Mathematics for Computer Science/AI

Weekly (Starting Friday 10th September, 2021, duration: 1 hour)

3 weeks: Linear Algebra

• Week 1: Linear systems, Theory of matrices,  Linear independence, inverse matrices, null space and uniqueness
• Week 2: Eigenvalues and eigenvectors, singular value decomposition.
• Week 3: Jacobian and Hessian matrices and their applications in AI systems.

3 weeks:  Graph theory and applications

• Week 1: Graphs - Introduction, Applications and Types
• Week 2: Adjacency matrix, Adjacency List, Incidence matrix, Edge
• Week 3: Graph operations and their applications  in AI.  Graphs and matrices

3 weeks:  Multivariable analysis  and optimization

• Week 1: Derivatives and antiderivatives of  multivariable functions, use the AI decision tree to perform integration of complicated functions.
• Week 2: Green’s, Stokes’, divergence theorems and applications
• Week 3: Lagrange multipliers and constrained optimization
• Week 4: Least squares and Hessians, Steepest descent

4 weeks: Probability and statistics in AI

• Week 1: Theory of sets, sample space, dependent and independent events, joint and conditional probability
• Week 2: Random variables- continuous and discrete, expectation,  Bayes’  inference, variance and covariance  operators
• Week 3. Binomial, Bernoulli, Poisson, exponential, Gaussian, and Gibbs statistics in AI.
• Week 4: Stochastic neural networks, Boltzman machine, and mathematical aspects of risk management

 2 weeks: Practical exercises and  final test

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