Mathematics

Explore mathematical foundations essential for artificial intelligence and robotics, including probability, linear algebra, and Lie theory.

Table of Contents

• Preface
• Probability
  • Introduction to Probability
  • Set Theory
  • Binomial and Multinomial Distribution
  • Conditional Distribution
  • Laws of Total Probability
  • Bayes' Theorem
  • Independence
  • Random Variables
  • Bernoulli Distribution
  • Binomial to Normal Distribution
  • Binomial to Poisson Distribution
  • Geometric Distribution
  • Exponential Distribution
  • Poisson Process
  • Function of Random Variables
  • Joint Distribution
  • Theory of Expectation
  • Variance and Standard Deviation
  • Markov's Inequality
  • Law of Large Numbers
  • Moment Generating Function
  • Covariance and Correlation
  • Tail Sum
  • Proof of Central Limit Theorem
• Linear Algebra
  • Singular Value Decomposition
  • Frobenius Inner Product
• Optimization
  • Least Squares
  • Non-Linear Least Squares
  • Approximation of Hessian
  • Optimization Procedure
    • Gradient-Descent
    • Newton-Rapshon
    • Gauss-Newton
    • Levenberg Marquardt
• Lie Theory
  • Preface
  • Lie Groups
  • Lie Algebra
  • Adjoint