Syllabus

Date Notes Text Topics
Sep 6 1.1, 1.2 1.1, 1.2 Integers: axioms and first consequences
Sep 10 1.2 1.2 Integers: first consequences
Sep 13 1.2, 1.3, 2.1 1.2, 1.3, 1.4, 2.1 More consequences of the axioms, subtraction, natural numbers
Sep 17 2.2, 2.3 2.2, 2.3 Ordering the integers, induction
Sep 20 2.3, 2.4 2.3, 2.4 Induction
Sep 24 2.4, 3.1–3.2 2.4, 3.1–3.2 The well-ordering principle, logic
Sep 27 3.2, 3.3, 4.1, 4.2 3.2–3.4, 4.1–4.3 Logic, finite series
Oct 1 4.2–4.4 4.2–4.6 The Binomial Theorem, strong induction
Oct 4 5.1, 5.2 5.1, 5.2 Sets, subsets, intersections, unions
Oct 11 5.3–5.5 5.3, 5.4 Cartesian products, functions
Oct 15 6.1, 6.2 6.1, 6.2 Equivalence relations, the division algorithm
Oct 18 6.3 6.3 The integers modulo n
Oct 24–28 Reading week
Oct 29 6.4 6.4 Prime numbers
Nov 1 1.1–6.2 1.1–6.2 Midterm test (Review questions, Solutions)
Nov 5 7.1 8.1 Axioms of the real numbers
Nov 8 7.2, 7.3 8.2, 8.3 Positive real numbers and ordering, the real numbers versus the integers
Nov 12 7.4 8.4 Upper and lower bounds
Nov 15 8.1 9.1 Injections, surjections, and bijections
Nov 19 8.1, 8.2 9.1, 9.2 Inverse functions, embedding Z in R
Nov 22 9.1–9.3 10.1–10.3 Unboundedness of the integers, absolute value, distance
Nov 26 9.4 10.4 Limits
Nov 29 9.4 10.4 Limits
Dec 3 9.5, 10.1, 10.2 10.5, 11.1, 11.2 Square roots, rational and irrational numbers
Dec 5 Review (Review questions, solutions)