Discrete mathematics is less a single subject than a federation of them — logic, combinatorics, graph theory, and the theory of computation — bundled together because they share a discrete, countable flavor and underpin computer science. That breadth is why a random reading order leaves students feeling they learned a dozen disconnected tricks.
The path that works is to build proof skills and a broad survey first, then go deep on combinatorics and graph theory, and finally reach logic and computability. Each book below is placed so the foundations come before the specializations that lean on them.
Build proofs and a broad base
Start with How to prove it by Daniel Velleman, which teaches the logic and proof techniques that every discrete math topic demands. Then Discrete Mathematics and Its Applications by Kenneth Rosen is the comprehensive, gentle survey that introduces sets, logic, counting, relations, and graphs with abundant examples. Together they give you both the proof toolkit and a map of the whole territory.
Go deep on combinatorics and graphs
With the survey behind you, specialize. Combinatorics and graph theory by Harris, Hirst, and Mossinghoff is a friendly bridge into the two central branches. Generatingfunctionology by Herbert Wilf reveals the powerful generating-function technique for solving counting problems. For graphs specifically, Introduction to Graph Theory by Douglas West is the thorough standard, and Graph theory by Reinhard Diestel is the more advanced, elegant reference for going deeper. To top off combinatorics with a beautiful method, The probabilistic method by Alon and Spencer shows how randomness proves the existence of structures you cannot easily construct.
Reach logic and computation
The final arc connects discrete math to the theory of computer science. A mathematical introduction to logic by Herbert Enderton develops formal logic rigorously, and Introduction to the Theory of Computation by Michael Sipser is the beloved text on automata, computability, and complexity. Finally, Concrete mathematics by Graham, Knuth, and Patashnik is the rich, playful synthesis of the mathematics behind computer science — a fitting capstone for the whole path.
Read in this order and discrete math stops feeling like a grab bag. Follow the full path to go from your first proof to a genuine command of combinatorics, graphs, logic, and computation.
