Welcome

Indiana University, Bloomington Professor of Mathematics Director, Program in Pure and Applied Logic Adjunct Professor: Computer Science, Informatics, Linguistics, and Philosophy Member, Programs in Cognitive Science and in Computational Linguistics

My general area of interest is applied logic: the study of mathematical and conceptual tools for use in computer science, linguistics, artificial intelligence and other areas.

Applied logic is applied mathematics. It is logic looking outward, reaching towards the diverse collection of worlds in which logic is used.

HON-H 305: Exploring Good and Bad Behavior with Mathematics

This course presents mathematical topics related to the Themester's focus on good and bad behavior. The leading idea is that mathematical models in the social sciences often use concepts such as 'payoff', 'strategy', and 'network'. This class presents the underlying mathematical ideas, the theory as well as many applications. One major topic in the course is basic game theory, since this is directly concerned with our topic. But we'll also look at voting theory and social choice, addressing the questions of what constitutes a fair election or a fair division of goods. The class is also likely to study models of 'spreading' behavior that we find in diseases, ideas, and fads. Finally, the class will try to ask whether the mathematical models can inform philosophical discussion about the nature of good behavior.

This Honors course is intended for majors in fields like Cognitive Science, Economics, and Philosophy who will already be concerned with the application areas and with mathematical models. (Of course, others may take the course as well). Prospective students need to be comfortable with mathematical notation and thinking, but there are no specific math prerequisites. The class will have weekly homework, and much of the learning will take place in the homework. The kind of thinking required would be closer to finite math (M118) and geometry (proofs) than to calculus, and so it's important to be good at these types of activities. But critical thinking and reasoning are also important for this course because we will always want to question the mathematical models that are presented.

M583: Set Theory

Our graduate math class in Set Theory. Topics include both the foundational aspects of set theory and also the mathematical contribution of set theory as a study of infinity. We'll see the axioms of set theory and late in the semester discuss what it means to be a model of those axioms. We'll also see standard material on the natural numbers and induction, well-orderings and ordinals, transfinite recursion, the sizes of infinite sets, and the Axiom of Choice.