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1 = Elements of set theory, spring 2014 =
2
3 === Lecturer ===
4
5 [[Fan Yang>>doc:mathstatHenkilokunta.Yang, Fan]]
6
7 === Scope ===
8
9 10 sp.
10
11 === Type ===
12
13 Intermediate studies
14
15 === Prerequisites ===
16
17 No special prerequisites.
18
19 (% style="margin-left: 0.0px;" %)
20 === Description ===
21
22 Set theory is widely accepted as the foundation of mathematics. In this course, we will go through chapter 1-7 of Enderton's book [[Elements of Set Theory>>url:http://www.amazon.com/Elements-Set-Theory-Herbert-Enderton/dp/0122384407||style="text-decoration: underline;" shape="rect"]]. The following topics will be covered: axioms and operations on sets, relations and functions, natural numbers, construction of real numbers, cardinal numbers, axiom of choice, orderings and ordinal numbers.
23
24 === Lectures ===
25
26 Weeks 3-8 and 11-18, Tuesday 12-14 in room B322 and Thursday 14-16 in room DK117.
27
28 (% style="color: rgb(0,0,0);" %)Easter Holiday 17.-23.4.
29
30 (% class="wrapped" %)
31 |=(((
32 \\
33 )))|=(% colspan="1" %)(((
34 contents
35 )))|=(% colspan="1" %)(((
36 handout
37 )))|=(% colspan="1" %)(((
38 last modified
39 )))
40 |(((
41 week 3 (Jan 14, 16)
42 )))|(% colspan="1" %)(((
43 chapter 1-2: introduction, axioms and operations
44 )))|(% colspan="1" %)(((
45 \\
46 )))|(% colspan="1" %)(((
47 Jan 16, 22:30
48 )))
49 |(% colspan="1" style="vertical-align: middle;" %)(((
50 week 4 (Jan 21, 23)
51 )))|(% colspan="1" style="vertical-align: middle;" %)(((
52 chapter 3: ordered pairs, relations and orderings,
53 equivalence relations. chapter 7: partial orderings
54 )))|(% colspan="1" style="vertical-align: middle;" %)(((
55 \\
56 )))|(% colspan="1" style="vertical-align: middle;" %)(((
57 Jan 24, 20:50
58 )))
59 |(% colspan="1" style="vertical-align: middle;" %)(((
60 week 5 (Jan 28, 30)
61 )))|(% colspan="1" %)(((
62 chapter 3: equivalence relations, functions, axiom of choice
63 )))|(% colspan="1" style="vertical-align: middle;" %)(((
64 \\
65 )))|(% colspan="1" style="vertical-align: middle;" %)(((
66 Jan 31, 13:40
67 )))
68 |(% colspan="1" style="vertical-align: middle;" %)(((
69 week 6 (Feb 4, 6)
70 )))|(% colspan="1" style="vertical-align: middle;" %)(((
71 chapter 4: construction of natural numbers,
72 transitive sets, ordering on (% style="color: rgb(68,68,68);" %)ω(%%), recursion theorem(% style="color: rgb(255,0,0);" %)
73 )))|(% colspan="1" style="vertical-align: middle;" %)(((
74 \\
75 )))|(% colspan="1" style="vertical-align: middle;" %)(((
76 Feb 6, 23:30
77 )))
78 |(% colspan="1" style="vertical-align: middle;" %)(((
79 week 7 (Feb 11, 13)
80 )))|(% colspan="1" style="vertical-align: middle;" %)(((
81 chapter 4: arithmetic. chapter 5: integers
82 )))|(% colspan="1" style="vertical-align: middle;" %)(((
83 \\
84 )))|(% colspan="1" style="vertical-align: middle;" %)(((
85 Feb 13, 23:30
86 )))
87 |(% colspan="1" %)(((
88 week 8 (Feb 18, 20)
89 )))|(% colspan="1" %)(((
90 chapter 5: rational numbers, Dedekind cuts
91 )))|(% colspan="1" %)(((
92 \\
93 )))|(% colspan="1" %)(((
94 Feb 20, 23:50
95 )))
96 |(% colspan="1" %)(((
