--- title: Logic description: Mathematical logic explores formal systems of reasoning, propositional calculus, and proof theory. Learners will understand how to construct valid arguments, evaluate truth tables, and apply logical principles to computer programming and hardware design. category: mathematics subcategory: discrete-math difficulty: beginner, intermediate, advanced url: /subject/logic --- # Logic Mathematical logic explores formal systems of reasoning, propositional calculus, and proof theory. Learners will understand how to construct valid arguments, evaluate truth tables, and apply logical principles to computer programming and hardware design. ## Available Resources 4 Books • 5 Courses • 3 Websites ## Courses ### 1. Logic II (MIT 24.242) **Author:** Vann McGee Computability theory followed by a detailed study of Gödel's incompleteness theorems and their applications, including Church's undecidability theorem and Tarski's theorem on the undefinability of truth. Lecture notes and problem sets with solutions let learners work through these proofs themselves. **Difficulty:** Intermediate | **Price:** Free **Link:** https://ocw.mit.edu/courses/24-242-logic-ii-spring-2004/ **Tags:** incompleteness-theorems, computability, undecidability, tarski-undefinability, recursion-theory ### 2. 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 ### 3. 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 ### 4. Introduction to Logic This course is an introduction to Logic from a computational perspective. It shows how to encode information in the form of logical sentences; it shows how to reason with information in this form; and it provides an overview of logic technology and its applications - in mathematics, science, engineering, business, law, and so forth. **Difficulty:** Beginner | **Language:** English | **Duration:** 10 weeks of study, 4-8 hours/week | **Price:** Free **Link:** https://www.coursera.org/learn/logic-introduction **Tags:** courses, mathematics-statistics, discrete-math ### 5. Introduction to Mathematical Thinking **Author:** Keith Devlin Stanford course by Keith Devlin on how mathematicians reason, starting with the logic of language (and, or, not, implication, quantifiers) and moving to the structure of proofs, including contradiction and induction. Learners become able to read, construct and critique simple mathematical proofs. **Difficulty:** Beginner | **Language:** English | **Duration:** Expect to require at least 10 hours of study per week to complete this course satisfactorily. | **Price:** Free **Link:** https://www.coursera.org/learn/mathematical-thinking **Tags:** mathematical-logic, proof-writing, quantifiers, mathematical-reasoning ## Books ### 1. Gödel, Escher, Bach: An Eternal Golden Braid **Author:** Douglas R. Hofstadter Pulitzer Prize-winning exploration of consciousness, artificial intelligence, and meaning through connections between mathematics, art, music, and formal systems. **Difficulty:** Advanced | **Language:** English | **Price:** Paid **Link:** https://www.amazon.com/G%C3%B6del-Escher-Bach-Eternal-Golden/dp/0465026567?tag=edmonddante07-20 **Tags:** book, mathematics, discrete-mathematics ### 2. Book of Proof **Author:** Richard Hammack Essential introduction to mathematical proof techniques covering logic, sets, relations, functions, and various proof methods for pure mathematics. **Difficulty:** Beginner | **Language:** English | **Price:** Free **Link:** https://richardhammack.github.io/BookOfProof/ **Tags:** book, mathematics, discrete-mathematics ### 3. Introduction to Mathematical Logic **Author:** Elliott Mendelson Mendelson's standard graduate-level treatment of first-order logic, formal systems, and computability. Working through it gives you the completeness and incompleteness theorems, axiomatic set theory, and recursive functions, with proofs stated in full and exercises throughout. **Difficulty:** Intermediate | **Language:** English | **Price:** Paid **Link:** https://www.amazon.com/dp/0534066240?tag=edmonddante07-20 **Tags:** books, mathematics-statistics, discrete-math ### 4. Mathematical Logic **Author:** Joseph R. Shoenfield Shoenfield's 1967 graduate text develops first-order logic from syntax and semantics through the completeness theorem, then model theory, recursion theory, the incompleteness theorems, and set theory. Terse and demanding; expect to reconstruct omitted steps yourself. **Difficulty:** Intermediate | **Language:** English | **Price:** Paid **Link:** https://www.amazon.com/dp/0201070286?tag=edmonddante07-20 **Tags:** books, mathematics-statistics, discrete-math ## Websites ### 1. 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 ### 2. proofwiki.org ProofWiki is a free, collaboratively edited online collection of mathematical proofs, theorems, and definitions organized by technique. It provides step-by-step proofs and explanations of proof strategies (such as induction, contradiction, and contrapositive) across a wide range of mathematical topics. **Difficulty:** Intermediate | **Language:** English | **Price:** Free **Link:** https://proofwiki.org **Tags:** websites, mathematics-statistics, mathematical-logic ### 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 --- *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/logic