Syllabus

Date Notes Text Topics
Sep 7 1.1, 1.2 1.1, 1.2 Integers: axioms and first consequences
Sep 11 1.2 1.2 Integers: first consequences
Sep 14 1.3, 2.1, 2.2 1.3, 1.4, 2.1, 2.2 Subtraction, natural numbers, ordering the integers
Sep 18 2.2, 2.3 2.2, 2.3 Ordering the integers, induction
Sep 21 2.3, 2.4 2.3, 2.4 Induction, the well-ordering principle
Sep 25 3.1–3.3 3.1–3.4 Logic
Sep 28 4.1, 4.2 4.1–4.3 Finite series
Oct 2 4.3, 4.4 4.4–4.6 The Binomial Theorem, strong induction
Oct 5 5.1, 5.2 5.1, 5.2 Naive set theory, subsets, intersections, unions
Oct 12 5.3–5.5 5.3, 5.4 Cartesian products, functions
Oct 16 6.1, 6.2 6.1, 6.2 Equivalence relations, the division algorithm
Oct 19 6.3 6.3 The integers modulo n
Oct 24–28 Reading week
Oct 30 6.4 6.4 Prime numbers
Nov 2 1.1–6.1 1.1–6.1 Midterm test
Nov 6 7.1 8.1 Axioms of the real numbers
Nov 9 7.2, 7.3 8.2, 8.3 Positive real numbers and ordering, the real numbers versus the integers
Nov 13 7.4 8.4 Upper and lower bounds
Nov 16 8.1 9.1 Injections, surjections, and bijections
Nov 20 8.1, 8.2 9.1, 9.2 Inverse functions, embedding Z in R
Nov 23 9.1–9.3 10.1–10.3 Unboundedness of the integers, absolute value, distance
Nov 27 9.4 10.4 Limits
Nov 30 9.4 10.4 Limits
Dec 4 9.5, 10.1, 10.2 10.5, 11.1, 11.2 Square roots, rational and irrational numbers
Dec 6 Review: Questions, Solutions