--- title: Mathematical Logic description: Mathematical logic explores the formal systems of reasoning, proof, and computation. Learners will understand propositional and predicate logic, model theory, and the foundational limits of mathematics, including Gödel's incompleteness theorems. category: mathematics subcategory: mathematical-logic difficulty: beginner, intermediate, advanced url: /subject/mathematical-logic --- # Mathematical Logic Mathematical logic explores the formal systems of reasoning, proof, and computation. Learners will understand propositional and predicate logic, model theory, and the foundational limits of mathematics, including Gödel's incompleteness theorems. ## Available Resources 1 Books • 5 Courses • 2 Websites ## Courses ### 1. Logic and Proofs Learn mathematical logic and master the art of proofs with this comprehensive course from the Open Logic Team. **Difficulty:** Advanced | **Price:** Free **Link:** https://logicforphilosophers.org/ ### 2. Category Theory for Scientists (MIT 18.S996) **Author:** David I. Spivak An open textbook presenting category theory as a language for scientific modeling: sets, monoids, graphs, orders, databases and ologs, categories, functors, natural transformations, limits, colimits and adjunctions. Includes instructor insights and example student projects; suits readers comfortable with proofs. **Difficulty:** Intermediate | **Price:** Free **Link:** https://ocw.mit.edu/courses/18-s996-category-theory-for-scientists-spring-2013/ **Tags:** category-theory, functors, ologs, limits-and-colimits, applied-category-theory ### 3. 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 ### 4. 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 ### 5. 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 ## Websites ### 1. Open Logic Project Free, open-source collection of logic textbooks maintained by logicians, including Sets, Logic, Computation and Incompleteness and Computability. Covers propositional and first-order logic, natural deduction, completeness, computability and incompleteness, so readers can work through formal proof systems and metatheory rigorously. **Difficulty:** Beginner | **Price:** Free **Link:** https://openlogicproject.org/ **Tags:** mathematical-logic, first-order-logic, proof-theory, computability, open-textbooks ### 2. logicmatters.net Logic Matters is a blog and resource site dedicated to mathematical logic. It provides expository notes, essays, and curated reading lists across topics such as model theory, proof theory, computability, and set theory, with materials for students and researchers. **Difficulty:** Intermediate | **Language:** English | **Price:** Free **Link:** https://logicmatters.net **Tags:** websites, mathematics-statistics, mathematics ## Books ### 1. Gödel’s Proof **Author:** Ernest Nagel, James R. Newman A short classic that walks non-specialists through the structure of Gödel's incompleteness proof: Hilbert's program, Gödel numbering, and the construction of a self-referential undecidable sentence. This revised edition includes a foreword by Douglas Hofstadter. **Difficulty:** Intermediate | **Language:** English | **Price:** Paid **Link:** https://www.amazon.com/dp/0814758169?tag=edmonddante07-20 **Tags:** books, mathematics-statistics, mathematical-logic --- *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/mathematical-logic