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Tu 09/01
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§1.1
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Sets, elements, and set notation; set builder notation
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Th 09/03
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§1.2–1.3
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Cartesian products; subsets; counting subsets
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Tu 09/08
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§1.4–1.5
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Power sets; union, intersection, and difference
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Th 09/10
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§1.6–1.8
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Complement; Venn diagrams; indexed sets
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Tu 09/15
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§2.1–2.3
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Statements and truth values; connectives; conditional statements
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Th 09/17
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§2.4–2.6
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Biconditionals; truth tables; logical equivalence
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Tu 09/22
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§2.7–2.8
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Quantifiers; paired quantifiers; implications with open sentences
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Th 09/24
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§2.9–2.11
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Translating into logic; negations; deduction rules
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Tu 09/29
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Review
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Th 10/01
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First Midterm
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Tu 10/06
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§3.1–3.2
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Multiplication principle; addition principle
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Th 10/08
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§3.3–3.5
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Permutations; combinations; Pascal’s triangle and binomial theorem
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Tu 10/13
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§4.1–4.2
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Theorems and definitions; division algorithm
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Th 10/15
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§4.3
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Direct proofs; examples
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Tu 10/20
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§4.3–4.4
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Using definitions in proofs; more direct proofs; proof by cases
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Th 10/22
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§5.1–5.2
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Proof by contrapositive; congruences; congruence arithmetic
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Tu 10/27
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§6.1, §7.1
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Proof by contradiction; Euclid’s proof of infinitely many primes; if-and-only-if proofs
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Th 10/29
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§7.3–7.4
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Existence proofs; Euclid’s algorithm; uniqueness proofs; constructive and non-constructive proofs
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Tu 11/03
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Review
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Th 11/05
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Second Midterm
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Tu 11/10
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§8.1–8.3
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Proving set membership; set inclusion proofs; set equality proofs
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Th 11/12
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§9.1–9.3
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Counterexamples; disproving universal statements; disproving existence claims
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Tu 11/17
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§10.1
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Introduction to induction; induction proofs; more examples
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Th 11/19
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§10.2–10.5
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Strong induction; strong induction continued; fundamental theorem of arithmetic; Fibonacci numbers; well-ordering principle
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Tu 11/24
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Thanksgiving Break
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Th 11/26
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Thanksgiving Break
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Tu 12/01
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§11.1–11.2
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Relations; reflexive, symmetric, and transitive properties
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Th 12/03
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§11.3–11.6
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Equivalence relations; partitions; integers mod n; relations between sets
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Tu 12/08
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§12.1–12.2
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Functions; injective, surjective, and bijective functions
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Th 12/10
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§12.3–12.6
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Pigeonhole principle; composition; inverse functions; image and preimage
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