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    • About me
    • Computer Science
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    GitHub
    • About me
    • Computer Science
      • TAOCP
        • Concrete Mathematics
          • 02 Sums
            • 06 FINITE AND INFINITE CALCULUS
            • 07 INFINITE SUMS
            • 08 EXERCISES
          • 03 Integer Functions
            • 01 FLOORS AND CEILINGS
            • 02 FLOOR/CEILING APPLICATIONS
        • 05 Sorting
            • 00 Introduction
            • 01 Multiway Merging and Replacement Selection
            • 02 The Polyphase Merge.md
      • Computer Organization and Design (RISC-V)
        • 01 Computer Abstractions and Technology
          • 01 Introduction
          • 02 Seven Great Ideas in Computer Architecture
          • 03 Below Your Program
          • 04 Under the Covers
          • 05 Technologies for Building Processors and Memory
          • 06 Performance
          • 07 The Power Wall
          • 08 The Sea Change The Switch from Uniprocessors to Multiprocessors
          • 09 Real Stuff: Benchmarking the Intel Core i7
          • 10 Going Faster: Matrix Multiply in Python
          • 11 Fallacies and Pitfalls
        • 02 Instructions Language of the Computer
          • 01 Introduction
          • 02 Operations of the Computer Hardware
          • 03 Operands of the Computer Hardware
          • 04 Signed and Unsigned Numbers
          • 05 Representing Instructions in the Computer
          • 06 Logical Operations
          • 07 Instructions for Making Decisions
          • 08 Supporting Procedures in Computer Hardware
          • 09 Communicating with People
          • 10 RISC V Addressing for Wide Immediates and Addresses
          • 11 Parallelism and Instructions Synchronization
          • 12 Translating and Starting a Program
          • 13 A C Sort Example to Put it All Together
          • 14 Arrays versus Pointers
          • 22 Fallacies and Pitfalls
        • 03 Arithmetic for Computers
          • 01 Introduction
          • 02 Addition and Subtraction
          • 03 Multiplication
          • 04 Division
          • 05 Floating Point
          • 06 Parallelism and Computer Arithmetic Subword Parallelism
          • 07 Real Stuff Streaming SIMD Extensions and Advanced Vector Extensions in x86
          • 09 Fallacies and Pitfalls
        • 04 The Processor
          • 01 Introduction
          • 03 Building a Datapath
          • 04 A Simple Implementation Scheme
          • 06 An Overview of Pipelining
          • 07 Pipelined Datapath and Control
          • 11 Parallelism via Instructions
          • 12 Putting it All Together
          • 15 Fallacies and Pitfalls
        • 05 Large and Fast Exploiting Memory Hierarchy
          • 01 Introduction
          • 02 Memory Technologies
          • 03 The Basics of Caches
          • 04 Measuring and Improving Cache Performance
          • 05 Dependable Memory Hierarchy
          • 06 Virtual Machines
          • 07 Virtual Memory
          • 08 A Common Framework for Memory Hierarchy
          • 09 Using a Finite State Machine to Control a–Simple Cache
          • 10 Parallelism and Memory Hierarchy Cache Coherence
        • 06 Parallel Processors from Client to Cloud
          • 01 Introduction
      • Professional C++
        • 00 Crash Course in C++
        • 01 Coding with Style
        • 02 Designing Professional C++ Programs
        • 03 Designing with Classes
        • 04 Designing for Reuse
        • 05 Memory Management
        • 06 Gaining Proficiency with Classes and Objects
        • 07 Mastering Classes and Objects
        • 08 Discovering Inheritance Techniques
        • 09 Modules Header Files and Miscellaneous Topics
