One of the most influential and fastest growing fields of research has been artificial intelligence. This technology has dramatically changed the job market, communication, search engines, and entertainment. The goal of this course is to take an interdisciplinary approach to introduce students to artificial intelligence.
In particular, we will learn about neural networks and belief propagation networks. The structure of this course will be to look at how neuroscience has inspired artificial intelligence models and then translate these ideas into mathematical models that can be programmed into a computer. We will read about the connectome project which is a current project to model neural networks in the human brain. This has been an ongoing project since the 1980s where the goal is to map the structural connectivity of the brain. This model has inspired the development of AI technology that has dramatically changed our world. The challenge is to translate these ideas into mathematical models that can be implemented in a computer. To accomplish this objective, we will learn several of the basics of linear algebra and probability. Once the students understand how to use these mathematical tools, we will learn how to build AI networks and use them to make decisions.
There are two mathematical topics and one neuroscience topic that we will learn about in this class.
(1) Neural networks in the brain and the connectome project
As an introduction to the course, we'll talk about the connectome project and how much progress scientists have made in the last 30 years. I'll talk about the project in class and assign readings from the book Connectome by Sebastian Seung and short videos.
(2) Neural networks
After describing the main idea of a neural network, the students will learn basic algebra such as vectors, matrices, and vector/matrix operations. Next, I will teach students on how to train a neural net by introducing them to derivatives/gradients. Then I'll explain what it means to optimize a function and the gradient decent algorithm. To conclude, we'll go over the perceptron algorithm and talk about how to add more layers on a neural net if time permits.
(3) Belief Propagation in graphical models
I'll teach the students about graphical models and how they can be used to make decisions in a network. The students will learn some very basic concepts in graph theory such as the definition of a graph, connectivity, and trees. To understand what a graphical model is, we'll review some concepts in probability such as random variables and probability distributions. Once we've covered this material, we'll learn about the belief propagation algorithm.
The primary objective of the course is to introduce high school students to artificial intelligence, which is a topic they've heard of but perhaps never formally studied. These students will leave the course with some mathematical knowledge of linear algebra, calculus, and probability. In addition, they will be introduced to two very active areas of research in artificial intelligence. Most importantly, I want the students to see that mathematics is essential to the process of developing artificial intelligence.
Prerequisites: I'm expecting that the students have taken algebra and know some basic probability. We will be taking a more abstract approach to learning about artificial intelligence, so no programming experience is needed.
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