Intermediate~8h

Discrete Mathematics Drills

The procedures, until they are fast

MA101 teaches each of these once, against one example, and moves on. This is the volume — thirty-one procedures from truth tables to the Chinese Remainder Theorem, on questions generated fresh that never run out. Each stays green only while your recent answers hold.

Start this project See the modules

Modules: 8
Drills: 31
Build steps: 0
Time: ~8h

Walk out able to

Negate a nested quantifier, count with inclusion–exclusion, and invert modulo $m$ — without stopping to rebuild the method first.

What you drill

Logic, quantifiers, proof

Tables, negations, and the halves of proof a machine marks.

Sets, maps and order

Sizes, injections, classes, Hasse diagrams, closures.

Counting and graphs

Sum and product, pigeonhole, edges, components, trees.

Arithmetic that wraps

Euclid, residues, factorisations, inverses, the CRT.

The pitch

What you practise, and what you leave with

Not an artifact — a set of reflexes. Thirty-one procedures that are each either current or not, and a rail that says which.

You will practise

Truth tables, normal forms, quantifiers
Proof technique, ordering and induction
Sets, relations, order, counting, graphs
Euclid, residues, inverses and the CRT

Afterwards you can

Negate a nested quantifier first time
Order a proof and name its technique
Count with pigeonhole and inclusion–exclusion
Invert mod $m$ and combine two congruences

Modules

8 modules, 34 items

Lessons explain one idea. Drills repeat it until it sticks. Build steps make something that exists afterwards.

1
Read logic at speed
~45 min
Evaluate, tabulate, shorten and normalise a formula without pausing on precedence.
- LessonWhat this project is for4 min
- DrillEvaluate on one row9 min
- DrillFill a truth table10 min
- DrillShorten it by one law11 min
- DrillName the form, then the status11 min
2
Say it with quantifiers
~39 min
Translate, negate and evaluate quantified claims — nested ones included — first time.
- DrillTranslate a quantified claim10 min
- DrillPush the negation inward11 min
- DrillEvaluate a nested pair18 min
3
The half of proof a machine marks
~1h
Refute, choose the technique, order the lines, and state an inductive step.
- LessonWhat is not graded here5 min
- LessonMark a proof against four criteria9 min
- DrillRefute it with one case16 min
- DrillChoose the opening move16 min
- DrillPut the lines back in order20 min
- DrillState the inductive step17 min
4
Sets, maps and relations
~43 min
Size any set expression, and classify a finite map or relation on sight.
- DrillSize a set expression10 min
- DrillClassify a finite map15 min
- DrillWhich properties does it have?18 min
5
Equivalence and order
~50 min
Read classes, covers and closures off a relation without redrawing it.
- DrillCount the classes and the pairs16 min
- DrillRead a Hasse diagram16 min
- DrillClose it, and count18 min
6
Counting without a formula sheet
~1h
Decide sum or product, choose between P and C, and know when to reach further.
- DrillAdd, or multiply?16 min
- DrillArrange it, or choose it11 min
- DrillCount with binomials11 min
- DrillGuarantee a collision16 min
- DrillSubtract the overlap16 min
- DrillUnroll it to the term asked for15 min
7
Graphs by their numbers
~50 min
Answer edge counts, components, tree facts and colourings without drawing it.
- DrillCount edges without drawing10 min
- DrillComponents and shortest paths18 min
- DrillTrees, forests and what breaks11 min
- DrillColour it, and count the faces11 min
8
Arithmetic that wraps
~55 min
Run Euclid, reduce mod m, factor, and invert — at the speed crypto assumes.
- DrillRun the Euclidean algorithm10 min
- DrillReduce it modulo m11 min
- DrillRead it off the factorisation16 min
- DrillInvert, solve, and combine18 min