Description:
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Course Description: Students will work through real-world problems and examples to understand the mathematical background for AI. By breaking concepts down and putting them in context, this course makes the math behind AI accessible for a wider audience.
Prerequisites:
Basic probability
Linear algebra
Ordinary differential equations (knowledge of ordinary differential equations will be valuable but is not required in order to be successful)
Learning Outcome:
– Analyze equations involving matrices by applying algebraic concepts such as rank, nullspace, linear independence, and eigenvalues
– Define properties of linear systems, including controllability, observability, and stability, and apply them to design state estimators and feedback controllers
– Define probability distributions and moments of random variables, and characterize the long-term behavior of stochastic processes
– Specify the fundamental optimality conditions for optimization problems, and implement basic algorithms to find the optimizers
| Module |
Topic & Readings |
| Module 1 |
Vectors and Matrices
System of Equations and Eigenvalues
Diagonalization and Definite Matrices
Norms |
| Module 2 |
Basics and Graph Properties
Search Algorithms and Trees
Shortest Paths |
| Module 3 |
Basics and Stability
Controllability and Observability
Lyapunov Theory |
| Module 4 |
Basics and Conditional Probability
Random Variables and Expectation
Markov Chains |
| Module 5 |
Extrema and Optimality
Infimum and Supremum
Convexity and Algorithms |
Faculty: Philip E. Paré and Shreyas Sundaram