Key takeaways
- The store screenshots show ten units, from logic and reasoning to graph theory, each broken into topics and lessons with knowledge checks and a mastery measure.
- Use the units in order for a first pass, because quantifiers, proofs and induction lean on the logic unit; jump around only when you are revising for a specific exam.
- The practice options have distinct jobs: quick practice for a warm-up, topic, timed and adaptive quizzes for coverage, review of missed questions for repair, custom homework mode for an assignment, and full-length practice exams for timing.
- The tools are for checking work you have already done by hand, such as a truth table or a contrapositive, not for replacing it; an exam will not hand you a truth-table generator.
- It is free on Google Play, supported by ads, and Google Play lists no in-app purchases for it.
Discrete Math: Study & Quiz is a study companion for a first course in discrete mathematics: logic, proofs, sets and functions, number theory, induction, counting, probability, recurrences and graphs. Its store listing is written for college students, computer science learners and anyone returning to the subject, and its approach is to learn the idea behind a symbol before practising with it. It is free on Google Play, supported by ads, and Google Play lists no in-app purchases for it.
The listing describes four parts: unit-by-unit lessons, a practice section, a tools section and a progress screen. This guide explains what each one is for, the order to take the units in, and how to turn a quiz score into a plan for the next study session.
The ten units, and what to read alongside each
The store screenshots show the course as a sequence of ten units, each broken into topics and lessons with knowledge checks and a mastery measure. The unit names below are as the listing gives them.
| # | Unit | Guides on this site |
|---|---|---|
| 1 | Logic and reasoning | Truth tables, logical equivalence |
| 2 | Quantifiers and rules of inference | Quantifiers, rules of inference |
| 3 | Proof techniques | Direct proof, contradiction |
| 4 | Sets, functions and countability | Set operations, countability |
| 5 | Number theory and modular arithmetic | Modular arithmetic, Euclidean algorithm |
| 6 | Induction and algorithms | Induction step by step, big-O |
| 7 | Combinatorics | Permutations vs combinations, pigeonhole |
| 8 | Probability | Bayes' theorem, expected value |
| 9 | Recurrences | Recurrence relations |
| 10 | Graph theory | Graph basics, Dijkstra's algorithm |
Textbooks do not all use this order. Oscar Levin's open textbook, Discrete Mathematics: An Open Introduction, teaches counting and then sequences, including induction, before its chapter on symbolic logic and proofs. If your course follows a different order, follow your course: the FAQ on the app's page here says your course's definitions and notation take priority where they differ.
A first pass through the course
If the course is new to you, take the units in order and do not skip the knowledge checks. They are a quick way to find out whether a definition actually stuck.
Three units deserve extra time on a first pass:
- Unit 1, logic and reasoning. Everything later is written in this language. If "if P then Q" still feels like it should be false when P is false, stop and work through the truth table for the conditional until it does not.
- Unit 3, proof techniques. This is the first point where an answer is an argument rather than a number, and the listing is candid that the app does not grade proofs written in your own words the way an instructor would. Read a proof, close the screen, try to write it again from the definitions, and then compare.
- Unit 6, induction and algorithms. Check that your inductive step actually uses the hypothesis; if it does not, the argument is not an induction proof. The step-by-step induction guide shows the template.
Combinatorics and probability belong together: when outcomes are equally likely, a probability is a count of favourable outcomes divided by a count of all outcomes, so the counting unit is the groundwork for the probability unit.
Which practice mode for which job
The listing names quick practice, topic, timed and adaptive quizzes, review of missed questions, a custom homework mode and full-length practice exams.
| Mode | Use it when | What to do with the result |
|---|---|---|
| Quick practice | You have five minutes, or need a warm-up | Nothing much; it is a warm-up |
| Topic, timed and adaptive quizzes | You need coverage of a topic, or practice under time pressure | Note which topics you missed, not just the score |
| Review of missed questions | Questions you got wrong have built up | Redo each one on paper before looking at the answer |
| Custom homework mode | You have an assignment on specific topics | Build the set around what you are studying this week |
| Full-length practice exams | An exam is a week or two away | Sit it under timed conditions, then review |
A useful rule: a quiz score tells you where to study, and the review of missed questions tells you what to study. When you review, label each miss by its cause: a definition you did not know, an implication read the wrong way round, or a case you did not check. The label tells you whether to reread a definition, redo a logic exercise or slow down and check small cases.
Tools: check your work, do not replace it
The tools section, as the listing describes it, includes:
- A truth-table generator, which builds the truth table of a statement.
- A logical-equivalence checker, which checks whether two statements are equivalent.
- A statement simplifier, which simplifies a statement.
- A converse-inverse-contrapositive helper, which forms the three variants of a conditional.
- Quantifier negation, which negates a quantified statement.
- An argument-validity checker, which tests whether an argument is valid.
Use them after you have an answer. If you built a truth table by hand, generate it and compare row by row; if the equivalence checker disagrees with you, find the row of your own table where the two statements part company. An exam will not let you run a generator, so a tool that replaces the hand method costs you marks later. The converse, inverse and contrapositive guide and the guide to negating quantifiers explain the hand methods those tools automate.
Reading the progress screen
The listing says the progress screen tracks accuracy, streaks, weekly goals and focus time, alongside mastery by unit and a focus timer.
Two of those are worth watching. Mastery by unit tells you which units to revisit; if a unit stays low after several sessions, reread its definitions before doing more questions. Weekly study goals let you plan steady sessions across the weeks before an exam instead of one long one the night before; the exam study plan explains why spacing practice out helps, and our guide to interleaving versus blocked practice covers how to order the questions within a session.
Planning the last two weeks before an exam
- List the units the exam covers and check mastery by unit for each.
- Spend the first week on the weakest two units: lessons, then topic quizzes, then the review of missed questions.
- Write out the key definitions by hand; the discrete math cheat sheet is a starting list.
- Sit one full-length practice exam under exam timing at the start of the second week.
- Spend the rest of the time on what that exam exposed, not on units you already score well in.
The exam study plan covers that fortnight in more detail. For background on the subject as a whole, start with what discrete math is, or browse every guide in the discrete math hub. The app sits alongside our other education and brain-training apps, including IQ Test & Brain Training Games for mental math and reasoning practice.
Good to know
Frequently asked questions
What does Discrete Math: Study & Quiz cover?
Is the discrete math app free?
Should I study the units in order?
What are the tools in the discrete math app for?
Sources
- Discrete Math: Study & Quiz (store listing) (opens in a new tab)Google Play — accessed
- Discrete Mathematics: An Open Introduction, 3rd edition (Oscar Levin) (opens in a new tab)Open Math Books — accessed
- 6.042J Mathematics for Computer Science, Spring 2015: Readings (opens in a new tab)MIT OpenCourseWare — accessed
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