Sep 5 
1.1, 1.2 
1.1, 1.2 
Integers: axioms and first consequences 
Sep 9 
1.2 
1.2 
Integers: first consequences 
Sep 12 
1.2, 1.3, 2.1 
1.2, 1.3, 1.4, 2.1 
More consequences of the axioms, subtraction, natural numbers 
Sep 16 
2.2, 2.3 
2.2, 2.3 
Ordering the integers, induction 
Sep 19 
2.3, 2.4 
2.3, 2.4 
Induction 
Sep 23 
2.4, 3.1–3.2 
2.4, 3.1–3.2 
The wellordering principle, logic 
Sep 26 
3.2, 3.3, 4.1, 4.2 
3.2–3.4, 4.1–4.3 
Logic, finite series 
Sep 30 
4.2–4.4 
4.2–4.6 
The Binomial Theorem, strong induction 
Oct 3 
5.1, 5.2 
5.1, 5.2 
Sets, subsets, intersections, unions 
Oct 7 
5.3–5.5 
5.3, 5.4 
Cartesian products, functions 
Oct 10 
6.1, 6.2 
6.1, 6.2 
Equivalence relations, the division algorithm 
Oct 14–18 
Reading week 
Oct 21 
6.3 
6.3 
The integers modulo n 
Oct 24 
6.4 
6.4 
Prime numbers 
Oct 28 
1.1–6.3 
1.1–6.3 
Midterm test 
Oct 31 
7.1 
8.1 
Axioms of the real numbers 
Nov 4 
7.2, 7.3 
8.2, 8.3 
Positive real numbers and ordering, the real numbers versus the integers 
Nov 7 
7.4 
8.4 
Upper and lower bounds 
Nov 11 
8.1 
9.1 
Injections, surjections, and bijections 
Nov 14 
8.1, 8.2 
9.1, 9.2 
Inverse functions, embedding Z in R 
Nov 18 
9.1–9.3 
10.1–10.3 
Unboundedness of the integers, absolute value, distance 
Nov 21 
9.4 
10.4 
Limits 
Nov 25 
9.4 
10.4 
Limits 
Nov 28 
9.5, 10.1, 10.2 
10.5, 11.1, 11.2 
Square roots, rational and irrational numbers 
Dec 2 


Review (Exercises, Solutions) 