Description:
The course will make some of the necessary mathematical background for AI accessible by decomposing and illustrating difficult concepts with a number of real-world examples and problems for students to work out. Namely, the course consists of five modules:
- Linear Algebra
- Basic Graph Theory
- Basic Control Theory
- Probability
- Optimization
This course will help provide students with an introductory overview and refresher on the above topics, thereby preparing them for advanced courses in machine learning, AI, cyber physical systems, data science, and autonomous systems, among others.
Topics Covered:
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Analyze equations involving matrices by applying algebraic concepts such as rank, nullspace, linear independence, and eigenvalues
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Define graph properties such as diameter, degrees, and connectivity, and apply them to analyze networked systems
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Define properties of linear systems, including controllability, observability, and stability, and apply them to design state estimators and feedback controllers
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Define probability distributions and moments of random variables, and characterize the long-term behavior of stochastic processes
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Specify the fundamental optimality conditions for optimization problems, and implement basic algorithms to find the optimizer