97 week 11 (Mar 11, 13)
98 )))|(% colspan="1" %)(((
99 chapter 5: real numbers
100 )))|(% colspan="1" %)(((
101 \\
102 )))|(% colspan="1" %)(((
103 Mar 13, 17:00
104 )))
105 |(% colspan="1" %)(((
106 week 12 (Mar 18, 20)
107 )))|(% colspan="1" %)(((
108 chapter 6: equinumerosity, finite sets, cardinal arithmetic
109 )))|(% colspan="1" %)(((
110 \\
111 )))|(% colspan="1" %)(((
112 Mar 20, 16:40
113 )))
114 |(% colspan="1" %)(((
115 week 13 (Mar 25, 27)
116 )))|(% colspan="1" %)(((
117 chapter 6: cardinal arithmetic, ordering cardinal numbers
118 )))|(% colspan="1" %)(((
119 \\
120 )))|(% colspan="1" %)(((
121 Mar 27, 17:00
122 )))
123 |(% colspan="1" style="vertical-align: middle;" %)(((
124 week 14 (Apr 1, 3)
125 )))|(% colspan="1" style="vertical-align: middle;" %)(((
126 chapter 6: ordering cardinal numbers, axiom of choice,
127 countable sets, absorption law of cardinals
128 )))|(% colspan="1" style="vertical-align: middle;" %)(((
129 \\
130 )))|(% colspan="1" style="vertical-align: middle;" %)(((
131 Apr 3, 21:40
132 )))
133 |(% colspan="1" %)(((
134 week 15 (Apr 8, 10)
135 )))|(% colspan="1" %)(((
136 chapter 7: well orderings, isomorphisms, ordinal numbers
137 )))|(% colspan="1" %)(((
138 \\
139 )))|(% colspan="1" %)(((
140 Apr 10, 17:00
141 )))
142 |(% colspan="1" %)(((
143 week 16 (Apr 15)
144 week 17 (Apr 24)
145 )))|(% colspan="1" style="vertical-align: middle;" %)(((
146 chapter 7: ordinal numbers, transfinite induction and recursion,
147 debts paid
148 )))|(% colspan="1" style="vertical-align: middle;" %)(((
149 \\
150 )))|(% colspan="1" style="vertical-align: middle;" %)(((
151 Apr 24, 17:20
152 )))
153 |(% colspan="1" %)(((
154 week 18 (Apr 29)
155 )))|(% colspan="1" %)(((
156 chapter 7: debts paid, rank
157 )))|(% colspan="1" %)(((
158 \\
159 )))|(% colspan="1" %)(((
160 Apr 29, 14:20
161 )))
162
163 === Exams ===
164
165 There will be a midterm exam and a final exam.
166
167 (% class="wrapped" %)
168 |=(((
169 \\
170 )))|=(((
171 Date
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173 Time
174 )))|=(((
175 Place
176 )))
177 |(((
178 Midterm Exam
179 )))|(((
180 Feb 28
181 )))|(((
182 10-12
183 )))|(((
184 B120
185 )))
186 |(% colspan="1" style="vertical-align: middle;" %)(((
187 Final Exam
188 )))|(% colspan="1" %)(((
189 May 9
190 )))|(% colspan="1" style="vertical-align: middle;" %)(((
191 10-12
192 )))|(% colspan="1" style="vertical-align: middle;" %)(((
193 B321
194 )))
195
196 (% style="color: rgb(51,51,51);font-size: 14.0pt;font-weight: bold;line-height: normal;" %)Bibliography
197
198 (% class="wrapped" %)
199 |(((
200 Textbook:
201 )))|(((
202 H. Enderton, [[Elements of Set Theory>>url:http://www.amazon.com/Elements-Set-Theory-Herbert-Enderton/dp/0122384407||shape="rect"]], Academic Press. ([[Errata>>url:http://www.math.ucla.edu/~~hbe/est/errata.html||shape="rect"]])
203 )))
204 |(((
205 References:
206 )))|(((
207 Introduction to Set Theory, Karel Hrbacek and Thomas Jech, 3rd Edition, Marcel Dekker.
208 )))
209 |(((
210 \\
211 )))|(((
212 Set Theory for the Working Mathematician, Krzysztof Ciesielski, (% style="color: rgb(51,51,51);" %)Cambridge University Press(%%).
