Discrete Mathematics Study Guide: 60 Flashcards on Graphs, Sets, Logic and Combinatorics

Discrete mathematics is the course where computer science students meet five subjects at once: graph theory, combinatorics, logic, set theory and algorithm analysis. Each has its own notation, and exams love asking for exact definitions. The Flip It deck Discrete Mathematics: Graphs & Structures (deck code HF1483, 60 flashcards) collects those definitions, formulas and theorems in one place so you can drill them until the symbols stop looking foreign.

Inside the deck: definitions with the formula attached

Most cards pair a concept with its precise definition and, where one exists, the formula you will need in a proof. Nine examples taken directly from the deck:

The full list of what the 60 cards cover: directed vs undirected graphs, paths, cycles, connected graphs, spanning trees, graph coloring and chromatic number, the Four Color Theorem, bipartite graphs, Hamiltonian paths, graph isomorphism; permutations (n!), combinations C(n,k), binomial coefficients, Pascal's triangle, inclusion-exclusion, generating functions, recurrence relations, the Fibonacci sequence, difference equations; propositions, logical connectives, truth tables, tautology, contradiction, logical equivalence, predicates, universal and existential quantifiers, Boolean algebra; sets, the empty set, subsets, Cartesian product, union, intersection, difference, complement, countable sets, lattices; algorithms, Big O notation, time and space complexity, P vs NP, and the uses of modular arithmetic in cryptography and hashing.

Study tips that fit this material

Learn the formulas as counting arguments, not strings. The deck gives you n-1 edges for a tree, n(n-1)/2 for Kₙ, 2ⁿ for a power set, mn for a Cartesian product. When a card comes up, say why before you flip it: each of n vertices in Kₙ touches n-1 others and every edge gets counted twice, hence the division by 2. That same double-counting idea is the Handshaking Lemma, so two cards become one insight.

Pair the Eulerian and Hamiltonian cards. They are the classic mix-up. Eulerian = every edge once, with an easy test (odd-degree vertices). Hamiltonian = every vertex once, with no easy test (NP-complete). Reviewing them back to back makes the contrast stick, and it links straight to the P vs NP card later in the deck.

Write the symbols by hand. Cards like ∀, ∃, ≡, ∪, ∩, ⊆ and ∅ are half notation. Keep a scrap of paper next to you and draw the symbol as you answer; recognising it on an exam paper is a different skill from reading it on a screen.

How to work through the 60 cards

Do not study them in order. The deck naturally splits into five clusters (graphs, combinatorics, logic, sets, algorithms), and the clusters reference each other: Boolean algebra uses the connectives, countable sets appear in the P vs NP discussion, recurrences lead into complexity classes. Run one cluster per session for five sessions, then let spaced repetition mix everything together. By that point you should be able to state the Four Color Theorem, De Morgan's laws and the Pigeonhole Principle without looking.

The deck is in the Flip It library: sign in at flip-it.app and search for HF1483 or Discrete Mathematics: Graphs & Structures.