数理视野下的易学(精)/跨学科视野下的易学丛书 (I Ching under the perspective of Mathematics and Science – The Series of I Ching Study under Transdisciplinary perspectives) ISBN: 9787562352761

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目录
第一章象数新探
第一节易卦是什么
一、易卦是数
二、易卦集是群
三、易卦集是几何模型
四、易卦集是二项式
五、易卦与集合
六、易卦与矩阵
七、易卦与代数域
第二节大衍之数的数学内涵
一、大衍之数的含义
二、大衍之数是互乘之数
三、大衍之数勾股解
四、大衍之数与占筮的性质和数学有关
第三节筮法程序、卦序和演卦中的数学
一、筮法程序中的数学
二、卦序中的数学
三、演卦中的数学
四、简短的评论
第二章演易新法
第一节爻群(爻式)演卦法
一、京房的八宫卦变
二、《周易》的太极原理
三、爻群(爻式)的特殊结构
第二节易矩阵研究
一、经典易矩阵理论述评
二、易矩阵理论的建构
三、邵雍演卦法的矩阵表示
第三节爻群的矩阵结构
一、易矩阵的本质
二、伏羲爻群的另一种表示方法
三、奇偶演卦法的矩阵表示
四、爻群的矩阵结构
五、满卦矩阵的爻群构造法
第三章易卦新证
第一节爻群的数学本质
一、加一倍法:经典演易理论新解
二、爻群演卦法:现代演易理论简介
第二节关于一个演易定理的数学证明
一、Gray码及其性质
二、演易爻群的数学本质:Walsh函数及其生成
三、演易定理及其证明
第三节完备的易卦演绎定理及其证明
一、Walsh函数的定义及性质
二、Walsh函数新应用:区组设计
三、Walsh函数、区组设计与演易
四、Walsh函数与加强演易定理
第四章易数新知
第一节爻群变序研究
一、爻群变序与易数
二、变序数列与变序卦群
三、变序与置换
四、变序规则的交比不变性
第二节八宫数论与爻群的构造
一、八宫矩阵与爻群的构造
二、八宫矩阵与沃尔什奇函数
三、完美的十六元变序爻群
第三节典型八卦次序的数学统一性
一、文献记载的经典八卦卦序举要
二、可表为数学函数式的八卦卦序
第五章变卦新解
第一节先天八卦方位图与周期对称函数
一、周期对称函数的性质
二、实例分析
第二节易卦的向量表示及其变换
一、易卦的数学内涵
二、易卦的向量表示
三、易向量的变换
四、对角矩阵:变卦的变换算子
第三节6阶算子:六十四卦的变换
一、不倒覆、只变号变换(主对角矩阵)
二、先倒覆、后变号变换(副对角矩阵)
三、对卦变换(Ⅰ型):上卦倒覆、下卦正置变换
四、对卦变换(Ⅱ型):下卦倒覆、上卦正置变换
第六章序卦新论
第一节今本《周易》卦序结构及其演绎
一、今本《周易》卦序的结构分析
二、今本《周易》卦序的演绎生成
三、讨论:关于特区A和B在今本《周易》卦序中的地位
第二节今本《周易》卦序排列数学规律初探
一、序卦及其卦序编码
二、序卦分布的基本规律
第三节今本《周易》卦序排列数学规律再探
一、再论一阴五阳卦分布律
二、再论三阴三阳卦分布律
三、试论十二辟卦分布律
四、序卦分布容斥律
第四节今本《周易》卦序排列数学规律i探
一、一类特殊的简单数列及其通项的数学表示
二、序卦布排的数列规律及其通项表示
三、序卦布排的统合原理
四、卦序数理的进一步探究
第五节今本《周易》序卦、杂卦分布规律坐标几何通解
一、杂卦及其卦序编码
二、三十六格棋盘与河洛七七方阵图的构建
三、直线的艺术:《序卦》卦序平面几何图解
四、平面的创造:《杂卦》卦序立体几何图解
五、讨论
参考文献
索引