        • 10 Writing Generic Code with Templates
        • 11 Demystifying C++ IO
        • 12 Handling Errors
        • 13 Overloading C++ Operators
        • 14 Understanding Iterators and the Ranges Library
        • 15 Standard Library Containers
        • 16 Function Pointers Function Objects and Lambda Expressions
        • 17 Mastering Standard Library Algorithms
        • 18 Customizing and Extending the Standard Library
        • X Date and Time Utilities
      • Effective Modern C++
        • 01 Deducing Types
          • 01 Understand template type deduction
          • 02 Understand auto type deduction
          • 03 Understand decltype
          • 04 Know how to view deduced types
        • 02 auto
          • 05 Prefer auto to explicit type declarations
          • 06 Use the explicitly typed initializer idiom when auto deduces undesired types
        • 03 Moving to Modern C++
          • 07 Distinguish between () and {} when creating objects
          • 08 Prefer nullptr to 0 and NULL
          • 09 Prefer alias declarations to typedefs
          • 10 Prefer scoped enums to unscoped enums
          • 11 Prefer deleted functions to private undefined ones
          • 12 Declare overriding functions override
          • 13 Prefer const_iterators to iterators
          • 14 Declare functions noexcept if they won't emit exceptions
          • 15 Use constexpr whenever possible
          • 16 Make const member functions thread safe
          • 17 Understand special member function generation
        • 04 Smart Pointers
          • 18 Use std::unique_ptr for exclusive-ownership resource management
          • 19 Use std::shared_ptr for shared-ownership resource management
          • 20 Use std::weak_ptr for std::shared_ptr-like pointers that can dangle
          • 21 Prefer std::make_unique and std::make_shared to direct use of new
          • 22 When using the Pimpl Idiom, define special member functions in the implementation file
        • 05 Rvalue References, Move Semantics, and Perfect Forwarding
          • 23 Understand std::move and std::forward
          • 24 Distinguish universal references from rvalue references
          • 25 Use std::move on rvalue references, std::forward on universal references
          • 26 Avoid overloading on universal references
          • 27 Familiarize yourself with alternatives to overloading on universal references
          • 28 Understand reference collapsing
          • 29 Assume that move operations are not present, not cheap, and not used
          • 30 Familiarize yourself with perfect forwarding failure cases
        • 06 Lambda Expressions
          • 31 Avoid default capture modes
          • 32 Use init capture to move objects into closures
          • 33 Use decltype on auto&& parameters to std::forward them
          • 34 Prefer lambdas to std::bind
        • 08 Tweaks
          • 41 Consider pass by value for copyable parameters that are cheap to move and always copied
          • 42 Consider emplacement instead of insertion
      • C++17 The Complete Guide
        • Part I Basic Language Features
          • 01 Structured Bindings
          • 02 if and switch with Initialization
          • 03 Inline Variables
          • 04 Aggregate Extensions
          • 05 Mandatory Copy Elision or Passing Unmaterialized Objects
          • 06 Lambda Extensions
          • 07 New Attributes and Attribute Features
          • 08 Other Language Features
        • Part II Template Features
          • 09 Class Template Argument Deduction
          • 10 Compile Time if
          • 11 Fold Expressions
          • 12 Dealing with String Literals as Template Parameters
          • 13 Placeholder Types like auto as Template Parameters
          • 14 Extended Using Declarations
