/math

Essentail Math for AI

Essential Math Concepts for Computer Science and AI

Algebra

  • Variables and Constants
  • Equations and Inequalities
  • Functions and Graphs
  • Linear Algebra (Vectors, Matrices, Operations)
  • Polynomials and Factoring
  • Exponents and Logarithms
  • Complex Numbers

Calculus

  • Limits and Continuity
  • Derivatives and Differentiation
  • Integration and Antiderivatives
  • Applications of Derivatives (Optimization, Rates of Change)
  • Multivariable Calculus (Partial Derivatives, Gradients, Hessians)
  • Differential Equations

Discrete Mathematics

  • Set Theory
  • Logic and Propositional Logic
  • Predicate Logic
  • Combinatorics (Permutations, Combinations, Probability)
  • Graph Theory (Vertices, Edges, Paths, Connectivity)
  • Trees and Binary Trees
  • Relations and Functions

Probability and Statistics

  • Probability Distributions (Discrete, Continuous)
  • Random Variables
  • Expected Value and Variance
  • Central Limit Theorem
  • Hypothesis Testing
  • Regression Analysis
  • Bayesian Inference

Numerical Methods

  • Root Finding (Bisection Method, Newton's Method)
  • Linear Systems (Gaussian Elimination, LU Decomposition)
  • Interpolation and Extrapolation
  • Numerical Integration (Trapezoidal Rule, Simpson's Rule)
  • Ordinary Differential Equations (Euler's Method, Runge-Kutta Methods)

Linear Algebra for AI

  • Scalars, Vectors, Matrices, Tensors
  • Matrix Operations (Addition, Multiplication, Transpose)
  • Matrix Decompositions (Eigenvalue Decomposition, Singular Value Decomposition)
  • Vector Spaces and Subspaces
  • Linear Transformations
  • Norms and Distance Metrics
  • Applications in Machine Learning (Regression, Classification, Dimensionality Reduction)

Optimization

  • Optimization Problems (Minimization, Maximization)
  • Convex and Non-convex Optimization
  • Gradient Descent and Variants
  • Newton's Method and Quasi-Newton Methods
  • Constrained Optimization (Lagrange Multipliers)

Information Theory

  • Entropy and Information
  • Shannon Entropy
  • Conditional Entropy
  • Mutual Information
  • Entropy Rates
  • Compression Algorithms (Huffman Coding, Arithmetic Coding)

Graphical Models

  • Bayesian Networks
  • Markov Chains
  • Hidden Markov Models (HMMs)
  • Markov Random Fields (MRFs)
  • Inference Methods (Exact Inference, Approximate Inference)
  • Learning in Graphical Models

Deep Learning Mathematics

  • Neural Networks Architecture (Layers, Activation Functions)
  • Backpropagation and Chain Rule
  • Loss Functions (Mean Squared Error, Cross Entropy)
  • Optimization Algorithms (Stochastic Gradient Descent, Adam)
  • Regularization Techniques (L1/L2 Regularization, Dropout)
  • Convolutional Neural Networks (CNNs)
  • Recurrent Neural Networks (RNNs)
  • Attention Mechanisms