Mathematics and Computer Science

This elective is an introduction to game theory and strategic thinking. The course covers mathematics – logic, probability and statistics – with an emphasis on application. Beginning with representations and basic assumptions, including the extensive form; strategies and the normal form; beliefs, mixed strategies, and expected payoffs; and general assumptions and methodology, the course moves on to analyzing behavior in static settings.

This course introduces the student to the study of vector spaces over the real numbers, linear mappings between vector spaces, and their matrix representations. Topics include an investigation of ways to represent and analyze lines and planes in space, with frequent use of the scalar product and cross product, the study of subspaces, bases and dimension, the kernel and image of a linear mapping, and determinants.

Students learn the basics of algorithmic thinking, and design programs to solve simple problems. A number of different programming environments are used including highly structured programming environments such as Alice and Scratch. Students gain familiarity with robust programming languages like Python. Students learn the basics of variables, loops, conditional statements and standard data structures such as arrays and dictionaries.

Machine learning is the process by which computers train themselves to make predictions and ultimately, decisions based upon data. In this course, students will use powerful software libraries to construct adaptive and predictive models.  Students learn the basic concepts, tools, and techniques of adaptive computation and machine learning and proceed through a series of increasingly complex projects, culminating in a project where students program and train their own intelligent systems.

For students with extensive programming experience, this course introduces the basics of mobile-platform application development. The programming language Objective-C is used as a basis for programming applications for iOS devices such as iPhones and iPads. Students complete both individual and group projects, based on student interests.