        • Part III New Library Components
          • 15 std optional
          • 16 std variant
          • 17 std any
      • The Art of Writing Efficient Programs
        • 准备工作
        • 基础知识
        • 第一个例子
      • Database
        • Papers
          • Concise Hash Table
          • Modern Column-Oriented Database Systems
      • Programming Language
        • C 语言预处理器、编译器、链接器简介
        • C 语言基本类型在内存中的表示
        • C 语言结构体、数组的内存布局
        • C-Style “泛型”：以 swap/lsearch/stack 为例
        • C++ Empty object & unique_ptr size
        • C++ Vector 增长因子
        • Scheme
      • C++ Concurrency
        • Hello, world of concurrency in C++
          • What is concurrency
          • Why use concurrency
          • Concurrency and multithreading in C++
          • Getting started
        • Managing threads
          • Basic thread management
          • Passing arguments to a thread function
          • Transferring ownership of a thread
          • Choosing the number of threads at runtime
          • Identifying threads
        • Sharing data between threads
          • Problems with sharing data between threads
          • Protecting shared data with mutexes
          • Alternative facilities for protecting shared data
        • Synchronizing concurrent operations
          • Waiting for an event or other condition
          • Waiting for one-off event with futures
          • Waiting with a time limit
          • Using synchronization of operations to simplify code
        • The C++ memory model and operations on atomic types
          • Memory model basics
          • Atomic operations and types in C++
          • Synchronizing operations and enforcing ordering
        • Designing lock-based concurrent data structures
          • What does it mean to design for concurrency
          • Lock-based concurrent data structures
      • 人
        • 软件工程中的人
        • 程序员都不读书
        • 什么时候学习编程都不晚
        • 工作 15 年后的反思
      • 值得一读
      • 面试题
        • 洗牌算法
        • 100 亿条 URL 去重
        • 找出缺少的数字
        • 找到重复的数字
        • 打印括号组合
        • 从点 (0,0) 到 (X,Y) 的通路
        • 求 $a_j-a_i$ 的最大值
        • 更新 0 所在的行和列
        • 不使用加操作实现加法
        • 不使用临时变量交换两个数
        • 旋转矩阵
        • 判断一个整数是否是回文
        • 翻转字符串
        • 两个字符串是否由同样的字符组成
        • 一个字符串是否能旋转得到另一个字符串
        • 字符串压缩
        • 将空格替换成 %20
        • 不使用额外的数据结构对栈元素进行排序
        • 常数时间返回最小值的栈
        • 使用两个栈实现队列
        • 使用两个队列实现栈
        • 找到单链表中环的入口
        • 从单链表中删除内容一样的节点
        • 从单链表中删除指定节点
        • 使用链表实现加法
        • 单链表中找到倒数第 $k$ 个节点
        • 分割单链表
        • 判断链表是回文
        • 查询 x 所在排位
        • 二叉树是平衡的吗？
        • 对有序数组生成高度最低的二叉搜索树
        • 找出重量较大的一瓶药
        • 有多少蓝眼睛的人？
        • 鸡蛋从多少层掉下不破
        • 能完全覆盖吗？
        • 有多少锁是开着的
    • Mathematics
      • 010 Calculus
        • 010 Functions
          • 010 函数及其图像 Functions and Their Graphs
          • 020 组合函数；变换与缩放图像 Combining Functions; Shifting and Scaling Graphs
          • 030 三角函数 Trigonometric Functions
          • 040 指数函数 Exponential Functions
          • 050 反函数和对数 Inverse Functions and Logarithms
        • 020 Limits and Continuity
          • 010 变化率和曲线的切线 Rates of Change and Tangent Lines to Curves
          • 020 函数的极限和极限运算法则 Limit of a Function and Limit Laws
          • 030 极限的精确定义 The Precise Definition of a Limit
          • 040 单边极限 One-Sided Limits
          • 050 涉及无穷的极限；渐近线 Limits Involving Infinity; Asymptotes of Graphs
          • 060 连续性 Continuity
        • 030 Derivatives
          • 010 切线和某点处的导数 Tangent Lines and the Derivative at a Point
          • 020 导函数 The Derivative as a Function
          • 030 求导法则 Differentiation Rules
          • 040 变化率 The Derivative as a Rate of Change
          • 050 三角函数的导数 Derivatives of Trigonometric Functions
          • 060 链式法则 The Chain Rule
