Syllabus

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