Introduction to Mathematical Thinking
Coursera
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.
More resources on Logic
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Classic problem-solving text teaching systematic heuristic methods for mathematical problem-solving applicable across disciplines and life.
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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.
