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 Transfinite Induction
Wikipedia
Overview, proofs, and examples of transfinite induction.
nLab
Comprehensive page on transfinite induction with references.
Set Theory
Learn set theory with Aleph 0! This course covers transfinite induction and more.
Set Theory
Learn Set Theory with Martin Zeman's course! Explore transfinite induction and build a strong foundation.
mathworld.wolfram.com
MathWorld is an online mathematics encyclopedia from Wolfram Research offering concise, authoritative articles on a broad range of topics, including definitions, theorems, proofs, and diagrams. Each topic—such as Transfinite Induction—includes explanations, formulas, and references.
ocw.mit.edu
MIT OpenCourseWare provides free, openly accessible course materials from MIT across many subjects. In mathematics, you can access lecture notes, problem sets, and exams from courses that cover topics like set theory and related foundations.