Schedule of Topics through Test I (9/26)

  • 1.1 (8/20-22)
    • Terms: ordered field, Archimedian property
    • Theorems: 1.1.1, 1.1.2
    • Problems: 2, 7, 10 (Due 8/29)
  • 1.2 (8/20-22)
    • Terms: set, subset, open interval, closed interval, half-open interval, empty set, natural numbers, integers, rationals, reals, union, intersection, complement, Cartesian product, function, domain, range, one-to-one, onto, inverse
    • Examples: 1-6
    • Problems: 1, 2, 4, 5, 8 (Due 8/29)
  • 1.3 (8/27)
    • Terms: cardinality, one-to-one correspondence, finite, infinite, countable
    • Theorems: 1.3.1-1.3.5
    • Examples: 1, 2
    • Problems: 1, 3 (Due 8/29)
  • 1.3 (8/29)
    • Terms: irrational, uncountable
    • Theorems: 1.3.6
    • Problems: 7, 9 (Due 9/17)
  • 1.4 (9/5-10)
    • Terms: converse, equivalent, if and only if, direct proof, contrapositive proof, proof by contradiction, induction, counterexample
    • Theorems: 1.4.1-1.4.3 (as examples of proof methods)
    • Examples: 1
    • Problems: 4 (direct), 5 (contrapositive), 6 (induction), 10 (Due 9/17)
  • 2.1 (9/10-12)
    • Terms: sequence, converge, limit, diverge
    • Examples: 1-5
    • Problems: 2a, 4d, 6, 8 (Due 9/17)
  • 2.2 (9/17)
    • Terms: bounded
    • Theorems: 2.2.1-2.2.6
    • Examples: 1-3
    • Problems: 4 (Due 9/26)
  • 2.4 (9/24)
    • Terms: Cauchy sequence, dense, complete, completeness axiom
    • Theorems: 2.4.1, 2.4.2
    • Examples: 1
    • Problems: 1, 2 (Due 9/26)
  • Test I (9/26)

USA Math Dept USA Last Modified 10th Sep 07