| 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) |