table of Contents
The first chapter explores the number of elephants
The first quarter is what is easy
One, easy to count
Second, easy to set is a group
Third, easy to set is a geometric model
Fourth, easy to set is binomial
V. Easy to collect and collect
Sixth, easy and matrix
Seven, easy-to-use and algebraic domains
The second part of the mathematical connotation of the number of students
First, the meaning of the number of major
Second, the number of major differences is the number of mutual multiplication
Third, the number of major gouache solution
4. The number of major differences is related to the nature and mathematics of divination.
Section III. Mathematics in Defamation Process, Order and Deduction
One, mathematics in the law of defamation
Second, the sequence of mathematics
Third, the interpretation of mathematics
Four, brief comments
The second chapter of the new law
The first section of the 爻 group (爻式) deduction method
I. The Eighth Palace Transmutation in Beijing
Second, the “Book of Changes” Tai Chi principle
Third, the special structure of the group
The second section of the matrix study
First, review of the classic matrix theory
Second, the construction of the matrix theory
Third, matrix representation of Shao Shao deduction method
Section III The Matrix Structure of the Quail Group
First, the nature of the matrix
Second, another way of expressing Fuxi Group
Third, the matrix representation of the parity deduction method
Fourth, the matrix structure of the group
Fifth, the ensemble group structure method
The third chapter is easy new certificate
Section 1 The Mathematical Essence of Qun Group
One, plus twice: a new solution to the theory of classical music
Second, the group deduction method: Introduction to modern theory
Section II Mathematical Proof of a Relevant Theorem
I. Gray code and its properties
Second, the mathematical nature of Yan Yiqun: Walsh function and its generation
Third, the recurrence theory and its proof
The Complete and Easy Interpretation of the Third Section Theorem and Its Proof
First, the definition and nature of the Walsh function
Second, the new application of Walsh function: block design
Third, Walsh function, block design and performance
Fourth, Walsh function and strengthen the relativity theory
The fourth chapter is the number of new knowledge
Section 1 Study on the Order of Groups
First, group order and number
Second, the order of the sequence and order group
Third, the order and replacement
Fourth, the invariance of cross ratio rules
The Second Section of Eighth Palace Number Theory and the Structure of Dai Group
The Structure of One and Eight Palaces and the Group
The two-octagon matrix and the Walsh function
Three, perfect sixteen yuan order group
The mathematical unity of the typical gossip sequence in the third quarter
First, the documentary records of the classic gossip sequence
Second, the table can be expressed as a mathematical function
The fifth chapter changes the new solution
Section 1 Intrinsic figure and periodic symmetry function
First, the nature of the periodic symmetry function
Second, the case analysis
The second section of the easy vector representation and its transformation
First, the easy mathematical connotation
Second, easy vector representation
Third, the transformation of the easy vector
IV. Diagonal matrix: transform operator
Section 6 6-order Operators: Sixty-four Shifts
One, no overturning, only change sign (main diagonal matrix)
Second, first inverted, post-transformation (subdiagonal matrix)
Third, pair transformation (I type): upside down, upside down transformation
Fourth, confrontation transformation (type II): squat down, upside down
Chapter 6: New Theory of Order
The first section of the current “Book of Changes” sequence structure and its interpretation
First, the structural analysis of this “Book of Changes” order
Second, today’s “Book of Changes” sequence deduction generation
III. Discussion: The status of SAR A and B in the current “Book of Changes” preface
A Preliminary Study on the Arrangement of Mathematical Rules in the Second Section of Today’s Book of Changes
