Introduction to Logic
Coursera
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.
More resources on Logic
How to Solve It: A New Aspect of Mathematical Method
Classic problem-solving text teaching systematic heuristic methods for mathematical problem-solving applicable across disciplines and life.
Gödel, Escher, Bach: An Eternal Golden Braid
Pulitzer Prize-winning exploration of consciousness, artificial intelligence, and meaning through connections between mathematics, art, music, and formal systems.
Book of Proof
Essential introduction to mathematical proof techniques covering logic, sets, relations, functions, and various proof methods for pure mathematics.
Discrete Math Textbook (free PDF)
Oscar Levin's free discrete math book with logic chapter
ProofWiki
Comprehensive wiki for mathematical proofs and logic
Modal Logic
Explore modal logic with Prof. Yablo's MIT course! Learn about necessity, possibility, and reasoning with possible worlds.