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. Doing so will increase your understanding of the material.
| Lec | Date | Reading | Topics |
|---|---|---|---|
| 1 | Jan 8 | §1.1 | First axioms of the integers |
| 2 | Jan 10 | §1.2 | Integers: first consequences |
| 3 | Jan 15 | §1.2, 1.3 | More consequences of the axioms, subtraction |
| 4 | Jan 17 | §2.1, 2.2 | Natural numbers, ordering the integers |
| 5 | Jan 22 | §2.3 | Induction |
| 6 | Jan 24 | §2.4–3.2 | The well-ordering principle, logic |
| 7 | Jan 29 | §3.3–4.2 | Logic, finite series |
| 8 | Jan 31 | §4.3, 4.4 | Binomial theorem, strong induction |
| 9 | Feb 5 | §5.1, 5.2 | Sets, subsets, intersections, unions |
| Feb 7 | §1.1–4.4 | Midterm test | |
| 10 | Feb 12 | §5.3–5.5 | Cartesian products, functions |
| 11 | Feb 14 | §6.1, 6.2 | Equivalence relations, the division algorithm | Feb 17–21 | Reading week |
| 12 | Feb 26 | §6.3 | The integers modulo n |
| 13 | Feb 28 | §6.4 | Prime numbers |
| 14 | Mar 5 | §7.1 | Axioms of the real numbers |
| 15 | Mar 7 | §7.2, 7.3 | Positive real numbers and ordering, the real numbers versus the integers |
| 16 | Mar 12 | §7.4 | Upper and lower bounds |
| Mar 14 | TBA | Midterm test | |
| 17 | Mar 19 | §8.1 | Injections, surjections, and bijections |
| 18 | Mar 21 | §8.1, 8.2 | Inverse functions, embedding Z in R |
| 19 | Mar 26 | §9.1–9.3 | Unboundedness of the integers, absolute value, distance |
| 20 | Mar 28 | §9.4 | Limits |
| 21 | Apr 2 | §9.4 | Limits |
| 22 | Apr 4 | Review |