First, sequence and sequence code
Second, the basic rules of order distribution
The Third Quarter: Revisiting the Mathematical Rules of the Book of Changes
First, discuss the distribution law of Yin and Wuyang
Second, discuss the distribution law of Sanyin Sanyang
Third, on the distribution law of the twelve rumor
IV. Ordinal Disposition Distribution
The fourth quarter of this book “Book of Changes” arranges the mathematics law
A mathematical representation of a special simple sequence and its general terms
Second, the order of the layout of the law and its general terms
Third, the principle of integration of sequence layout
Fourth, the further study of order and order
Section 5: The Coordinate Geometric Solution to the Distribution Rules of Preface and Miscellaneous in Zhouyi
First, hybrid and its code sequence
The construction of two, thirty-six grid checkerboard and Helu seventy-six square chart
Third, the art of straight lines: “Preface and Postscript”
Fourth, the creation of the plane: “mixed mantis” order three-dimensional geometric illustration
V. Discussion
references
index

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(I Ching under the perspective of Mathematics and Science - The Series of I Ching Study under Transdisciplinary perspectives) 数理视野下的易学(精)/跨学科视野下的易学丛书

Author: 王俊龙
Pages: 192
Category: Mathematics 數學 道象理數 算術
Publisher: South China University of Technology Press
Publication Date: 2017
Finished? No
Signed? No
First Edition? No

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王俊龙著的《数理视野下的易学(精)》从数理的视野解读演易新法、易卦新证、易数新知、变卦新解和《序卦》新论,使易学成为当代知识体系中一个组成部分,使得易卦数理在现代科学中的主导地位而显得尤为突出。具体包括第一章象数新探,第二章演易新法,第三章易卦新证,第四章易数新知,第五章变卦新解,第六章序卦新论。 目录 第一章象数新探 第一节易卦是什么 一、易卦是数 二、易卦集是群 三、易卦集是几何模型 四、易卦集是二项式 五、易卦与集合 六、易卦与矩阵 七、易卦与代数域 第二节大衍之数的数学内涵 一、大衍之数的含义 二、大衍之数是互乘之数 三、大衍之数勾股解 四、大衍之数与占筮的性质和数学有关 第三节筮法程序、卦序和演卦中的数学 一、筮法程序中的数学 二、卦序中的数学 三、演卦中的数学 四、简短的评论 第二章演易新法 第一节爻群(爻式)演卦法 一、京房的八宫卦变 二、《周易》的太极原理 三、爻群(爻式)的特殊结构 第二节易矩阵研究 一、经典易矩阵理论述评 二、易矩阵理论的建构 三、邵雍演卦法的矩阵表示 第三节爻群的矩阵结构 一、易矩阵的本质 二、伏羲爻群的另一种表示方法 三、奇偶演卦法的矩阵表示 四、爻群的矩阵结构 五、满卦矩阵的爻群构造法 第三章易卦新证 第一节爻群的数学本质 一、加一倍法:经典演易理论新解 二、爻群演卦法:现代演易理论简介 第二节关于一个演易定理的数学证明 一、Gray码及其性质 二、演易爻群的数学本质:Walsh函数及其生成 三、演易定理及其证明 第三节完备的易卦演绎定理及其证明 一、Walsh函数的定义及性质 二、Walsh函数新应用:区组设计 三、Walsh函数、区组设计与演易 四、Walsh函数与加强演易定理 第四章易数新知 第一节爻群变序研究 一、爻群变序与易数 二、变序数列与变序卦群 三、变序与置换 四、变序规则的交比不变性 第二节八宫数论与爻群的构造 一、八宫矩阵与爻群的构造 二、八宫矩阵与沃尔什奇函数 三、完美的十六元变序爻群 第三节典型八卦次序的数学统一性 一、文献记载的经典八卦卦序举要 二、可表为数学函数式的八卦卦序 第五章变卦新解 第一节先天八卦方位图与周期对称函数 一、周期对称函数的性质 二、实例分析 第二节易卦的向量表示及其变换 一、易卦的数学内涵 二、易卦的向量表示 三、易向量的变换 四、对角矩阵:变卦的变换算子 第三节6阶算子:六十四卦的变换 一、不倒覆、只变号变换(主对角矩阵) 二、先倒覆、后变号变换(副对角矩阵) 三、对卦变换(Ⅰ型):上卦倒覆、下卦正置变换 四、对卦变换(Ⅱ型):下卦倒覆、上卦正置变换 第六章序卦新论 第一节今本《周易》卦序结构及其演绎 一、今本《周易》卦序的结构分析 二、今本《周易》卦序的演绎生成 三、讨论:关于特区A和B在今本《周易》卦序中的地位 第二节今本《周易》卦序排列数学规律初探 一、序卦及其卦序编码 二、序卦分布的基本规律 第三节今本《周易》卦序排列数学规律再探 一、再论一阴五阳卦分布律 二、再论三阴三阳卦分布律 三、试论十二辟卦分布律 四、序卦分布容斥律 第四节今本《周易》卦序排列数学规律i探 一、一类特殊的简单数列及其通项的数学表示 二、序卦布排的数列规律及其通项表示 三、序卦布排的统合原理 四、卦序数理的进一步探究 第五节今本《周易》序卦、杂卦分布规律坐标几何通解 一、杂卦及其卦序编码 二、三十六格棋盘与河洛七七方阵图的构建 三、直线的艺术:《序卦》卦序平面几何图解 四、平面的创造:《杂卦》卦序立体几何图解 五、讨论 参考文献 索引 table of Contents The first chapter explores the number of elephants The first quarter is what is easy One, easy to count Second, easy to set is a group Third, easy to set is a geometric model Fourth, easy to set is binomial V. Easy to collect and collect Sixth, easy and matrix Seven, easy-to-use and algebraic domains The second part of the mathematical connotation of the number of students First, the meaning of the number of major Second, the number of major differences is the number of mutual multiplication Third, the number of major gouache solution 4. The number of major differences is related to the nature and mathematics of divination. Section III. Mathematics in Defamation Process, Order and Deduction One, mathematics in the law of defamation Second, the sequence of mathematics Third, the interpretation of mathematics Four, brief comments The second chapter of the new law The first section of the 爻 group (爻式) deduction method I. The Eighth Palace Transmutation in Beijing Second, the "Book of Changes" Tai Chi principle Third, the special structure of the group The second section of the matrix study First, review of the