Category theory is a relatively new branch of mathematics that has transformed …
Category theory is a relatively new branch of mathematics that has transformed much of pure math research. The technical advance is that category theory provides a framework in which to organize formal systems and by which to translate between them, allowing one to transfer knowledge from one field to another. But this same organizational framework also has many compelling examples outside of pure math. In this course, we will give seven sketches on real-world applications of category theory.
The goal of this class is to prove that category theory is …
The goal of this class is to prove that category theory is a powerful language for understanding and formalizing common scientific models. The power of the language will be tested by its ability to penetrate into taken-for-granted ideas, either by exposing existing weaknesses or flaws in our understanding, or by highlighting hidden commonalities across scientific fields.
Advances in cognitive science have resolved, clarified, and sometimes complicated some of …
Advances in cognitive science have resolved, clarified, and sometimes complicated some of the great questions of Western philosophy: what is the structure of the world and how do we come to know it; does everyone represent the world the same way; what is the best way for us to act in the world. Specific topics include color, objects, number, categories, similarity, inductive inference, space, time, causality, reasoning, decision-making, morality and consciousness. Readings and discussion include a brief philosophical history of each topic and focus on advances in cognitive and developmental psychology, computation, neuroscience, and related fields. At least one subject in cognitive science, psychology, philosophy, linguistics, or artificial intelligence is required. An additional project is required for graduate credit.
Students are going to play a categories game as their warm up, …
Students are going to play a categories game as their warm up, and then create questions to be used in the next activity. As a category is displayed on the screen, students will go around and say things that fall under that category. They will use example questions to create their own.
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