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CMSC 130: Foundations of Rigorous Thinking

Prerequisites: Permision of instructor

• A successful understanding of many scientific subjects requires the ability to reason about mathematical objects. This is a course which develops rigorous thinking skills: the ability to formally reason about abstract objects.The traditional way of achieving this goal is to teach the fundamental foundations of mathematics: logic and sets.
• A familiar example from high school is Euclidean geometry, in which the properties of planar figures (formed by straightedge and compass) are deduced by formal proofs.The objects encountered (such as triangles and circles), are types of set abstractions that are built upon the more fundamental objects of point and line.The line-by-line proofs used to reason in this system are built upon the axioms of geometry and logical rules of deduction.
• This course could serve students in many ways.In addition to providing non-science students with the tools to take regular computer science courses, it could also serve as a "transition" between calculus and higher mathematics for a potential mathematics student, or might be useful for the increasing number of students interested in cognitive science, neuro-science, psychology, and the philosophy of mind. With enough student interest, it could lead into a more advanced course in mathematical logic or set theory.
• One of the unique features of the course will be the use of the cooperative learning paradigm, where students are split into groups of 3 to 4 to solve problems in a supervised fashion during class (typically the last third of an extended period) and present their results. Because of this discussion-oriented approach, the course will have the flavor of a 'Q' seminar. A combined laboratory component is also a possibility.

For more details, see the course syllabus

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Computer Science Department, Haverford College.