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CS202: Discrete Structures

Introduction to the mathematical foundations from discrete mathematics for analyzing computer algorithms, both for correctness and performance. Focuses on the introduction to models of computation, including finite state machines and Turing machines.

Skill Level: Beginner

Course Introduction

Course Syllabus

Course Terms of Use

Unit 1: The Logic of Compound Statements

Unit 1 Learning Outcomes

Unit 1 Activities

1.1: Compound Statements

1.1.1: The NOT, AND, OR, and XOR Symbols

Massachusetts Institute of Technology: Srini Devadas and Eric Lehman's "Logic"

University of California, San Diego: Edward Bender and S. Williamson's "Arithmetic, Logic and Numbers: Boolean Functions and Computer Arithmetic"

1.1.2: Translating from English to Symbols

Massachusetts Institute of Technology: Srini Devadas and Eric Lehman's "Logic"

University of California, San Diego: Edward Bender and S. Williamson's "Arithmetic, Logic, and Numbers: Logic"

Translating from English to Logic Symbols

1.1.3: Double Negative Property

University of California, San Diego: Edward Bender and S. Williamson's "Arithmetic, Logic and Numbers: Boolean Functions and Computer Arithmetic"

1.1.4: Negations of AND and OR: DeMorgan's Law

University of California, San Diego: Edward Bender and S. Williamson's "Arithmetic, Logic and Numbers: Boolean Functions and Computer Arithmetic"

University of California, San Diego: Edward Bender and S. Williamson's "Arithmetic, Logic, and Numbers: Logic"

1.1.5: Tautologies and Contradictions

University of California, San Diego: Edward Bender and S. Williamson's "Arithmetic, Logic, and Numbers: Logic"

1.2: Conditional Statements

1.2.1: Logical Equivalences Using Conditional Statements

Massachusetts Institute of Technology: Srini Devadas and Eric Lehman's "Logic"

University of California, San Diego: Edward Bender and S. Williamson's "Arithmetic, Logic, and Numbers: Logic"

1.2.2: If and Only If, Necessary and Sufficient Conditions

University of California, San Diego: Edward Bender and S. Williamson's "Arithmetic, Logic, and Numbers: Logic"

1.2.3: Proving Validity or Invalidity of an Argument Using Truth Tables

Massachusetts Institute of Technology: Srini Devadas and Eric Lehman's "Logic"

University of California, San Diego: Edward Bender and S. Williamson's "Arithmetic, Logic and Numbers: Boolean Functions and Computer Arithmetic"

Validity and Arguments

1.3: Modus Ponens and Modus Tollens

Wikipedia: "List of Rules of Inference"

Massachusetts Institute of Technology: Srini Devadas and Eric Lehman's "Proofs"

University of California, San Diego: Edward Bender and S. Williamson's "Arithmetic, Logic, and Numbers: Logic"

Modus Ponens and Other Types of Reasoning

Unit 2: The Logic of Quantified Statements

Unit 2 Learning Outcomes

Unit 2 Activities

2.1: Quantified Statements

Massachusetts Institute of Technology: Srini Devadas and Eric Lehman's "Logic"

University of California, San Diego: Edward Bender and S. Williamson's "Arithmetic, Logic and Numbers: Logic"

Massachusetts Institute of Technology: Srini Devadas and Eric Lehman's "Logic"

University of California, San Diego: Edward Bender and S. Williamson's "Arithmetic, Logic and Numbers: Logic"

2.2: Operating on Quantified Statements

Massachusetts Institute of Technology: Srini Devadas and Eric Lehman's "Logic"

University of California, San Diego: Edward Bender and S. Williamson's "Arithmetic, Logic and Numbers: Logic"

Massachusetts Institute of Technology: Srini Devadas and Eric Lehman's "Logic"

University of California, San Diego: Edward Bender and S. Williamson's "Arithmetic, Logic and Numbers: Logic"

2.3: Statements Containing Multiple Quantifiers

University of California, San Diego: Edward Bender and S. Williamson's "Arithmetic, Logic and Numbers: Logic"

Definition of a Limit

Unit 3: Introduction to Number Theory and Proof Methods

Unit 3 Learning Outcomes

Unit 3 Activities

3.1: Direct Proofs and Indirect Proofs

Massachusetts Institute of Technology: Srini Devadas and Eric Lehman's "Proofs"

University of California, San Diego: Edward Bender and S. Williamson's "Arithmetic, Logic and Numbers: Sets and Functions"

3.1.1: Odd and Even Numbers

University of California, San Diego: Edward Bender and S. Williamson's "Arithmetic, Logic and Numbers: Number Theory"

3.1.2: Prime Numbers

University of California, San Diego: Edward Bender and S. Williamson's "Arithmetic, Logic and Numbers: Number Theory"

3.1.3: Proving and Disproving Universal Statements

3.1.3.1: Proof by Using the Method of Exhaustion

University of California, San Diego: Edward Bender and S. Williamson's "Arithmetic, Logic and Numbers: Number Theory"

3.1.3.2: Disproof by Counterexample

University of California, San Diego: Edward Bender and S. Williamson's "Arithmetic, Logic and Numbers: Number Theory"

3.1.4: Proving and Disproving an Existential Statement

University of California, San Diego: Edward Bender and S. Williamson's "Arithmetic, Logic and Numbers: Number Theory"

3.2: Numbers: Direct Proofs and Counterexamples

3.2.1: Rational Numbers

University of California, San Diego: Edward Bender and S. Williamson's "Arithmetic, Logic and Numbers: Number Theory"

3.2.2: Irrational Numbers

University of California, San Diego: Edward Bender and S. Williamson's "Arithmetic, Logic and Numbers: Number Theory"

3.2.3: Proving Properties of Rational Numbers

Massachusetts Institute of Technology: Srini Devadas and Eric Lehman's "Notes for Recitation 2"

3.3.1.1: Divisibility Definition

Massachusetts Institute of Technology: Srini Devadas and Eric Lehman's "Number Theory I"

University of California, San Diego: Edward Bender and S. Williamson's "Arithmetic, Logic and Numbers: Number Theory"

3.3.1.2: Divisibility of Algebraic Expressions