1. Logic Basics
1.1 Introduction
1.2 Basic Logical Operators
1.3 Logical Equivalences
1.4 Conditional Statements
1.5 Universal and Existential Quantifiers
1.6 Negating Quantifiers
2. Deductive Reasoning
2.1 Introduction
2.2 Valid Argument
2.3 Rules of Inference
2.4 Quantified Rules of Inference
2.5 Heuristic Diagrams
3. Elementary Set Theory
3.1 Introduction
3.2 Set Fundamentals
3.3 Set Operations
3.4 Element Chasing
3.5 Set Identities and Laws
3.6 The Pigeonhole Principle
4. Proof Methods
4.1 Introduction
4.2 Grammar and Fundamentals
4.3 Quantified Statements
4.4 Direct Proofs
4.5 Indirect Proofs: Contradictions
4.6 Indirect Proofs: Contrapositive
4.7 Mathematical Induction
4.8 Strong Mathematical Induction
4.9 Other Proof Methods
4.10 Developing Conjectures
5. Boolean Algebra
5.1 Introduction
5.2 Boolean Algebra
5.3 Canonical Forms: SOP and POS
5.4 Karnaugh Maps
5.5 Digital Circuits
5.6 Universal Gates
Appendix
A.1 Rules of Inferences
A.2 Quantified Rules of Inferences
A.3 Logic and Venn Diagrams
A.4 Well-Ordering Principle
A.5 List of Commonly Used Symbols
Biography
James L. Burk is Professor of Mathematics at Harding University, where he teaches linear algebra, discrete mathematics, proof writing, and graph theory. He is the department’s Putnam Exam Supervisor and an AP Calculus Reader for the College Board. Beyond the classroom, Dr. Burk engages students worldwide through online platforms at MathThought.com. He also serves as a lead mathematician and expert reviewer on artificial intelligence research projects. His mathematical interests include topics found in discrete mathematics and linear algebra.
