Short readings with activities you work as you go — one per class session. Each activity gives instant, targeted feedback (with answer options shuffled each visit), and your progress is saved in this browser. Every reading ends with an Exam practice section (easy / medium / challenge) for review.
Testing vs. verification; the greedy-scheduling motivation; counterexamples.
Predicates, types, arguments, arity.
Satisfiable / falsifiable / tautological / contradictory; entailment; complements.
Ordered tuples and Cartesian products; the product rule and sum rule; functions and strings.
Selections without repetition; factorials; ordered versus unordered outcomes; permutations and combinations.
∀ and ∃; English↔logic; ∀-with-→ / ∃-with-∧; quantifier order.
Truth conditions; vacuous truth; the converse.
The Known/Goal method; using what you know — with a guided proof builder.
Attacking the goal; proving implications and universals.
Equational reasoning and algebra as legal steps; proving mathematical facts.
Inductively-defined objects; constructors → recursion → structural induction.
ℕ as the simplest inductive structure; the base/step rule; closed forms.
Existential generalization, naming a witness, the rules for “and.”
“Eventually greater than”; the ∃-then-∀ pattern; transitivity and thresholds.
Pushing ¬ through quantifiers and →; refuting by counterexample.
DeMorgan; proving vs. using “or”; proof by cases; a constructor as a disjunction.
Assume the opposite; parity arguments; non-existence claims.
Max/min axioms; max<z ↔ ∧, min<z ↔ ∨; tree height as max.
Built to sit alongside the class notes (book.tex), the guided-inquiry activities, and the in-class problem sets. Readings are consolidation and practice — assign each one after its class activity so it doesn’t pre-empt the in-class discovery. Logical connectives appear only after they’re introduced in class (∀/∃/∧/→ from Reading 6; negation from 15; ∨, DeMorgan, and proof by cases from 16; contradiction from 17). Structural induction (11) precedes induction on ℕ (12). The Exam-practice sections (384 problems in all) are not graded and don’t affect the progress bar.