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 Logical Foundations of Mathematics
nLab: Foundations of Mathematics
Modern perspectives including HoTT
Mathematical Logic Playlist
Introductory series on logic foundations from Reddit recs
Introduction to Mathematical Logic
Learn the foundations of mathematical logic with this introductory course by Scott Aaronson. Explore the logical basis of mathematics!
Mathematical Logic
Learn mathematical logic with Hans-Peter Beck! Explore the logical foundations of mathematics in this comprehensive course.
How to Prove It - Daniel J. Velleman
A clear, step-by-step transition from computational math to proof-based math, focusing on logic and set theory.
plato.stanford.edu
Stanford Encyclopedia of Philosophy is a peer‑reviewed, open online encyclopedia of philosophy with in‑depth, expert‑written articles. It covers logical foundations of mathematics (logic, set theory, model theory, type theory) and related topics, each with extensive bibliographies.