수학(3판)

1장 Mathematical Proof

1.1 Mathematical Theorems ---------------------------------------------------------------------------- 2

1.2 직관과 관찰 --------------------------------------------------------------------------------------- 20

1.? 완벽하고 일관된 논리체계 ----------------------------------------------------------------------- 24

1.t 불완전한 논리체계의 풍요로움 ------------------------------------------------------------------- 42

2장 Equation of Nature

2.1 Introduction to Equation of Nature -------------------------------------------------------------- 59

2.2 1차 미분방정식의 Solution ----------------------------------------------------------------------- 71

2.3 고차(高次) DE의 Solution ------------------------------------------------------------------------- 82

2.4 Variable Coefficient Differential Equations ------------------------------------------------------ 102

2.5 State Equation and Numerical Solution --------------------------------------------------------- 110

2.N Examples of Equation of Nature ---------------------------------------------------------------- 114

▩ 과도(過度)한 공부는 좋은가? -------------------------------------------------------------------- 124

3장 Free from Infinity and Infinitesimal

3.0 Introduction to Modulo Operation -------------------------------------------------------------- 127

3.1 Finite Field ---------------------------------------------------------------------------------------- 133

3.2 A Small Field: {0, 1} ------------------------------------------------------------------------------ 138

3.3 Cryptography ------------------------------------------------------------------------------------- 144

3.omg An Extraordinary Connection ---------------------------------------------------------------- 151

▩ 공부는 재미있는가? ------------------------------------------------------------------------------ 157

4장 Domains

4.1 Time Domain과 s-Domain ----------------------------------------------------------------------- 161

4.2 Analog Domain과 Digital Domain -------------------------------------------------------------- 183

4.3 Time Domain과 Frequency Domain ------------------------------------------------------------ 191

4.D Natural Digital Domain -------------------------------------------------------------------------- 199

4.R Spacetime Domains ------------------------------------------------------------------------------ 213

4.Ж Body-Mind Transform -------------------------------------------------------------------------- 225

5장 Array of Numbers

5.1 Vector Operations -------------------------------------------------------------------------------- 230

5.2 Vector Space ------------------------------------------------------------------------------------- 243

5.3 Matrix Operations -------------------------------------------------------------------------------- 250

5.4 Solution of Linear Systems ---------------------------------------------------------------------- 255

5.5 Matrix Determinant ------------------------------------------------------------------------------ 266

5.6 Inverse Matrix ------------------------------------------------------------------------------------ 279

5.7 Eigenvector --------------------------------------------------------------------------------------- 284

5.8 Matrix Decomposition --------------------------------------------------------------------------- 296

5.9 Least Square Method ---------------------------------------------------------------------------- 307

5.? A Glimpse of Infinity : Universe ----------------------------------------------------------------- 318

6장 Differentiation and Integration by Vectors

6.1 Gradient, Jacobian, Directional Derivatives ----------------------------------------------------- 331

6.F Forces --------------------------------------------------------------------------------------------- 354

6.2 Convex Optimization ----------------------------------------------------------------------------- 361

6.3 Line Integration ---------------------------------------------------------------------------------- 383

6.4 Double Integration ------------------------------------------------------------------------------- 389

6.5 An Application: Machine Learning -------------------------------------------------------------- 409

6.ε A Glimpse of Infinitesimal ----------------------------------------------------------------------- 428

7장 Imaginary Numbers

7.1 Complex Number Field -------------------------------------------------------------------------- 447

7.2 Concept of Complex Function ------------------------------------------------------------------- 456

7.3 Analyticity of Complex Function ---------------------------------------------------------------- 461

7.4 Complex Functions ------------------------------------------------------------------------------- 468

7.5 Riemann Surface: An Example ------------------------------------------------------------------- 482

7.6 An Application: Digital Communication --------------------------------------------------------- 489

7.NE 합리적인 판단의 한계: Nash Equilibrium ----------------------------------------------------- 492

8장 Sum of Numbers

8.1 Sequence and Series ----------------------------------------------------------------------------- 497

8.2 Taylor Series -------------------------------------------------------------------------------------- 510

8.3 Series Solution of DE ---------------------------------------------------------------------------- 517

8.☎ Connected in Infinite Series -------------------------------------------------------------------- 522

▩ Is Mathematics Invented or Discovered? -------------------------------------------------------- 533



9장 Number As Uncertainty

9.1 Definition of Probability ------------------------------------------------------------------------- 552

9.2 Law of Large Numbers --------------------------------------------------------------------------- 555

9.3 Is the Coin Fair? ---------------------------------------------------------------------------------- 574

9.4 Deterministic or Probabilistic? ------------------------------------------------------------------- 585

9.5 Information --------------------------------------------------------------------------------------- 592

▩ Logical Quests ------------------------------------------------------------------------------------ 596

▩ Beyond Logic: 절망, 신, 초인 ------------------------------------------------------------------- 603



Reference ------------------------------------------------------------------------------------------ 608

Index ------------------------------------------------------------------------------------------------ 612

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