The course consisted of 18 two-hour lectures. On these lectures, we discussed the underlying theory and solved problems. The lectures took place at various locations at the KTH campus (lecture rooms E34, D31, D42, Q11, Q17, K53, and M37).
Lecture notes were posted here after each lecture.
| Monday | Oct 26 | 15-17 | E34 |
1. Introduction and overview Relations Sections in Biggs: 7.1-3 Exercises: 7.2: all, 7.3: all, 7.7: 1-3, 5 Lecture notes |
| Wednesday | Oct 28 | 10-12 | D42 |
2. Integers, divisibility, primes Sections in Biggs: 8.1-6 Exercises: 8.1-6: all, 8.7: 1-6, 8, 11, 13-14. Hard one: 8.7.7 Lecture notes |
| Thursday | Oct 29 | 10-12 | Q11 |
3. Principles of counting, Euler's function, words Sections in Biggs: 10.1-5, parts of 10.6 and 11.5 Exercises: 10.1-5: all, 10.7: 1-7, 10, 12, 14-15, 17, 11.5: 1 (only φ(n)), 2-4 Lecture notes |
| Monday | Nov 2 | 15-17 | E34 |
4. Binomial numbers, selections with repetition, sieve principle Sections in Biggs: 11.1-4 Exercises: 11.1-4: all Lecture notes |
| Wednesday | Nov 4 | 10-12 | D42 |
5. Partitions, multinomial numbers, permutations Sections in Biggs: 10.6, 12.1-5 Exercises: 10.6: all, 12.1-5: all Lecture notes |
| Thursday | Nov 5 | 10-12 | M37 |
6. Modular arithmetic Sections in Biggs: 13.1-3 Exercises: 13.1-3: all Lecture notes |
| Wednesday | Nov 18 | 10-12 | E34 |
7. Basic properties of graphs Sections in Biggs: 15.1-5 Lecture notes |
| Thursday | Nov 19 | 10-12 | K53 |
8. Graph colourings and matchings Sections in Biggs: 15.6-7, 17.1, 17.4-6 Lecture notes |
| Friday | Nov 20 | 08-10 | Q11 |
9. Basic properties of groups Sections in Biggs: 20.1-5 Lecture notes |
| Monday | Nov 23 | 15-17 | E34 |
10. Groups: cyclic groups, subgroups, cosets Sections in Biggs: 20.6-8 Deadline for Home Assignment 1 Lecture notes |
| Wednesday | Nov 25 | 10-12 | E34 |
11. Characterization of cyclic groups, orbits Sections in Biggs: 20.9, 21.1-3 Lecture notes |
| Thursday | Nov 26 | 10-12 | Q17 |
12. Orbit counting, rings, fields, polynomials Sections in Biggs: 21.4, 22.1-22.4 Lecture notes |
| Monday | Nov 30 | 15-17 | E34 |
13. More on polynomials Sections in Biggs: 22.5-8 Lecture notes |
| Thursday | Dec 3 | 10-12 | D31 |
14. Finite fields Sections in Biggs: 23.1-23.3 Lecture notes |
| Friday | Dec 4 | 13-15 | K53 |
15. Primitive element theorem, codes Sections in Biggs: 23.4, 24.1-2 Lecture notes |
| Monday | Dec 7 | 15-17 | E34 |
16. Linear codes Sections in Biggs: 24.3-4 Deadline for Home Assignment 2 Lecture notes |
| Thursday | Dec 10 | 10-12 | K53 |
17. Repetition |
| Friday | Dec 11 | 15-17 | E34 |
18. Repetition |