Logic

Modal Logic

Explore modal logic with Prof. Yablo's MIT course! Learn about necessity, possibility, and reasoning with possible worlds.

Logic II

Explore advanced logic with Prof. Vann McGee's Logic II course. Delve into model theory, incompleteness, and more.

Logic I

Learn introductory logic with Dr. Glick's MIT "Logic I" course. Explore fundamental principles and improve your reasoning skills.

Problems of Philosophy

Explore fundamental questions in logic and philosophy with Prof. Schoenfield's MIT course, "Problems of Philosophy." Sharpen your critical thinking skills!

Discrete mathematics forms the mathematical foundation of computer and information science. It is also a fascinating subject in itself. Learners will become familiar with a broad range of mathematical objects like sets, functions, relations, graphs, that are omnipresent in computer science. Perhaps more importantly, they will reach a certain level of mathematical maturity - being able to understand formal statements and their proofs; coming up with rigorous proofs themselves; and coming up with interesting results. This course attempts to be rigorous without being overly formal. This means, for every concept we introduce we will show at least one interesting and non-trivial result and give a full proof. However, we will do so without too much formal notation, employing examples and figures whenever possible. The main topics of this course are (1) sets, functions, relations, (2) enumerative combinatorics, (3) graph theory, (4) network flow and matchings. It does not cover modular arithmetic, algebra, and logic, since these topics have a slightly different flavor and because there are already several courses on Coursera specifically on these topics.

Mathematics for Computer Science

Learn logic and discrete math essentials for computer science in this comprehensive course by Leighton & van Dijk.

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Introduction to Mathematical Thinking

Learn how to think the way mathematicians do – a powerful cognitive process developed over thousands of years. Mathematical thinking is not the same as doing mathematics – at least not as mathematics is typically presented in our school system. School math typically focuses on learning procedures to solve highly stereotyped problems. Professional mathematicians think a certain way to solve real problems, problems that can arise from the everyday world, or from science, or from within mathematics itself. The key to success in school math is to learn to think inside-the-box. In contrast, a key feature of mathematical thinking is thinking outside-the-box – a valuable ability in today’s world. This course helps to develop that crucial way of thinking.

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.

Logic for Computer Science

Unlock the power of logical thinking and formal reasoning essential for success in computer science, data analysis, and software development with this dynamic course. Ideal for students, software engineers, data scientists, and IT professionals, this comprehensive program delves into logic foundations critical for advanced computing careers. Starting with fundamental proofs and proof systems, you’ll explore soundness, completeness, first-order propositional, and predicate logic. Dive into advanced topics like modeling, program verification, and temporal logic. Master Gentzen’s natural deduction, and understand the semantics and syntax of logical forms. Tackle the undecidability of logic and learn model checking using temporal logics (LTL, CTL, CTL*) to verify system properties, applying Floyd-Hoare logics to ensure program correctness. Our structured approach incorporates practical techniques to enhance memory and overcome procrastination, benefiting both academic learning and professional efficiency. Engaging case studies offer hands-on experience verifying algorithms, such as array searching and sorting, essential for real-world problem solving. Geared towards those aiming for roles in tech innovation, this course equips you with the analytical tools and logical proficiency to excel in computing, programming, and data-driven problem-solving. Elevate your career and expertise in the ever-evolving technology landscape.

📚Books(6)

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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.

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Book of Proof

Essential introduction to mathematical proof techniques covering logic, sets, relations, functions, and various proof methods for pure mathematics.

Introduction to Mathematical Logic

Introduction to Mathematical Logic - A book resource

Logic for Mathematicians

Logic for Mathematicians - A book resource

Mathematical Logic

Mathematical Logic - A book resource

🌐Websites(5)

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Discrete Math Textbook (free PDF)

Oscar Levin's free discrete math book with logic chapter

ProofWiki

Comprehensive wiki for mathematical proofs and logic

mathworld.wolfram.com

MathWorld is a comprehensive online mathematics encyclopedia by Wolfram Research that provides detailed articles with definitions, theorems, formulas, and worked examples across topics including logic, algebra, calculus, and geometry.

ocw.mit.edu

MIT OpenCourseWare provides free, openly licensed MIT course materials—lectures, notes, assignments, and exams—across a wide range of subjects, including logic, for self-paced study.

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.