"Math for AI" vs "Math for ML"

The syllabuses for "Math for AI" (Artificial Intelligence) and "Math for ML" (Machine Learning) have significant overlap but also some differences due to the distinct focuses and applications of these fields. Below is an outline highlighting the typical contents of each:

Key Differences:

• AI Syllabus:

  • Broader in scope, covering more topics from discrete mathematics, logic, and algorithms, which are crucial for understanding various AI paradigms such as symbolic AI and heuristic search.
  • Includes more emphasis on operations research and game theory, which are useful for decision-making processes and strategic planning in AI applications.

• ML Syllabus:

  • More focused on statistical methods, probability theory, and optimization techniques directly applicable to learning algorithms.
  • Greater emphasis on numerical methods and information theory as they apply to data-driven models.
  • Includes specific topics related to training, regularization, and evaluation of models.

In summary, while both fields require a strong foundation in linear algebra, calculus, and probability, "Math for AI" tends to cover a broader range of topics related to different AI methodologies, whereas "Math for ML" focuses more deeply on statistical and optimization methods directly relevant to building and refining machine learning models.

Math for AI

1. Linear Algebra

   • Vectors and matrices
   • Eigenvalues and eigenvectors
   • Singular value decomposition (SVD)
   • Norms and orthogonality

2. Calculus

   • Differential and integral calculus
   • Multivariable calculus
   • Optimization (gradient descent, Lagrange multipliers)
   • Taylor series and approximations

3. Probability and Statistics

   • Probability theory
   • Distributions (e.g., Gaussian, Bernoulli)
   • Bayesian probability
   • Hypothesis testing and confidence intervals
   • Markov chains and stochastic processes

4. Algorithms and Data Structures

   • Graph theory and graph algorithms
   • Search algorithms (e.g., A*, minimax)
   • Dynamic programming
   • Data structures (e.g., trees, heaps, hash tables)

5. Discrete Mathematics

   • Combinatorics
   • Logic and set theory
   • Boolean algebra
   • Formal languages and automata

6. Optimization and Operations Research

   • Linear programming
   • Integer programming
   • Game theory

7. Advanced Topics (dependent on focus area)

   • Information theory
   • Complex systems
   • Symbolic logic

Math for ML

1. Linear Algebra

   • Vector spaces and linear transformations
   • Eigenvalues and eigenvectors
   • Matrix decompositions (SVD, QR decomposition)
   • Principal component analysis (PCA)

2. Calculus

   • Single-variable and multivariable calculus
   • Chain rule and partial derivatives
   • Gradient descent and backpropagation
   • Jacobian and Hessian matrices

3. Probability and Statistics

   • Probability distributions (e.g., Gaussian, Binomial)
   • Bayesian inference
   • Expectation and variance
   • Maximum likelihood estimation (MLE)
   • Markov chains and Monte Carlo methods

4. Optimization

   • Convex optimization
   • Stochastic optimization
   • Constrained and unconstrained optimization
   • Regularization techniques

5. Information Theory

   • Entropy and mutual information
   • Kullback-Leibler divergence
   • Information gain

6. Algorithms and Complexity

   • Computational complexity
   • Optimization algorithms (e.g., SGD, Adam)
   • Numerical linear algebra

7. Advanced Topics in Statistics and Probability

   • Hypothesis testing and p-values
   • Confidence intervals
   • Statistical learning theory