Wiki source code of Ergodic theory, spring 2015

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1 = Ergodic theory, spring 2015 =
2
3 === Lecturer ===
4
5 [[Mikko Stenlund>>url:http://www.math.helsinki.fi/mathphys/mikko.html||shape="rect"]]
6
7 === Scope ===
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9 5 sp.
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11 === Type ===
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13 Advanced studies
14
15 === Course advertisement ===
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17 ~[[[PDF>>attach:ET_kurssimainos_2015.pdf]]]
18
19 === Prerequisites ===
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21 The student should know the basics of measure theory, Lebesgue integration and elementary topology, and be comfortable with the notions of Banach/Hilbert spaces (in particular L^p spaces) and bounded linear operators on them. We will use several theorems (Hahn–Banach, Riesz representation, Radon–Nikodym, ...) from real and functional analysis, which will be recalled during the lectures; the courageous student could take the course without prior knowledge of these results, but understanding the precise statements is essential, for which the mentioned prerequisites are key.
22
23 === Lectures ===
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25 Period IV (9.3.–3.5. excluding Easter break 2.4.–8.4.) as follows:
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27 Tuesdays and Fridays 14:15–16:00 in room CK111 (Exactum). **Exception:** Tuesday 21.4. in B119.
28
29 === Bibliography ===
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31 ~[[[Lecture notes>>attach:ET.pdf]]] – **Version: March 30**; consider printing only what you really need on paper as the notes are evolving.
32
33 === [[Registration>>url:https://oodi-www.it.helsinki.fi/hy/opintjakstied.jsp?html=1&Tunniste=57072||shape="rect"]] ===
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35 Registration should be done through ~[[[WebOodi>>url:https://weboodi.helsinki.fi/hy/||shape="rect"]]]. (Once logged in, look up the course by entering Ergodic theory in the search field.)
36
37 === Office hours ===
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39 Please **schedule a meeting** by email on all matters, including assistance with homework.
40
41 === Exercises ===
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43 Mondays 14:15–16:00 in room CK108 (Exactum). First session March 23.
44
45 (% style="list-style-type: square;" %)
46 * Set #1: (1) **2.6 & 2.7**; (2) **2.11**; (3) **2.16**; (4) **2.22**; (5) **2.23**; (6) **2.26** . Note: numbers refer to the **March 18 version** of the notes.
47 * Set #2: (1) **2.32**; (2) **2.35**; (3) **2.42**; (4) **2.43**; (5) **2.47**; (6) **2.51**.
48 * Set #3: (1) **3.8**; (2) **3.11**; (3) **3.13**; (4) **3.17**; (5) **3.22**; (6) **3.24**.
49 * Set #4: (1) **3.29 & 3.31**; (2) **3.32**; (3) **4.6**; (4) **4.8**; (5) **4.12**; (6) **4.13**. (A tiny bit of Fourier analysis required in (3) & (4).)
50 * Set #5: (1) **3.14**; (2) **4.22**; (3) **4.24**; (4) **4.25**; (5) **4.30**; (6) **4.31**. ((5) & (6) require studying the proof of Theorem 4.29.)