Syllabus
Here is a basic outline of the topics we will cover (time permitting!) this semester.
 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 inclusionexclusion principle.
 Proving conditional statements
 Direct proof: Theorems and definitions, cases.
 Contrapositives: Proofs and exposition.
 Proof by contradiction: Proof and combining techniques in a proof.
 More Proofs
 Nonconditional statements: Equivalences, existence and uniqueness.
 Proofs and sets: Set inclusion, subsets, equality.
 Disproof: Counterexamples and contradiction.
 Induction: Mathematical induction, examples.
 Relations, functions and cardinality
 Relations: Relations, equivalence relations, partitions.
 Functions: Injectivity, surjectivity, compositions, inverses, images.
 Cardinality: Equal cardinality, countability, CantorSchroderBernstein Theorem
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