To introduce the student to the mathematical tools of logic and induction, and to the basic definitions and theorems concerning relations, functions, and sets. Later courses in the computer science curriculum build on the mathematical foundations covered here. Particular emphasis is placed on inductive definitions and proofs, with application to problems in computer science.
Basic Set Notation, Propositional Logic, Truth Tables, Boolean Circuits
First-Order Logic, Predicates. Quantifiers
Mathematical Induction: Program Correctness, Trees, Grammars
Relations: Closures of relations. Orders, Equivalence Relations, Functions
Regular class assignments; no programming.
- will be prepared to contribute to a rapidly changing field by acquiring a thorough grounding in the core principles and foundations of computer science (e.g., techniques of program design, creation, and testing; key aspects of computer hardware; algorithmic principles).
- will acquire a deeper understanding on (elective) topics of more specialized interest, and be able to critically review, assess, and communicate current developments in the field.
- will be prepared for the next step in their careers, for example, by having done a research project (for those headed to graduate school), a programming project (for those going into the software industry), or some sort of business plan (for those going into startups).