          • 070 隐式求导 Implicit Differentiation
          • 080 反函数的导数；对数函数 Derivatives of Inverse Functions and Logarithms
          • 090 反三角函数 Inverse Trigonometric Functions
          • 100 相关速率 Related Rates
          • 110 线性化和微分 Linearization and Differentials
        • 040 Applications of Derivatives
          • 010 函数在闭区间上的极值 Extreme Values of Functions on Closed Intervals
          • 020 中值定理 The Mean Value Theorem.md
          • 030 单调函数和一阶导测试 Monotonic Functions and the First Derivative Test
          • 040 凹凸性和曲线轮廓 Concavity and Curve Sketching
          • 050 不定式和洛必达法则 Indeterminate Forms and L'Hôpital's Rule
          • 060 应用优化 Applied Optimization
          • 070 牛顿法 Newton's Method
          • 080 反导数 Antiderivatives
        • 050 Integrals
          • 010 面积与有限和的估算 Area and Estimating with Finite Sums
          • 020 西格玛符号和有限和的极限 Sigma Notation and Limits of Finite Sums
          • 030 定积分 The Definite Integral
          • 040 微积分基本定理 The Fundamental Theorem of Calculus
          • 050 不定积分和换元法 Indefinite Integrals and the Substitution Method
          • 060 定积分换元法和曲线间面积 Definite Integral Substitutions and the Area Between Curves
          • 070 高级主题 Additional and Advanced
        • 060 Applications of Definite Integrals
          • 010 横截面计算体积 Volumes Using Cross-Sections
          • 020 利用圆柱形壳计算体积 Volumes Using Cylindrical Shells
          • 030 弧长 Arc Length
          • 040 旋转体的表面积 Areas of Surfaces of Revolution
          • 050 功和流体力学 Work and Fluid Forces
          • 060 矩和质心 Moments and Centers of Mass
        • 070 Integrals and Transcendental Functions
          • 010 定义为积分的对数 The Logarithm Defined as an Integral
          • 020 指数变化和可分离微分方程 Exponential Change and Separable Differential Equations
          • 030 双曲函数 Hyperbolic Functions
          • 040 相对增长率 Relative Rates of Growth
        • 080 Techniques of Integration
          • 010 应用基本的积分公式 Using Basic Integration Formulas
          • 020 分部积分法 Integration by Parts
          • 030 三角函数的积分 Trigonometric Integrals
          • 040 三角函数代换 Trigonometric Substitutions
          • 050 部分分式法求有理函数积分 Integration of Rational Functions by Partial Fractions
          • 060 积分表和计算机代数系统 Integral Tables and Computer Algebra Systems
          • 070 数值积分法 Numerical Integration
          • 080 广义积分 Improper Integrals
          • 090 习题 Exercises
        • 090 Infinite Sequences and Series
          • 010 数列 Sequences
          • 020 无穷级数 Infinite Series
          • 030 积分测试 The Integral Test
          • 040 比较测试 Comparison Tests
          • 050 绝对收敛；比值测试和根测试 Absolute Convergence; The Ratio and Root Tests
          • 060 交错级数和条件收敛 Alternating Series and Conditional Convergence
          • 070 幂级数 Power Series
          • 080 泰勒级数和麦克劳林级数 Taylor and Maclaurin Series
          • 090 泰勒级数的收敛 Convergence of Taylor Series
          • 010 泰勒级数的应用 Applications of Taylor Series
          • 110 附录 Appendix
        • 100 Parametric Equations and Polar Coordinates
          • 010 平面曲线的参数化 Parametrizations of Plane Curves
          • 020 参数曲线积分 Calculus with Parametric Curves
          • 030 极坐标 Polar Coordinates
          • 040 极坐标方程作图 Graphing Polar Coordinate Equations
          • 050 极坐标系下的面积和长度 Areas and Lengths in Polar Coordinates
          • 060 圆锥曲线 Conic Sections
          • 070 极坐标系的圆锥曲线 Conics in Polar Coordinates
          • 080 附录 Appendix
        • 110 Vectors and the Geometry of Space
          • 010 三维坐标系 Three-Dimensional Coordinate Systems
          • 020 矢量 Vectors
          • 030 点积 The Dot Product
          • 040 叉积 The Cross Product
          • 050 空间中的直线与平面 Lines and Planes in Space
          • 060 圆柱体和二次曲面 Cylinders and Quadric Surfaces
        • 120 Vector Valued Functions and Motion in Space
          • 010 空间中的曲线及其切线 Curves in Space and Their Tangents
