Department of Computer Science

Michael Bender

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.

Bulletin Link

One MAT course that satisfies D.E.C. C or QPS or score of level 4 on the math placement exam; admission to the Computer Science Honors or the Honor College or the WISE Honors or University Scholars

• An ability to use logic and basic proof techniques, such as mathematical induction.
• To understand recursion as a computing paradigm.
• An ability to define and use discrete structures such as functions, graphs and tree.

James L. Hein, Discrete Structures, Logic and Computability, Jones and Bartlett, 978-0763772062.
Supplementary Material: 
Eric Lehman and Tom Leighton, Mathematics for Computer Science, Online.

• 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

CSE150