Discrete Math Speedrun

Crush your Discrete Math exam.

A single, focused study companion built around your syllabus. Every topic broken down from first principles — definitions, intuition, worked examples, exam-style problems with full solutions, and the tricks that separate a good answer from a perfect one.

Start with Logic → Exam strategy

How to use this site

Read each topic page top-to-bottom — they're written so that if you understand the theory and work through the examples, you should be able to answer almost anything in the exam. After theory, every page ends with a problem bank pulled from your DPPs, worksheets, and past papers, with hidden solutions you can reveal once you've attempted them.

Study method that works

Read theory → close the page → try the problem on paper → reveal the solution → review the proof structure (not just the answer). Subjective exams reward clear, well-justified arguments far more than the final number.

Topics

1

Logic & Its Applications

Propositional logic, predicates & quantifiers, Boolean algebra, K-maps. Truth tables, equivalences, satisfiability, and circuit design.

PropositionsQuantifiersK-maps
2

Proofs

Axiomatic systems, rules of inference, direct/contrapositive/contradiction/induction proofs, program correctness and loop invariants.

InferenceInductionInvariants
3

Set Theory

Russell's paradox, countable vs uncountable sets, Cantor's diagonal argument, and the connection to computability and undecidability.

RussellCountabilityDiagonalization
4

Abstract Algebra

Groups, subgroups, cyclic groups, Lagrange's theorem, rings, polynomial rings, fields, primitive elements, Diffie–Hellman key exchange.

GroupsLagrangeFieldsDH
5

Advanced Counting

Recurrence relations from algorithms, divide-and-conquer, Master Theorem, generating functions, and solving recurrences with them.

RecurrencesMaster TheoremGFs
6

Graph Theory

Graph terminology, Kn, Cn, Wn, Qn, Km,n, bipartite graphs, Euler paths and Hamiltonian paths.

BipartiteEulerHamilton
≡

Cheat Sheet

Every formula, theorem, and rule on a single dense page. Printable, two-column layout — pin it above your desk.

FormulasReferencePrintable
▦

Flashcards

120+ active-recall flashcards across all six topics. Filter, shuffle, mark known/review. Progress is saved automatically.

Active recallSaved progress
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Tips, Tricks & Exam Strategy

Topic-specific shortcuts, common pitfalls students fall into, how to write proofs that earn full marks, and a last-minute revision sheet.

StrategyTricksRevision

What's in each topic page

Theory, the way you'd want it taught

Concepts built from the definition up, with intuition stated in plain words before any formal statement. We do not drop a theorem on you and walk away — every result is followed by why it's true and where it's used.

Worked examples

Each new idea comes with a worked example showing how to apply it. We label the steps so you can mimic the structure in your own exam answers.

Problems with hidden solutions

Every page ends with a problem bank — DPP questions, worksheet questions, past-paper questions — with click-to-reveal solutions. Try first, peek second.

Tricks & common pitfalls

The little things that cost marks: forgetting a base case, dropping a domain, citing the wrong rule of inference. We flag them where they happen.

Suggested study order

  1. Logic → the language everything else is written in.
  2. Proofs → the techniques that turn logic into arguments.
  3. Set Theory → uses both logic and proof technique.
  4. Abstract Algebra → heavy on proofs; pace yourself, it's the longest topic.
  5. Advanced Counting → recurrence and generating-function manipulation.
  6. Graph Theory → easier conceptually; do this last to build confidence before the exam.
  7. Tips & Strategy → read the night before the exam.