Fifteen guides for a first discrete math course: logic and truth tables, the main proof methods, induction, then number theory, functions and counting. Each one works real examples and ends with practice problems and full solutions.
Start at the top if you are working through the course, or jump to the idea that is costing you marks. The Previous and Next links at the bottom of every guide follow this same order.
Every connective, the one row where a conditional is false, and what a tautology actually is — the definitions a first test opens with.
Only one of the three says the same thing as the original — plus the “only if” vocabulary that causes the swap.
Push the negation inward, flip every quantifier it passes, and don’t let the conditional survive.
The skeleton a grader wants to see, two worked examples, and the line where the hypothesis must appear.
What each one assumes, what each must produce, and how to spot a proof wearing the wrong label.
The division algorithm hands you an exhaustive case split — and even/odd is often too coarse.
Name the witness, then verify it. The half that gets skipped is the half worth marks.
Truth table or chain of named laws — the same result two ways, and when each one is what was asked.
Every connective as a 0/1 formula, the p² = p rule, and how to prove an equivalence by multiplying out.
Line up every player so each beat the next. Induction on the number of players, with the insertion step case by case.
Read a ≡ b (mod n), add and multiply congruences safely, find 3100 mod 7, and meet the composites that fool Fermat.
Write any number as non-consecutive Fibonacci numbers, and the strong induction proof that the greedy method always works.
One-to-one, onto, both: the exact first line of each proof, five worked examples, and why counting is a bijection.
Why x ↦ 3x mod 7 shuffles 1 to 6, how to trace an orbit, and why 3 is a primitive root of 7 but 2 is not.
Fill positions and multiply: the two formulas, the induction behind each, and the traps between them.
Reproduce a known parity result, explore the example, and learn why a large formula does not prove a problem is hard.
Reading an explanation is not the same as producing the answer under time pressure. The free Discrete Math practice app draws from 500 written questions, every one with a worked explanation, and you can pick the topic you just read about. It runs offline, keeps your progress on your own device, and asks for nothing.
Want the overview first? The Discrete Math practice test page lists every topic the app covers.
Topic-selectable practice with worked explanations. Offline, no ads, no account.
Start practising →Looking for a different class? Java · Python · Networking · Security+ · Calculus, or the full guide catalog.
