--- title: Boolean Algebra description: Boolean algebra is the branch of mathematics dealing with variables that have two truth values: true and false. Learners will understand how to simplify logical expressions, design digital logic circuits, and analyze formal mathematical systems. category: mathematics subcategory: discrete-math difficulty: beginner, intermediate, advanced url: /subject/boolean-algebra --- # Boolean Algebra Boolean algebra is the branch of mathematics dealing with variables that have two truth values: true and false. Learners will understand how to simplify logical expressions, design digital logic circuits, and analyze formal mathematical systems. ## Where to start Start with AllAboutCircuits Boolean Algebra, a free chapter on Boolean simplification. If you only use one resource, make it J. Eldon Whitesitt's Boolean Algebra and Its Applications, a book devoted to Boolean algebra and how it is applied. For the wider logic and proof background, Mathematics for Computer Science (MIT 6.042J) from MIT OpenCourseWare is the natural next step. ## Available Resources 2 Books • 3 Courses • 3 Websites ## Websites ### 1. AllAboutCircuits Boolean Algebra A chapter from Tony Kuphaldt's open textbook Lessons in Electric Circuits, hosted by All About Circuits. It walks through the rules for simplifying Boolean expressions, with worked examples tied to logic gate circuits, so readers can reduce digital logic designs by hand. **Difficulty:** Beginner | **Price:** Free **Link:** https://www.allaboutcircuits.com/textbook/digital/chpt-7/boolean-rules-for-simplification/ **Tags:** boolean-algebra, logic-simplification, digital-logic, logic-gates ### 2. Wolfram MathWorld **Author:** Eric W. Weisstein MathWorld is an online mathematics encyclopedia from Wolfram Research offering detailed, browsable articles on topics across the math spectrum, including algebra, geometry, calculus, and number theory. Each entry includes definitions, theorems, formulas, diagrams, worked examples, and links to further reading. **Difficulty:** Intermediate | **Language:** English | **Price:** Free **Link:** https://mathworld.wolfram.com **Tags:** mathematics-reference, encyclopedia, abstract-algebra, number-theory, geometry ### 3. plato.stanford.edu The Stanford Encyclopedia of Philosophy is a peer‑reviewed online encyclopedia of philosophy featuring in‑depth, scholarly articles written and regularly updated by experts, including comprehensive coverage of logic topics. **Difficulty:** Intermediate | **Language:** English | **Price:** Free **Link:** https://plato.stanford.edu **Tags:** websites, mathematics-statistics, discrete-math ## Courses ### 1. Mathematics for Computer Science (MIT 6.042J) **Author:** Tom Leighton, Marten van Dijk Discrete mathematics for computer science with an emphasis on definitions and proofs: logic, induction, sets and relations, graph theory, modular arithmetic, asymptotics, counting and discrete probability. 25 lecture videos, problem sets and exams with solutions build fluency in writing proofs. **Difficulty:** Intermediate | **Price:** Free **Link:** https://ocw.mit.edu/courses/6-042j-mathematics-for-computer-science-fall-2010/ **Tags:** discrete-mathematics, mathematical-proofs, induction, graph-theory, combinatorics, discrete-probability ### 2. Discrete Mathematics **Author:** Dominik Scheder Dominik Scheder's proof-based course on sets, functions and relations, enumerative combinatorics, graph theory, and network flows and matchings, each concept paired with a fully proved non-trivial result. Learners read formal statements and write rigorous proofs of their own. **Difficulty:** Intermediate | **Language:** English | **Duration:** 11 weeks of study, 3-5 hours per week. | **Price:** Free **Link:** https://www.coursera.org/learn/discrete-mathematics **Tags:** discrete-math, combinatorics, graph-theory, network-flows, proofs ### 3. Logic for Computer Science A Coursera course from BITS Pilani on computational logic: propositional and predicate logic, natural deduction, soundness and completeness, undecidability, LTL and CTL model checking, and Floyd-Hoare program verification. Learners can write formal proofs and verify properties of algorithms and systems. **Difficulty:** Intermediate | **Language:** English | **Price:** Free **Link:** https://www.coursera.org/learn/bits-logic-for-computer-science **Tags:** propositional-logic, predicate-logic, model-checking, temporal-logic, hoare-logic, program-verification ## Books ### 1. Boolean Algebra and Its Applications **Author:** J. Eldon Whitesitt A short Dover textbook that builds Boolean algebra from sets and propositional logic, then derives its axioms and theorems. Later chapters apply the theory to switching circuits, relay networks and probability, giving readers a rigorous footing for digital logic design. **Difficulty:** Intermediate | **Language:** English | **Price:** Paid **Link:** https://www.amazon.com/dp/0486684830?tag=edmonddante07-20 **Tags:** boolean-algebra, propositional-logic, switching-circuits, set-theory ### 2. Logic and Boolean Algebra **Author:** Kathleen Levitz, Hilbert Levitz A compact study guide covering propositional logic, truth tables, quantifiers and proof, followed by the laws of Boolean algebra and their use with sets and switching circuits. Readers learn to manipulate logical expressions and check arguments for validity. **Difficulty:** Intermediate | **Language:** English | **Price:** Paid **Link:** https://www.amazon.com/dp/0812005376?tag=edmonddante07-20 **Tags:** boolean-algebra, propositional-logic, truth-tables, discrete-math --- *This content is part of Dantes.io - Your Treasure Map to Knowledge* *Curated by humans at Dantes.io. Personal study use welcome; republishing this curation requires permission (team@dantes.io).* View this page online: https://dantes.io/subject/boolean-algebra