Tentative schedule
Date Topic Sections Materials
9/3 (Wed) about the class, syllabus, sandwich activity Sandwich activity
9/5 (Fri) sets, element argument, small proofs, subset 1.1-1.2Â Â
9/8 (Mon) subset proofs, arbitrary elt, powerset eg, index set 1.3-1.4 Worksheet 1
9/10 (Wed) index set (cont.), set equality, uniqueness 1.5-1.6
9/12 (Fri) uniqueness(cont.), metric space, proof of axioms 2.2
9/15(Mon) statements/predicates/quantifiers, and, or, logical equiv., negations 3.1-3.2 Worksheet 2
9/17(Wed) implications and negations 3.3-3.4
9/19(Fri) Hamming code, implications(cont.), logic puzzle, iff 3.4-3.5
9/22(Mon) graphs 2.3
9/24(Wed) proofs: direct, contrapositive, contradiction 4.1-4.3 Worksheet 3
9/26(Fri) contradiction (cont.), proof of existence and uniqueness 4.4-4.5
9/29(Mon) group axioms, uniqueness of 1, Cayley table 2.1
10/1(Wed) subset, complement, intersection 5.1-5.3 Worksheet 4
10/3(Fri) union and intersection 5.3-5.4 (This is the last class Exam 1 covers)
10/6(Mon) Review Session for Exam 1
10/8(Wed) power set, Cartesian product, 5.5-5.6
10/10(Fri) disjoint intersection, subgroups, intersection preserves subgroups 5.6-5.7 Worksheet 5
10/13-10/14 Fall break
10/15(Wed) intersection preserves comvex sets 5.7
10/17(Fri) induction 9.1
10/20(Mon) complete induction 9.1-9.2 Worksheet 6
10/22(Wed) complete induction(cont.) more examples 9.2
10/24(Fri) well-ordering principle 9.3
10/27(Mon) partitions, relations 7.1-7.2
10/29(Wed) equivalence classes, quotient sets 7.3-7.5
10/31(Fri) angles, constructing rationals, well-definedness 7.6-7.7 WS 7; Lecture notes
11/3(Mon) modular arithmetic 7.8 WS 7.5
11/5(Wed) function def, graph of a function 8.1-8.2
11/7(Fri) restriction and composition of function, commutativity 8.4-8.5
11/10(Mon) surjectivity, injectivity, bijectivity, inverse 8.7 WS 8
11/12(Wed) group homomorphism, permutations* 8.7, additional materials
11/14(Fri) permutations as composition of transpositions 9.1
11/17(Mon) Review Session for Exam 2
11/19(Wed) Review Q&A + More on permutations, cycle notation
11/21(Fri) Cardinality of finite and infinite sets, comparing cardinalities 10.1-10.2
12/1(Mon) countable and uncountable sets, Hilbert's hotel 10.3-10.4
12/3(Wed) card(X)<card(P(X)); Cantor-Bernstein Theorem 10.5-10.6
12/5(Fri) Finishing Section 10.6 if needed, discussing projects in groups