- Introduction: Some motiviation and preliminary definitions and examples can be found in the slides used in the first lecture.
- Covered: Sections 4.1/2/3.
- Recommended Exercises: 4.7.1/5/6/7/8. Problem sessions will start next week.
- Preparation: read Chapter 4, Section 1,2,3, and Chapter 5, Section 1.
- Covered: Sections 5.1/2/3/4, including the preparatory material on Numeration Systems from Sections 3.1/6/7.
- Recommended Exercises: 5.8.2/3/4/5.
- First Homework Assignment Ex. 4.7.8, Ex. 5.8.2a, and one exercise to be chosen (by you) from {4.7.5/6/7 and 5.8.3/4/5}.
- Due date: September 20.
- Preparation: read Chapter 5, Sections 5,6,7, and Chapter 6, Section 1.
- Covered: Sections 5.3/4/5/6/7.
- Additional Material: slides by Alf van der Poorten.
- Second Homework Assignment Choose (at least two) of Ex. 5.8.8/10/11/12/13. Full marks possible for two correct solutions (or enough partial credit for more solutions handed in).
- Due date: September 27 (next Tuesday).
- Preparation: read Chapter 1, Sections 1, 2, 3, 4, and Chapter 6, Sections 1,2,3.
- Covered: Sections 1.4. 2.4 and 2.10 (in part), 6.1/2/3/5.
- Third Homework Assignment Choose (at least three) of Ex. 5.8.7, Ex. 6.11.1/6/9/11/14. Full marks possible for three correct solutions (or enough partial credit for more solutions handed in).
- Due date: October 4 (next Tuesday).
- Solutions: some solutions
- Preparation: read Chapter 6, Sections 6, 7, 8, 9.
- Covered: Sections 6.6/7/8/9/10.
- Fourth Homework Assignment Choose (at least) one of Ex. 6.11.23/24/25, and one of Ex. 6.11.18/19/34/35/36.
- Due date: October 11 (next Tuesday).
- Solutions: some solutions
To bring back some excitement, we will not continue (immediately) with Chapter 7, but we will instead jump to some of the applications in Chapter 12. We will go through that Chapter more slowly and carefully.
- Preparation: read Chapter 2, Section 10 and Chapter 12, Section 1.
- Covered: Sections 2.10, 12.1/2.
- Fifth Homework Assignment Choose three out of Ex. 12.8.1/2/4/9/10. This time grading does not depend on your choice.
- Preparation: read Chapter 12, Section 2, 3.
- Covered: Sections 12.3/4/5.
- Sixth Homework Assignment Choose three out of Ex. 12.8.14/21/24/25/26/27/28; for Ex.27 you also need to do Ex. 2.14.13 (or find an alternative). Note on grading: 2 complete and correct solutions leads to 6, and 3 (correct, complete, but standard) solutions to 9 out of 10; original, non-standard, or additional solutions may lead to a perfect score of 10.
- Due date: November 1.
please note that there will be no lecture on October 25
- Preparation: read Chapter 12, Section 7.
- Covered: Section 12.7; also some comments on parts of Chapter 14 needed for the proof of Furstenberg's theorem, and Rigo's counterexample to Lemma 11.2.2.
- Seventh Homework Assignment Choose two out of Ex. 12.8.31/32/33/34/35/36; for Ex.32 parts d/e on continued fractions are optional). Bonus points can be earned by an alternative proof of an easier case of half of Furstenberg's Theorem: every formal Laurent series over a finite field that is a rational function is the diagonal of a rational formal Laurent series in two variables over that field.
- Due date: November 8.
- Preparation: read Chapter 13, Sections 1/2.
- Covered: Section 13.1/3/4 (first part).
- Eighth Homework Assignment Choose three out of Ex. 13.8.2/3/7/13/16/19abc/21/22; for Ex.19 parts d/e on are optional). Also: do have a look at the proof of Lemma 13.1.4 and in particular: provide a sketch for the construction of Automaton M4 in there!
- Due date: November 22 (!).
please note that there will be no lecture on November 15
- Preparation: read Chapter 13, Sections 4/5.
- Covered: paper on palindromic continued fractions and Section 13.1/3/4 (first part).
- Ninth Homework Assignment Choose two out of Ex. 13.8.9/10/23 (choose 2 theorems) and Ex. 2.14.12/13.
- Due date: November 29.
- Preparation: read Chapter 13, Sections 4/5.
- Covered: By way of illustration, a paper of J.W. Klop, and Chapter 14.
- Tenth Homework Assignment This time 3 exercises will have to be completed; at least one should be an Exercise chosen from Ex. 14.7.1/7/8/9, and at least one should consist of a proof chosen from the following four possibilities: proof of Theorem 14.2.2, proof of 14.2.3, proof of Theorem 14.4.1 in one direction, proof of Theorem 14.4.1 in the other direction.
- Due date: To be announced by Robbert
- Preparation: read Chapter 11, Sections 1/2.
Since I will abroad from now on, please consult the web page of Robbert for further news! Also, do not forget to send your solutions to Robbert if you do not hand them in personally.
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Last update: 5 December 2011