          • 020 矢量函数的积分；抛射体运动 Integrals of Vector Functions; Projectile Motion
          • 030 空间中的弧长 Arc Length in Space
          • 040 曲线的曲率和法向矢量 Curvature and Normal Vectors of a Curve
          • 050 加速度的切向分量和法向分量 Tangential and Normal Components of Acceleration
          • 060 极坐标下的速度与加速度 Velocity and Acceleration in Polar Coordinates
        • 130 Partial Derivatives
          • 010 多元函数 Functions of Several Variables
          • 020 更高维度的极限和连续性 Limits and Continuity in Higher Dimensions
          • 030 偏微分 Partial Derivatives
          • 040 链式法则 The Chain Rule
          • 050 方向导数和梯度矢量 Directional Derivatives and Gradient Vectors
          • 060 切平面和微分 Tangent Planes and Differentials
          • 070 极值和鞍点 Extreme Values and Saddle Points
          • 080 拉格朗日乘子 Lagrange Multipliers
          • 090 二元函数的泰勒公式 Taylor's Formula for Two Variables
          • 100 带约束条件的偏微分 Partial Derivatives with Constrained Variables
          • 110 习题 Exercises
        • 140 Multiple Integrals
          • 010 矩阵上的二重积分 Double and Iterated Integrals over Rectangles
          • 020 一般区域上的二重积分 Double Integrals over General Regions
          • 030 二重积分求面积 Area by Double Integration
          • 040 极坐标的二重积分 Double Integrals in Polar Form
          • 050 直角坐标系的三重积分 Triple Integrals in Rectangular Coordinates
          • 060 应用 Applications
          • 070 柱坐标和球坐标系下的三重积分 Triple Integrals in Cylindrical and Spherical Coordinates
          • 080 多重积分的替换法 Substitutions in Multiple Integrals
        • 150 Integrals and Vector Fields
          • 010 标量函数的线积分 Line Integrals of Scalar Functions
          • 020 矢量场和线积分：功、环量、通量 Vector Fields and Line Integrals: Work, Circulation, and Flux
          • 030 路径无关，保守场和势函数 Path Independence, Conservative Fields, and Potential Functions
          • 040 平面内的格林定理 Green's Theorem in the Plane
          • 050 曲面和面积 Surfaces and Area
          • 060 曲面积分 Surface Integrals
          • 070 斯托克斯定理 Stokes' Theorem
          • 080 散度定理和统一理论 The Divergence Theorem and a Unified Theory
      • 020 Elementary Differential Equations
        • 010 Introduction
          • 010 一些基本数学模型；方向场 Some Basic Mathematical Models; Direction Fields
          • 020 一些微分方程的解 Solutions of Some Differential Equations
          • 030 微分方程的分类 Classification of Differential Equations
        • 020 First Order Differential Equations
          • 010 线性微分方程；积分因子法 Linear Differential Equations; Method of Integrating Factors
          • 020 可分离变量的微分方程 Separable Differential Equations
          • 030 使用微分方程建模 Modeling with First-Order Differential Equations
          • 040 线性和非线性微分方程的差异 Differences Between Linear and Nonlinear Differential Equations
          • 050 自治微分方程和种群动态 Autonomous Differential Equations and Population Dynamics
      • 200 Discrete Mathematics and Its Applications
        • 040 Number Theory and Cryptography
          • 010 Divisibility and Modular Arithmetic
          • 020 Integer Representations and Algorithms
          • 030 Primes and Greatest Common Divisors
          • 040 Linear Congruences
          • 050 Applications of Congruences
          • 060 Classical Cryptography
          • 01 Seven Is More Than Six. The Pigeon Hole Principle
          • 02 One Step at a Time. The Method of Mathematical Induction
          • 03 There Are A Lot Of Them. Elementary Counting Problems
          • 04 No Matter How You Slice It. The Binomial Theorem and Related Identities
          • 05 Divide and Conquer. Partitions
          • 06 Not So Vicious Cycles. Cycles inPermutations
          • 07 You Shall Not Overcount. The Sieve
          • 08 A Function Is Worth Many Numbers.Generating Functions
          • 09 Dots and Lines. The Origins of Graph Theory
          • 10 Staying Connected. Trees
