Syllabus

Date Notes Text Topics
Sep 5 1.1, 1.2 1.1, 1.2 Integers: axioms and first consequences
Sep 9 1.2 1.2 Integers: first consequences
Sep 12 1.2, 1.3, 2.1 1.2, 1.3, 1.4, 2.1 More consequences of the axioms, subtraction, natural numbers
Sep 16 2.2, 2.3 2.2, 2.3 Ordering the integers, induction
Sep 19 2.3, 2.4 2.3, 2.4 Induction
Sep 23 2.4, 3.1–3.2 2.4, 3.1–3.2 The well-ordering principle, logic
Sep 26 3.2, 3.3, 4.1, 4.2 3.2–3.4, 4.1–4.3 Logic, finite series
Sep 30 4.2–4.4 4.2–4.6 The Binomial Theorem, strong induction
Oct 3 5.1, 5.2 5.1, 5.2 Sets, subsets, intersections, unions
Oct 7 5.3–5.5 5.3, 5.4 Cartesian products, functions
Oct 10 6.1, 6.2 6.1, 6.2 Equivalence relations, the division algorithm
Oct 14–18 Reading week
Oct 21 6.3 6.3 The integers modulo n
Oct 24 6.4 6.4 Prime numbers
Oct 28 TBA TBA Midterm test
Oct 31 7.1 8.1 Axioms of the real numbers
Nov 4 7.2, 7.3 8.2, 8.3 Positive real numbers and ordering, the real numbers versus the integers
Nov 7 7.4 8.4 Upper and lower bounds
Nov 11 8.1 9.1 Injections, surjections, and bijections
Nov 14 8.1, 8.2 9.1, 9.2 Inverse functions, embedding Z in R
Nov 18 9.1–9.3 10.1–10.3 Unboundedness of the integers, absolute value, distance
Nov 21 9.4 10.4 Limits
Nov 25 9.4 10.4 Limits
Nov 28 9.5, 10.1, 10.2 10.5, 11.1, 11.2 Square roots, rational and irrational numbers
Dec 2 Review