classic matrix theory Second, the construction of the matrix theory Third, matrix representation of Shao Shao deduction method Section III The Matrix Structure of the Quail Group First, the nature of the matrix Second, another way of expressing Fuxi Group Third, the matrix representation of the parity deduction method Fourth, the matrix structure of the group Fifth, the ensemble group structure method The third chapter is easy new certificate Section 1 The Mathematical Essence of Qun Group One, plus twice: a new solution to the theory of classical music Second, the group deduction method: Introduction to modern theory Section II Mathematical Proof of a Relevant Theorem I. Gray code and its properties Second, the mathematical nature of Yan Yiqun: Walsh function and its generation Third, the recurrence theory and its proof The Complete and Easy Interpretation of the Third Section Theorem and Its Proof First, the definition and nature of the Walsh function Second, the new application of Walsh function: block design Third, Walsh function, block design and performance Fourth, Walsh function and strengthen the relativity theory The fourth chapter is the number of new knowledge Section 1 Study on the Order of Groups First, group order and number Second, the order of the sequence and order group Third, the order and replacement Fourth, the invariance of cross ratio rules The Second Section of Eighth Palace Number Theory and the Structure of Dai Group The Structure of One and Eight Palaces and the Group The two-octagon matrix and the Walsh function Three, perfect sixteen yuan order group The mathematical unity of the typical gossip sequence in the third quarter First, the documentary records of the classic gossip sequence Second, the table can be expressed as a mathematical function The fifth chapter changes the new solution Section 1 Intrinsic figure and periodic symmetry function First, the nature of the periodic symmetry function Second, the case analysis The second section of the easy vector representation and its transformation First, the easy mathematical connotation Second, easy vector representation Third, the transformation of the easy vector IV. Diagonal matrix: transform operator Section 6 6-order Operators: Sixty-four Shifts One, no overturning, only change sign (main diagonal matrix) Second, first inverted, post-transformation (subdiagonal matrix) Third, pair transformation (I type): upside down, upside down transformation Fourth, confrontation transformation (type II): squat down, upside down Chapter 6: New Theory of Order The first section of the current "Book of Changes" sequence structure and its interpretation First, the structural analysis of this "Book of Changes" order Second, today's "Book of Changes" sequence deduction generation III. Discussion: The status of SAR A and B in the current "Book of Changes" preface A Preliminary Study on the Arrangement of Mathematical Rules in the Second Section of Today's Book of Changes First, sequence and sequence code Second, the basic rules of order distribution The Third Quarter: Revisiting the Mathematical Rules of the Book of Changes First, discuss the distribution law of Yin and Wuyang Second, discuss the distribution law of Sanyin Sanyang Third, on the distribution law of the twelve rumor IV. Ordinal Disposition Distribution The fourth quarter of this book "Book of Changes" arranges the mathematics law A mathematical representation of a special simple sequence and its general terms Second, the order of the layout of the law and its general terms Third, the principle of integration of sequence layout Fourth, the further study of order and order Section 5: The Coordinate Geometric Solution to the Distribution Rules of Preface and Miscellaneous in Zhouyi First, hybrid and its code sequence The construction of two, thirty-six grid checkerboard and Helu seventy-six square chart Third, the art of straight lines: "Preface and Postscript" Fourth, the creation of the plane: "mixed mantis" order three-dimensional geometric illustration V. Discussion references index
Notes
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