          • 11 Finding A Good Match. Coloring andMatching
          • 12 Do Not Cross. Planar Graphs
          • 13 Does It Clique. Ramsey Theory
          • 14 So Hard To Avoid. Subsequence Conditions on Permutations
          • 15 Who Knows What It Looks Like, But It Exists. The Probabilistic Method
          • 16 At Least Some Order. Partial Orders and Lattices
          • As Evenly As Possible. Block Designs and Error Correcting Codes
          • Does Many Mean More Than One? Computational Complexity
      • Differential Equations
        • 0101 The Exponential Function
        • 0102 Variables and Parameters
        • 0103 Notations for Derivatives
        • 0104 Differential Equations
        • 0201 Introduction The Most Important DE
        • 0202 Other Basic Examples
        • 0203 Separation of Variables
        • 0204 Solutions that Blow Up The Domain of a Solution
        • 0205 Modeling by First Order Linear ODE's
        • 0301 Geometric Methods Introduction
        • 0302 Direction Fields, Isoclines, Integral Curves
        • 0303 Existence and Uniqueness Theorem for ODE's
        • 0304 Long term Behavior Fences, Funnels and Separatrices
        • 0401 Numerical Methods Introduction
        • 0402 Motivation and Implementation of Euler's Method
        • 1801 Introduction
        • 1802 Operators
        • 1803 Linear Differential Operators With Constant Coefficients
        • 1804 Operator Rules
        • 1805 Time Invariance
        • 1806 Proof of the Generalized Exponential Response Formula
        • 1807 Exercises
        • 1901 Introduction
        • 1902 The Exponential Response Formula Resonant Case
        • 1903 Undamped Forced Systems
        • 2001 Introduction
        • 2002 Sinusoidally Driven Systems Second Order LTI DE's
        • 2003 Frequency Response and Practical Resonance
        • 2004 Mechanical Vibration System Driving Through the Spring
        • 2005 Mechanical Vibration System Driving Through the Dashpot
        • 2006 Exercises
        • 2101 Introduction
        • 2102 RLC Circuits
        • 2103 Impedance
        • 2201 Fourier Series Basics Introduction
        • 2202 Periodic Functions
        • 2203 Fourier Series Definitions and Coefficients
        • 2204 Fourier Series for Functions with Period 2L
        • 2205 Orthogonality Relations
        • 2301 Operations on Fourier Series
        • 2302 Even and Odd Functions
        • 2303 Scaling and Shifting
        • 2304 Integration and Differentiation
        • 2305 Convergence of Fourier Series
        • 2306 An Interpretation of Fourier Series
        • 2307 Gibbs' Phenomenon
        • 2308 Application to Infinite Series
        • 2309 Exercises
        • 2401 ODE's with Periodic Input, Resonance
        • 2402 Example Simple Harmonic Oscillator
        • 2403 General Case
        • 2404 Exercises
        • 2501 Step and Delta Functions Introduction
        • 2502 Step and Box Functions
        • 2503 Delta Functions Unit Impulse
        • 2601 Unit Step and Unit Impulse Response Introduction
        • 2602 Initial Conditions
        • 2603 First order Unit Step Response
        • 2604 First order Unit Impulse Response
        • 2605 Second order Unit Step Response
        • 2606 Second order Unit Impulse Response
        • 2607 Higher Order Unit Impulse Response
        • 2701 Convolution Introduction
        • 2702 Definition and Properties
        • 2703 Green's Formula
        • 2704 Proof of Green's Formula
        • 2705 Examples
        • 2706 Exercises
        • 2801 Laplace Transform Basics Introduction
        • 2802 Definition of Laplace Transform
        • 2803 Domain of F(s)
        • 2804 More Entries for the Laplace Table
        • 2805 Laplace Transform Table
        • 2806 The Laplace Transform of the Delta Function
