What makes discrete math different
Up through calculus, most math questions have a procedure. Discrete math is the course where that stops being true. The question is no longer "what is the answer" but "is this argument valid" — and a correct answer reached by faulty reasoning earns nothing.
That shift is why students who were comfortable in calculus can struggle here, and why the failure modes are so consistent. Almost nobody loses points on the arithmetic. They lose points by proving the converse, by negating half a statement, by writing an induction that never uses its own hypothesis, or by labeling a contraposition as a contradiction. Those are learnable, checkable errors, and they are what this practice targets.
Who this practice is for
- Undergraduates in a first discrete mathematics or discrete structures course
- Computer science and cybersecurity majors taking discrete math as a degree requirement
- Students in a transition-to-proofs or mathematical foundations course
- Anyone who can follow a proof when reading one but freezes when asked to start one
Topics in the current release
Each topic can be selected independently, so you can drill the exact thing that is costing you points rather than reshuffling the whole course.
Topic weights guide balanced practice sessions; they are not course-grade weights.
What is not written yet
This release covers the logic-and-proofs half of a standard course, plus induction. Four further units are planned and are deliberately named here rather than left as a surprise: sets, functions and sequences; algorithms; number theory; and counting. If you arrived for permutations or the pigeonhole principle, they are not in the bank today.
How the app handles proofs
An app cannot grade a written proof, and one that claimed to would be lying. So this one tests the part of proof writing that is objectively checkable — the structure.
- Which line opens the proof. A proof by contraposition of p → q starts by assuming ¬q. A proof by contradiction starts by assuming both p and ¬q. Different sentences, and only one answers each question.
- What the inductive hypothesis is, exactly. Not the claim for all n, not the claim at k+1 — the claim at k, written out.
- Where a broken proof breaks. Real proofs with one bad step: a missing basis case, a division by a possibly-zero quantity, a converse proved by mistake.
- Which counterexample kills a claim. Disproving a universal statement takes exactly one object that meets the hypothesis and fails the conclusion.
Alongside those, the bank uses typed numeric answers for anything with a definite value — how many rows a truth table has, how many of five statements are tautologies, the smallest n where an inequality first holds, how many basis cases a strong induction needs. Typing a number removes the one-in-four guess that multiple choice hands you.
Live with 150 original questions across all eight topics: 86 multiple choice, 34 numeric entry, and 30 select-all-that-apply, split 38 easy / 75 medium / 37 hard. Every item carries a worked explanation, and every choice-based item explains what misconception produces each wrong option.
Study guides for this subject
- Converse, inverse, and contrapositive — which one is equivalent to the original, and the "only if" vocabulary that causes the swap
- How to negate a quantified statement — push the negation inward, flip every quantifier, and don't lose the conditional
- How to write an induction proof — the skeleton a grader wants, and the line where the hypothesis must appear
- Contraposition vs. contradiction — what each assumes, what each must produce, and how to spot a mislabeled proof
Frequently asked questions
Is the Discrete Math practice app available now?
Yes. The app is live and free with 150 original practice questions across eight topics. It works offline, requires no account, and stores your progress only on your own device.
What topics does the Discrete Math app cover?
The current release covers the first half of a standard discrete mathematics course: propositional logic, logical equivalences, predicates and quantifiers, rules of inference, proof methods, divisibility and parity, mathematical induction, and strong induction with well-ordering. Sets and functions, algorithms, number theory, and counting are planned and are not written yet.
Can the app grade a written proof?
No, and it does not pretend to. Instead it tests proof structure — which assumption opens a proof by contraposition, what the inductive hypothesis is exactly, which case split is exhaustive, and where a flawed proof breaks. That is the part of proof writing that is objectively checkable and the part most often lost on a test.
Is this tied to a specific textbook or instructor?
No. The material follows the standard topic sequence of an introductory discrete mathematics course, so it lines up with any common syllabus. All questions are original study material written by Kestrel Exams, not questions taken from any course examination.
Kestrel Exams Discrete Math material is independent study practice. Questions and guides are original and AI-generated, written against standard course topics.