ぱらぱらめくる『Stochastic Models, Information Theory, and Lie Groups』

• この本は最終的には、確率・統計・解析に関することにつながるようなので、こちらのオレンジブログに書く方が良いかもしれないが、難所の多くが幾何・多様体・微積・ベクトル解析などになりそうなので、まずはここ(ブルーブログ)で全体像をぼんやりつかんでみてから、オレンジでの捉え方については(もし可能なら)考えることにする

Stochastic Models, Information Theory, and Lie Groups, Volume 1: Classical Results and Geometric Methods (Applied and Numerical Harmonic Analysis)

Stochastic Models, Information Theory, and Lie Groups, Volume 2: Analytic Methods and Modern Applications (Applied and Numerical Harmonic Analysis)

• まずは、目次までを眺めて、いったいこれは何のかの俯瞰図を得る
• タイトルはStochastic Models, Information Theory, and Lie Groups
• 全２巻構成
  • Volume 1 Classical Results and Geometric Methods
  • Volume 2 Analytic Methods and Modern Applications
• 目次
• Volume 1 Classical Results and Geometric Methods
  • ANHA Series Preface(この本は、Applied and Numerical Harmonic Analysisシリーズという領域の中の一つなわけだが、ANHAの中でのこの本の位置づけ)と本自体のPreface
  • 1 Introduction
  • 2 Gaussian Distributions and the Heat Equation
  • 3 Probability and Information Theory
  • 4 Stochastic Differential Equations
  • 5 Geometry of Curves and Surfaces
  • 6 Differential Forms
  • 7 Polytopes and Manifolds
  • 8 Stochastic Processes on Manifolds
  • 9 Summary (of volume 1)
  • Appendix Review of Linear Algebra, Vector Calculus, and Systems Theory
• Volume 2 Analytic Methods and Modern Applications
  • 10 Lie Groups I: Introduction and Examples
  • 11 Lie Groups II: Differential-Geometric Properties
  • 12 Lie Groups III: Integration, Convolution, and Fourier Analysis
  • 13 Variational Calculus on Lie Groups
  • 14 Statistical Mechanics and Ergotic Theory
  • 15 Parts Entropy and the Principal Kinematic Formula
  • 16 Multivariate Statistical Analysis and Random Matrix Theory
  • 17 Information, Communication, and Group Theory
  • 18 Algebraic and Geometric Coding Theory
  • 19 Information Theory on Lie Group
  • 20 Stochastic Processes on Lie Group
  • 21 Locomotion and Perception as Communication overt Principal Fiber Bundles
  • 22 Summary (of volumes 1 and 2)