        • 2807 Exercises
        • 2901 Partial Fractions and Inverse Laplace Transform
        • 2902 Laplace Inverse by Table Lookup
        • 2903 Partial Fractions Undetermined Coefficients
        • 2904 Heaviside Cover up Method
        • 2905 Table Entries Repeated Quadratic Factors
        • 3001 Laplace Transform Solving IVP's Introduction
        • 3002 Table Entries Derivative Rules
        • 3003 Precise Definition of Laplace Inverse
        • 3004 Laplace Solving Initial Value Problems
        • 3005 IVP's and t translation
        • 3006 IVP's Longer Examples
        • 3101 Transfer and Weight Functions, Green's Formula
        • 3102 The Transfer Function
        • 3103 Modified Input
        • 3104 Green's Formula, Laplace Transform of Convolution
        • 3105 Block Diagrams
        • 3201 Poles, Amplitude Response, Connection to ERF
        • 3202 Definition of Poles
        • 3203 Pole Diagrams
        • 3204 Poles and Stability
        • 3205 Poles and Amplitude Response
        • 3301 Linear Systems Introduction
        • 3302 First order Linear Systems
        • 3303 Describing a First order System Using Matrix Notation
        • 3304 The Companion Matrix
        • 3401 Matrix Methods Eigenvalues and Normal Modes
        • 3402 Vectors and Matrices Homogeneous Systems
        • 3403 Motivation and Derivation Worked Example
        • 3404 General Case Eigenvalues and Eigenvectors
        • 3405 Worked Example Distinct Real Roots
        • 3406 Complex Eigenvalues
        • 3407 Repeated Eigenvalues
        • 3501 Introduction
        • 3502 The Phase Plane
        • 3503 Sketching the Basic Linear Systems
        • 3504 Sketching More General Linear Systems
        • 3505 Trace Determinant Diagram
        • 3506 A Computer Generated Portrait Gallery
        • 3601 Introduction
        • 3602 General Linear ODE Systems and Independent Solutions
        • 3603 The Existence and Uniqueness Theorem for Linear Systems
        • 3604 The Wronskian
        • 3605 Existence and Uniqueness and Superposition in the General Case
        • 3606 Fundamental Matrices
        • 3607 The Normalized Fundamental Matrix
        • 3608 The Exponential Matrix
        • 3609 Inhomogeneous Case Variation of Parameters Formula
        • 3610 Exercises
        • 3701 Introduction
        • 3702 The Phase Plane
        • 3703 First Order Autonomous ODE Systems and First Order ODE's
        • 3801 Introduction
        • 3802 Sketching Non linear Systems
        • 3803 Structural Stability
        • 3804 The Borderline Geometric Types
        • 3805 Structural Stability for Non linear Systems
        • 3901 Introduction
        • 3902 Limit Cycles
        • 3903 Showing Limit Cycles Exist
        • 3904 Non Existence of Limit Cycles
        • 3905 The Van der Pol Equation
        • 3906 Chaos
      • Formula
        • A Brief Table of Integrals
        • All
        • 12 Simple Graphs
        • Whose Game
    • Project Euler
        • 14 Longest Collatz Sequence
        • 26 Reciprocal Cycles
        • 43 Sub string Divisibility
        • 100 Arranged Probability
        • 51 Prime Digit Replacements
        • 52 Permuted Multiples
        • 53 Combinatoric Selections
        • 61 Cyclical Figurate Numbers
        • 64 Odd Period Square Roots
        • 66 Diophantine Equation
        • 68 Magic 5 gon Ring
        • 69 Totient Maximum
        • 72 Counting Fractions
        • 74 Digit Factorial Chains
        • 75 Singular Integer Right Triangles
        • 77 Prime Summations
        • 80 Square Root Digital Expansion
        • 82 Path Sum Three Ways
        • 83 Path Sum Four Ways
        • 84 Monopoly Odds
        • 86 Cuboid Route
        • 88 Product sum Numbers
        • 89 Roman Numerals
