The table below indicates which topics we will cover in each class. Before each class, you should read the lecture notes up to and including the place indicated below. Then you should complete the corresponding quiz, which can be found on Brightspace. You must complete the quiz before the start of the class.
| Lec | Date | Reading | Topics | ||
|---|---|---|---|---|---|
| 1 | Sep 9 | §1.1 | First axioms of the integers | ||
| 2 | Sep 13 | §1.2 (up to Prop. 1.18) | Integers: first consequences | ||
| 3 | Sep 16 | §1.2, 1.3 | More consequences of the axioms, subtraction | ||
| 4 | Sep 20 | §2.1, 2.2 | Natural numbers, ordering the integers | ||
| 5 | Sep 23 | §2.3, 2.4 | Induction, the well-ordering principle | ||
| 6 | Sep 27 | §3.1–3.3 | Logic | ||
| 7 | Sep 30 | §4.1, 4.2 | Finite series | ||
| 8 | Oct 4 | §4.3, 4.4 | Binomial theorem, strong induction | ||
| 9 | Oct 7 | §5.1, 5.2 | Sets, subsets, intersections, unions | ||
| 10 | Oct 14 | §5.3–5.5 | Cartesian products, functions | ||
| 11 | Oct 18 | §6.1, 6.2 | Equivalence relations, the division algorithm | ||
| 12 | Oct 21 | §6.3 | The integers modulo n | ||
| Oct 25–29 | Reading week | ||||
| 13 | Nov 1 | §6.4 | Prime numbers | ||
| Nov 4 | §1.1–6.3 | Midterm test | |||
| 14 | Nov 8 | §7.1 | Axioms of the real numbers | ||
| 15 | Nov 11 | §7.2, 7.3 | Positive real numbers and ordering, the real numbers versus the integers | ||
| 16 | Nov 15 | §7.4 | Upper and lower bounds | ||
| 17 | Nov 18 | §8.1 (up to Prop. 8.12) | Injections, surjections, and bijections | ||
| 18 | Nov 22 | §8.1, 8.2 | Inverse functions, embedding Z in R | ||
| 19 | Nov 25 | §9.1–9.3 | Unboundedness of the integers, absolute value, distance | ||
| 20 | Nov 29 | §9.4 (up to Prop. 9.19) | Limits | ||
| 21 | Dec 2 | §9.4 | Limits | ||
| 22 | Dec 6 | §9.5, 10.1, 10.2 | Square roots, rational and irrational numbers | ||
| 23 | Dec 8 | Review | |||