MIT’s “Mathematics for Computer Science” (2018) remains the best free on-ramp to discrete math rigor

MIT’s 2018 edition of “Mathematics for Computer Science” is the rare free resource that actually meets developers where they live: proofs as tools, not ceremony. What’s notable here is how cleanly the text connects core techniques-induction, invariants, recurrences, graphs, modular arithmetic, counting, and probability-to the things engineers care about: algorithm correctness, cryptographic primitives, hashing, randomized algorithms, and reliability in distributed systems. Under the hood, it treats proofs like programs and maintains an algorithmic lens throughout, which makes the jump from math to production reasoning feel natural.

The bigger picture: as tooling automates more coding grunt work, advantage shifts to people who can reason formally about systems. This book’s problem-first structure and tight linkage between theory and practice make it a durable reference for anyone moving beyond “it works on my machine” toward “it’s correct, performant, and secure.” Worth noting: the PDF is stable, widely assigned in curricula, and permissively licensed for self-study and teaching, making it a more dependable backbone than scattershot tutorials. If you’re upgrading your mental model for complexity, verification, or security, this remains the most accessible, industry-relevant discrete math playbook you can download today.