213 )))
214
215 === Exercise class ===
216
217 (% class="wrapped" %)
218 |=(((
219 Group
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221 Day
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223 Time
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225 Place
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227 Teacher
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229 |(((
230 1.
231 )))|(((
232 Friday
233 )))|(((
234 10-12
235 )))|(((
236 B321
237 )))|(% colspan="1" %)(((
238 Miguel Moreno
239 )))
240
241 (% style="margin-left: 0.0px;" %)
242 === Exercises ===
243
244 (% class="wrapped" %)
245 |=(((
246 \\
247 )))|=(((
248 Date of exercise class
249 )))
250 |(((
251 1.
252 )))|(((
253 Jan 24
254 )))
255 |(% colspan="1" %)(((
256 2.
257 )))|(% colspan="1" %)(((
258 Jan 31
259 )))
260 |(% colspan="1" %)(((
261 3.
262 )))|(% colspan="1" %)(((
263 Feb 7
264 )))
265 |(% colspan="1" %)(((
266 4.
267 )))|(% colspan="1" %)(((
268 Feb 14
269 )))
270 |(% colspan="1" %)(((
271 5.
272 )))|(% colspan="1" %)(((
273 Feb 21
274 )))
275 |(% colspan="1" %)(((
276 6.
277 )))|(% colspan="1" %)(((
278 Mar 14
279 )))
280 |(% colspan="1" %)(((
281 7.
282 )))|(% colspan="1" %)(((
283 Mar 21
284 )))
285 |(% colspan="1" %)(((
286 8.
287 )))|(% colspan="1" %)(((
288 Mar 28
289 )))
290 |(% colspan="1" %)(((
291 9.
292 )))|(% colspan="1" %)(((
293 Apr 4
294 )))
295 |(% colspan="1" %)(((
296 10.
297 )))|(% colspan="1" %)(((
298 Apr 11
299 )))
300 |(% colspan="1" %)(((
301 11.
302 )))|(% colspan="1" %)(((
303 Apr 25
304 )))
305 |(% colspan="1" %)(((
306 12.
307 )))|(% colspan="1" %)(((
308 May 2
309 )))
310 |(% colspan="1" %)(((
311 13.
312 )))|(% colspan="1" %)(((
313 No exercise class
314 )))
315
316 (% style="margin-left: 0.0px;" %)
317 === Grading ===
318
319 To pass the course, you need to take two course exams (midterm and final). Attending only one exam (even if you score full marks) is not sufficient. From each of the two exams, you can score (4 questions × 6 points =) 24 points. The passing mark for the course is around 24 points (the exact passing mark will be decided by the lecturer at the end of the semester according to the overall performances of the students).
320
321 By solving a certain amount of the exercise problems, you will be awarded extra points (see the table below for details). "Solving" here means that you have honestly tried to give solutions to the problems.
322
323 (% class="wrapped" %)
324 |=(% style="vertical-align: middle;" %)(((
325 percentage of exercise
326 problems solved
327 )))|=(% style="vertical-align: middle;" %)(((
328 extra points
329 )))
330 |(((
331 ≥40%
332 )))|(((
333 1
334 )))
335 |(((
336 ≥50%
337 )))|(((
338 2
339 )))
340 |(((
341 ≥60%
342 )))|(((
343 3
344 )))
345 |(% colspan="1" %)(((
346 ≥70%
347 )))|(% colspan="1" %)(((
348 4
349 )))
350 |(% colspan="1" %)(((
351 ≥80%
352 )))|(% colspan="1" %)(((
353 5
354 )))
355 |(% colspan="1" %)(((
356 ≥90%
357 )))|(% colspan="1" %)(((
358 6
359 )))
360
361 \\
362
363 (% style="margin-left: 0.0px;" %)
364 === [[Registration>>url:https://oodi-www.it.helsinki.fi/hy/opintjakstied.jsp?html=1&Tunniste=57088||style="text-decoration: underline;" shape="rect"]] ===
365
366
367 Did you forget to register? [[ What to do?>>doc:mathstatOpiskelu.Kysymys4]]