A "mathematics curriculum in a box": An accelerated but friendly introduction to higher mathematics topics in calculus, linear algebra, set theory, proofs, logic, number theory, abstract algebra, and real analysis. Precalculus is the only prerequisite. Strongly recommended for students considering a major in mathematics or a mathematical discipline such as computer science.

- Instructor: Bill Shillito

The varieties of potential social structures are infinite. For any natural language, the number of potential sentences is also infinite. In both cases, this suggests a computational operation in which atomic mental symbols compose to form complex molecular representations. This raises a number of questions. Is the computational component of interpersonal cognition an offshoot of language? Is language an offshoot of interpersonal cognition? Without thinking in language, are non-human animals using a computational system to build their social structures? Does one have to say that the mind is literally computational in order to account for infinite variety in language or interpersonal cognition? Could the infinity of language and social structure exist on a wholly abstract level, like numbers, a level which the mind simply grasps? What does it mean for the mind to “grasp” something abstract? Integers also form an infinite set. How is mathematical cognition relation to social and language cognition?

- Instructor: John Bolender

Audio annotations will be posted lecture-by-lecture as time permits.

This course is free. Assignments will be graded only on request. Suggested prerequisites include an understanding of basic Java or C++ programming and basic familiarity with discrete mathematics.

Suggested donation: $140 for the whole course.

Offered online at this website. The lectures may be viewed at your own convenience.

Prerequisites: Basic computer skills, familiarity with Microsoft Windows.

Initially offered from April 4 to June 6, 2009. Lectures will remain online indefinitely, but no new webspace on our servers or certificates will be issued for this course. Cost: Free. Suggested donation: $10 per lecture.

- Instructor: Michael Barnathan