INTRODUCTION TO DISCRETE MATHEMATICS

Prerequisites & course information

Requisites: MATH 217 or 221 Course Designation: Core GenEd - Mathematics & Quantitative Reasoning Breadth - Natural Science Level - Intermediate L&S Credit - L&S Liberal Arts and Science Repeatable for Credit: No Last Taught: Fall 2026 Learning Outcomes: 1. Demonstrate proficiency with basic skills for constructing and evaluating mathematically rigorous arguments and proofs. Audience: Undergraduate 2. Construct proofs by induction to prove properties in a variety of domains (mathematical formulas, recursively-defined structures, loop invariants, program correctness). Audience: Undergraduate 3. Demonstrate a familiarity with and an ability to reason about discrete structures/data types (integers, strings, bit strings, sets, relations, functions, graphs, trees). Audience: Undergraduate 4. Employ basic program analysis techniques to evaluate behavior of functions and simple algorithms such as assessing correctness and termination of simple algorithms, constructing recurrences, solving simple recurrences, and applying asymptotic analysis. Audience: Undergraduate 5. Apply basic combinatoric techniques to counting problems. Audience: Undergraduate 6. Demonstrate the connections between a description of a simple language and a finite state machine or regular expression. Given a finite state machine or regular expression, determine the language it defines and/or whether a given string is recognized by it. Given a simple language, construct a finite state machine or regular expression that recognizes it. Audience: Undergraduate Learning Outcomes: 1. Demonstrate proficiency with basic skills for constructing and evaluating mathematically rigorous arguments and proofs. Audience: Undergraduate 2. Construct proofs by induction to prove properties in a variety of domains (mathematical formulas, recursively-defined structures, loop invariants, program correctness). Audience: Undergraduate 3. Demonstrate a familiarity with and an ability to reason about discrete structures/data types (integers, strings, bit strings, sets, relations, functions, graphs, trees). Audience: Undergraduate 4. Employ basic program analysis techniques to evaluate behavior of functions and simple algorithms such as assessing correctness and termination of simple algorithms, constructing recurrences, solving simple recurrences, and applying asymptotic analysis. Audience: Undergraduate 5. Apply basic combinatoric techniques to counting problems. Audience: Undergraduate 6. Demonstrate the connections between a description of a simple language and a finite state machine or regular expression. Given a finite state machine or regular expression, determine the language it defines and/or whether a given string is recognized by it. Given a simple language, construct a finite state machine or regular expression that recognizes it. Audience: Undergraduate