Program
History and progress transfer
Session summary
Homework — optional, outside the timer
Theory of all steps of the program by blocks. Open a topic to read it.
How a session goes
A session is 10–90 minutes: a warm-up on what you've learned, new steps with short theory and problems, practice. Each problem gives two tries: 100 points on the first, 60 on the second; after the second mistake the correct answer is shown. You move on in the program if 70 % of the problems are solved.
Problems with numbers are generated anew every time a step is repeated. A fractional answer can be entered with a comma, a point or as a fraction: 0,5, 0.5, 1/2. In Practice any topic is available without a timer.
About the course
Statements and connectives, implication, truth tables, equivalence and De Morgan's laws, the quantifiers ∀ and ∃, sets, necessary and sufficient conditions, the converse; proofs: direct, by contradiction, counterexample, induction, the pigeonhole principle. Grade 7–8 math is enough.
Course program: 28 lessons
Statements and connectives
- What a proposition is
- AND, OR, NOT
- Implication: if…, then…
- Connectives: more
- Checkpoint: statements and connectives
Truth tables and equivalence
- Truth tables
- Equivalent formulas
- Negation: De Morgan's laws
- Negations: more
- Checkpoint: tables and equivalence
Quantifiers and sets
- The quantifiers ∀ and ∃
- Sets and operations
- Sets and quantifiers: more
- Checkpoint: quantifiers and sets
How theorems are built
- Necessary and sufficient conditions
- Converse and inverse statements
- Conditions and converses: more
- Checkpoint: theorems and conditions
Methods of proof
- Direct proof
- Proof by contradiction
- Counterexample
- Proofs: more
- Checkpoint: methods of proof
Induction and the pigeonhole principle
- Mathematical induction
- Induction: more
- The pigeonhole principle
- The pigeonhole principle: more
- Checkpoint: induction and the pigeonhole principle