b
Springer International Publishing :
$b
Imprint: Springer,
$c
2019.
300
$a
xvii, 313 p. :
$b
ill., digital ;
$c
24 cm.
490
1
$a
The Western Ontario series in philosophy of science ;
$v
v.82
505
0
$a
Part I: The Continuous, the Discrete, and the Infinitesimal in the History of Thought -- Chapter 1. The Continuous and the Discrete in Ancient Greece, the Orient, and the European Middle Ages -- Chapter 2. The 16th and 17th Centuries: The Founding of the Infinitesimal Calculus -- Chapter 3. The 18th and Early 19th Centuries: The Age of Continuity -- Chapter 4. The Reduction of the Continuous to the Discrete in the 19th and early 20th Centuries -- Chapter 5. Dissenting Voices: Divergent Conceptions of the Continuum in the 19th and Early 20th Centuries -- Part II: Continuity and Infinitesimals in Today's Mathematics -- Chapter 6. Topology -- Chapter 7. Category/Topos Theory -- Chapter 8. Nonstandard Analysis -- Chapter 9. The Constructive and Intuitionistic Continua -- Chapter 10. Smooth Infiniteimal Analysis/Synthetic Geometry.
520
$a
This book explores and articulates the concepts of the continuous and the infinitesimal from two points of view: the philosophical and the mathematical. The first section covers the history of these ideas in philosophy. Chapter one, entitled 'The continuous and the discrete in Ancient Greece, the Orient and the European Middle Ages,' reviews the work of Plato, Aristotle, Epicurus, and other Ancient Greeks; the elements of early Chinese, Indian and Islamic thought; and early Europeans including Henry of Harclay, Nicholas of Autrecourt, Duns Scotus, William of Ockham, Thomas Bradwardine and Nicolas Oreme. The second chapter of the book covers European thinkers of the sixteenth and seventeenth centuries: Galileo, Newton, Leibniz, Descartes, Arnauld, Fermat, and more. Chapter three, 'The age of continuity,' discusses eighteenth century mathematicians including Euler and Carnot, and philosophers, among them Hume, Kant and Hegel. Examining the nineteenth and early twentieth centuries, the fourth chapter describes the reduction of the continuous to the discrete, citing the contributions of Bolzano, Cauchy and Reimann. Part one of the book concludes with a chapter on divergent conceptions of the continuum, with the work of nineteenth and early twentieth century philosophers and mathematicians, including Veronese, Poincare, Brouwer, and Weyl. Part two of this book covers contemporary mathematics, discussing topology and manifolds, categories, and functors, Grothendieck topologies, sheaves, and elementary topoi. Among the theories presented in detail are non-standard analysis, constructive and intuitionist analysis, and smooth infinitesimal analysis/synthetic differential geometry. No other book so thoroughly covers the history and development of the concepts of the continuous and the infinitesimal.
650
0
$a
Mathematics
$x
Philosophy.
$3
523930
650
1 4
$a
Philosophy of Mathematics.
$3
2192005
650
2 4
$a
History of Philosophy.
$3
896985
650
2 4
$a
Mathematical Logic and Formal Languages.
$3
892517
650
2 4
$a
Analysis.
$3
891106
650
2 4
$a
Differential Geometry.
$3
891003
650
2 4
$a
History of Mathematical Sciences.
$3
1530523
710
2
$a
SpringerLink (Online service)
$3
836513
773
0
$t
Springer eBooks
830
0
$a
Western Ontario series in philosophy of science ;
$v
v.82.
$3
3414555
856
4 0
$u
https://doi.org/10.1007/978-3-030-18707-1
950
$a
Religion and Philosophy (Springer-41175)
筆 0 讀者評論
館藏地:
全部
電子資源
出版年:
卷號:
館藏
1 筆 • 頁數 1 •
1
條碼號
典藏地名稱
館藏流通類別
資料類型
索書號
使用類型
借閱狀態
預約狀態
備註欄
附件
W9375702
電子資源
11.線上閱覽_V
電子書
EB QA8.4 .B455 2019
一般使用(Normal)
在架
0
1 筆 • 頁數 1 •
1
多媒體
評論
新增評論
分享你的心得
Export
取書館
處理中
...
變更密碼
登入