Syllabus

1. Fundamental Concepts
   • Sets: Describing sets, products, unions, intersections and complements, Venn diagrams.
   • Logic: Statements, compounds, conditional statements, quantifiers, negations.
   • Counting: (optional) Lists, factorials, combinatorics, the inclusion-exclusion principle.
2. Proving conditional statements
   • Direct proof: Theorems and definitions, cases.
   • Contrapositives: Proofs and exposition.
   • Proof by contradiction: Proof and combining techniques in a proof.
3. More Proofs
   • Non-conditional statements: Equivalences, existence and uniqueness.
   • Proofs and sets: Set inclusion, subsets, equality.
   • Disproof: Counterexamples and contradiction.
   • Induction: Mathematical induction, examples.
4. Relations, functions and cardinality
   • Relations: Relations, equivalence relations, partitions.
   • Functions: Injectivity, surjectivity, compositions, inverses, images.
   • Cardinality: Equal cardinality, countability, Cantor-Schroder-Bernstein Theorem
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