        • 90 Cube Digit Pairs
        • 93 Arithmetic Expressions
        • 95 Amicable Chains
        • 96 Su Doku
        • 98 Anagramic Squares
        • 101 Optimum Polynomial
        • 102 Triangle Containment
        • 104 Pandigital Fibonacci Ends
        • 107 Minimal Network
        • 110 Diophantine Reciprocals
        • 113 Non bouncy Numbers
        • 115 Counting Block Combinations
        • 116 Red Green or Blue Tiles
        • 117 Red Green and Blue Tiles
        • 118 Pandigital Prime Sets
        • 119 Digit Power Sum
        • 120 Square Remainders
        • 121 Disc Game Prize Fund
        • 123 Prime Square Remainders
        • 124 Ordered Radicals
        • 125 Palindromic Sums
        • 145 Reversible Numbers
        • 173 Hollow Square Laminae I
        • 174 Hollow Square Laminae II
        • 179 Consecutive Positive Divisors
        • 187 Semiprimes
        • 203 Squarefree Binomial Coefficients
        • 205 Dice Game
        • 206 Concealed Square
        • 243 Resilience
        • 301 Nim
        • 315 Digital Root Clocks
        • 323 Bitwise OR Operations on Random Integers
        • 329 Prime Frog
        • 345 Matrix Sum
        • 346 Strong Repunits
        • 347 Largest Integer Divisible by Two Primes
        • 348 Sum of a Square and a Cube
        • 357 Prime Generating Integers
        • 381 Prime Factorial
        • 429 Sum of Squares of Unitary Divisors
        • 491 Double Pandigital Number Divisible by 11
        • 493 Under the Rainbow
        • 500 Problem 500
        • 504 Square on the Inside
        • 516 5 smooth Totients
        • 518 Prime Triples and Geometric Sequences
        • 549 Divisibility of Factorials
        • 601 Divisibility Streaks
        • 613 Pythagorean Ant
        • 684 Inverse Digit Sum
        • 686 Powers of Two
        • 700 Eulercoin
        • 719 Number Splitting
        • 743 window into a matrix
        • 745 Sum of Squares
        • 757 Stealthy Numbers
        • 788 Dominating Numbers
        • 800 Hybrid Integers
        • 808 Reversible Prime Squares
        • 816 Shortest Distance Among Points
        • 836 A Bold Proposition
        • 853 Pisano Periods 1
        • 872 Recursive Tree
    • Reading
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        • 上帝掷骰子吗？量子物理史话
        • 人类简史
        • 怎样解题
        • 思考的乐趣
        • 可能与不可能的边界
      • 文学
        • 美丽新世界
        • 地心游记
        • 1984
      • 其他
        • 空谷幽兰
        • 黑客与画家
        • 怪诞行为学
        • 谈判
        • 美国对抗美国
          • Notes on the Text 2
          • Notes on the Text 3
          • Notes on the Text 4
          • Key Structures
          • Special Difficulties
          • Some Strategies for Learning English
          • How to Improve Your Study Habits
          • Sailing Round the World
          • To Swim English Channel at 58
          • The Present
          • The Young and the Old
          • Turning Off TV: A Quiet Hour
          • A New Toy
          • I Never Write Right
          • Bookshoppers' Paradise
          • Sam Adams, Industrial Engineer
          • The Sampler
          • If Only
          • A Magician at Stretching a Dollar
          • An English Christmas
          • Is There Life on Earth?
          • Fresh Air Will Kill You
          • Going Home
          • The Hitchhiker
          • The Dinner Party
          • An Important Lesson
          • Lessons from Jefferson
          • The American Ideal of a Great Leader
        • The World's History
      • 时间线
        • 2023
        • 2024
        • 2025

    04 Number Theory and Cryptography

    May 8, 2024 May 8, 2024

    TODO

    section list

    本书的这一章只覆盖最关键的主题，更全面详尽地阐述可以参考 Kenneth H. Rosen 的 Elementary Number Theory and Its Applications

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