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 10 | §1.1 | First axioms of the integers | ||
| 2 | Sep 14 | §1.2 (up to Prop. 1.18) | Integers: first consequences | ||
| 3 | Sep 17 | §1.3 | More consequences of the axioms, subtraction | ||
| 4 | Sep 21 | §2.1, 2.2 | Natural numbers, ordering the integers | ||
| 5 | Sep 24 | §2.3, 2.4 | Induction, the well-ordering principle | ||
| 6 | Sep 28 | §3.1–3.3 | Logic | ||
| 7 | Oct 1 | §4.1, 4.2 | Finite series | ||
| 8 | Oct 5 | §4.3, 4.4 | Binomial theorem, strong induction | ||
| 9 | Oct 8 | §5.1, 5.2 | Sets, subsets, intersections, unions | ||
| 10 | Oct 15 | §5.3–5.5 | Cartesian products, functions | ||
| 11 | Oct 19 | §6.1, 6.2 | Equivalence relations, the division algorithm | ||
| 12 | Oct 22 | §6.3 | The integers modulo n | ||
| Oct 26–30 | Reading week | ||||
| 13 | Nov 2 | §6.4 | Prime numbers | ||
| Nov 5 | §1.1–6.3 | Midterm test | |||
| 14 | Nov 9 | §7.1 | Axioms of the real numbers | ||
| 15 | Nov 12 | §7.2, 7.3 | Positive real numbers and ordering, the real numbers versus the integers | ||
| 16 | Nov 16 | §7.4 | Upper and lower bounds | ||
| 17 | Nov 19 | §8.1 (up to Prop. 8.12) | Injections, surjections, and bijections | ||
| 18 | Nov 23 | §8.1, 8.2 | Inverse functions, embedding Z in R | ||
| 19 | Nov 26 | §9.1–9.3 | Unboundedness of the integers, absolute value, distance | ||
| 20 | Nov 30 | §9.4 (up to Prop. 9.19) | Limits | ||
| 21 | Dec 3 | §9.4 | Limits | ||
| 22 | Dec 7 | §9.5, 10.1, 10.2 | Square roots, rational and irrational numbers | ||
| 23 | Dec 9 | Review | |||