AI and Mathematical Tools

Course Description 

This 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:

1. Linear Algebra
2. Basic Graph Theory
3. Basic Control Theory
4. Probability
5. Optimization

The 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. 

Below is the course schedule. It is recommended that you work through one module per week. The entire course is estimated to take 15 hours to complete. Each module is estimated to take 15 hours to complete. Note: Quizzes are mandatory, the next module will not appear until you have successfully completed the previous module and achieved an 80% or higher on the quiz.

This is an asynchronous, self-paced course with no live instructor. The schedule is flexible and allows learners to complete coursework and assignments at their own pace and time. 

Learning Outcomes

At the end of this course, you should be able to:

• Analyze equations involving matrices by applying algebraic concepts such as rank, nullspace, linear independence and eigenvalues
• Define graph properties such as diameter, degrees, and connectivity and apply them to analyze networked systems.
• 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.

Course Schedule and Duration

Below is the course schedule. It is recommended that you work through one module per week. The entire course is estimated to take 15 hours to complete. Each module is estimated to take 15-18 hours to complete. Note: Quizzes are mandatory, and assignments and discussions are optional.