Introduction to the logical and mathematical foundations of computer science for computer science honors students. Topics include functions, relations, and sets; recursion and functional programming; basic logic; and mathematical induction and other proof techniques.

One MAT course that satisfies DEC category C or score of level 4 on the math placement exam; admission to the Computer Science Honors Program or the Honors College or WISE or permission of the instructor

• To provide students with a rigorous introduction to proof techniques including propositional logic and mathematical induction.
• Introduce recursion as a basic paradigm for computing with functions
• Introduce fundamental discrete structures such as functions, graphs, and trees.
• To build a strong theoretical foundation for subsequent courses in the computer science curriculum.

• James A. Anderson, Discrete Mathematics with Combinatorics, Prentice Hall, 2001.

• Propositional logic
• Syntax and semantics (truth tables); logical equivalences and logical consequence; basic proof theory (e.g., modus ponens); boolean algebra; application: digital logic circuits; application: number systems
• Functions
• Basic concepts and standard functions; sequences; basic properties of functions; composition of functions
• Recursion
• Recursive definitions of functions and sequences; application: functional programming
• Mathematical induction
• Principle of mathematical induction; examples of induction proofs; strong induction principle
• Lists and trees
• Basic definitions and operations; for both data structures; specific examples of list operations and tree algorithms to illustrate functional programming and mathematical induction