Introduction to sequences of real numbers, which serves as a gateway to 18.100 (Real Analysis). Who Should Take It?
Many students encounter a hidden challenge in advanced math: you might be great at solving equations, but proving why a solution must exist requires a different kind of thinking. 18.090 is MIT’s solution to this challenge. The focus is not on learning new formulas but on understanding and constructing rigorous mathematical arguments. Its central mission is to serve as a "proofs bridge," providing students with the experience in mathematical logic and proof construction needed to succeed in higher-level, proof-based courses in analysis, algebra, and topology. 18.090 introduction to mathematical reasoning mit
"Book of Proof" by Richard Hammack (free online). This is more gentle than Velleman but excellent for drilling. Introduction to sequences of real numbers, which serves
If you are a student looking for a rigorous, foundational class that will unlock the doors to advanced theoretical mathematics, 18.090 is an excellent starting point at MIT. "Book of Proof" by Richard Hammack (free online)
To practice these proof techniques, the course introduces foundational topics from higher-level math:
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