Wiki source code of Ramsey theory, fall 2016
Last modified by asaekman@helsinki_fi on 2024/03/27 10:51
Show last authors
author | version | line-number | content |
---|---|---|---|
1 | = Ramsey theory, fall 2016 = | ||
2 | |||
3 | |||
4 | |||
5 | {{panel}} | ||
6 | **[[Ramsey theory Moodle page>>url:https://moodle.helsinki.fi/course/view.php?id=21531||shape="rect"]] | ||
7 | ** | ||
8 | |||
9 | **Teacher:** [[Åsa Hirvonen>>doc:mathstatHenkilokunta.Hirvonen, Åsa]] | ||
10 | |||
11 | **Scope:** 10 cr | ||
12 | |||
13 | **Type:** Advanced studies | ||
14 | |||
15 | **Teaching: **Four hours of lectures and two hours of exercises per week. | ||
16 | |||
17 | **Topics: **Ramsey theory considers unavoidable regularities in large structures: If all k-subsets of the integers are finitely coloured, then there is an infinite homogeneous set (Ramsey); if the positive integers are finitely coloured then one colour class contains arithmetic progressions of arbitrary length (van der Waerden); an n-dimensional cube (for n large enough) is r-coloured then there exists a monochromatic 'line' (Hales-Jewett theorem), etc. We will look at basic proof techniques of both finite and infinite Ramsey theory. | ||
18 | |||
19 | This is not really a logic course, although there are some applications to logic, but Ramsey theory is about phenomena that occur in areas as varied as combinatorics, algebra, analysis, geometry, set theory and logic. | ||
20 | |||
21 | **Prerequisites:** This course does not really require any logic background, but some 'mathematical routine' is assumed (this is an advanced course, so some intermediate courses such as Algebra I and Topology I are assumed). | ||
22 | {{/panel}} | ||
23 | |||
24 | === {{toc maxLevel="4" minLevel="2" indent="20px"/}} === | ||
25 | |||
26 | == News == | ||
27 | |||
28 | * The course has a [[Moodle page>>url:https://moodle.helsinki.fi/course/view.php?id=21531||shape="rect"]] that will be used for exercises, news, etc. It is now available (although not in final shape). | ||
29 | * Note that exercises start already the first week (i.e. Friday 9.9.) | ||
30 | * Due to the University's opening ceremony there will be no lecture on Monday 5.9. | ||
31 | |||
32 | == Teaching schedule == | ||
33 | |||
34 | Weeks 36-42 and 44-50, Monday 14-16 and Tuesday 10-12 in room C123, exercises Friday 10-12 in room C122. | ||
35 | |||
36 | == Exams == | ||
37 | |||
38 | |||
39 | |||
40 | Exam lasts 2,5 hours. | ||
41 | |||
42 | You can use (lecturer will fill in) in the exam. | ||
43 | |||
44 | == Course material == | ||
45 | |||
46 | We will mainly follow the book Graham, Rothschild, Spencer, Ramsey Theory (second edition). | ||
47 | |||
48 | == [[Registration>>url:https://oodi-www.it.helsinki.fi/hy/opintjakstied.jsp?html=1&Tunniste=57221||shape="rect"]] == | ||
49 | |||
50 | |||
51 | (% style="color: rgb(96,96,96);" %)Did you forget to register? (%%)[[What to do?>>url:https://wiki.helsinki.fi/display/mathstatOpiskelu/Kysymys4||style="text-decoration: underline;" shape="rect"]] | ||
52 | |||
53 | == Exercises == | ||
54 | |||
55 | === Assignments === | ||
56 | |||
57 | will be published on the [[Moodle page>>url:https://moodle.helsinki.fi/course/view.php?id=21531||shape="rect"]] of the course | ||
58 | |||
59 | === Exercise classes === | ||
60 | |||
61 | |=((( | ||
62 | Group | ||
63 | )))|=((( | ||
64 | Day | ||
65 | )))|=((( | ||
66 | Time | ||
67 | )))|=((( | ||
68 | Room | ||
69 | )))|=(% colspan="1" %)((( | ||
70 | Instructor | ||
71 | ))) | ||
72 | |((( | ||
73 | 1. | ||
74 | )))|((( | ||
75 | Friday | ||
76 | )))|((( | ||
77 | 10-12 | ||
78 | )))|((( | ||
79 | C122 | ||
80 | )))|(% colspan="1" %)((( | ||
81 | Åsa Hirvonen | ||
82 | ))) | ||
83 | |||
84 | == Course feedback == | ||
85 | |||
86 | Course feedback can be given at any point during the course. Click [[here>>url:https://elomake.helsinki.fi/lomakkeet/11954/lomake.html||style="line-height: 1.4285;" shape="rect"]]. |