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1 = Mathematical methods in biology, fall 2007 to spring 2008 =
2
3 === Lecturer ===
4
5 [[Eva Kisdi>>doc:mathstatHenkilokunta.Kisdi, Eva]]
6
7 === Scope ===
8
9 Each part of the course gives separate credits (3 sp per part).
10
11 === Type ===
12
13 Advanced studies.
14
15 === Time and place (spring 2008): ===
16
17 Part 3: weeks 3 - 9 ( = first study period of the spring semester)
18 Part 4: weeks 11 - 18 ( = second study period of the spring semester, with Easter break)
19
20 Lectures:
21
22 Tuesday 12:15 - 13:45
23 Viikki campus, Kehitystalo (Koetilantie 3, next to Gardenia; see map), room 117
24
25 Exercises:
26
27 Thursday 12:15 - 13:45
28 17 Jan, 24 Jan, 31 Jan, 7 Feb (first four weeks): Viikki D-rakennus LS (see map)
29 17 Apr: Viikki E-rakennus LS
30 All other times: Viikki Kehitystalo 117 (same as lectures)
31
32 Don't be misled by the unusual location: this course is intended for biology/medical students. The best place would be Biokeskus 3, but it turned out that the nearest rooms in Viikki with real blackboards are in Kehitystalo!
33
34 === Contents: ===
35
36 This course gives a highly practical introduction to mathematical concepts and methods applied in the life sciences. We learn mathematics through solving problems of biological interest, with emphasis on applicable skills and hands-on experience.
37
38 The full course consists of four parts (each can be taken separately):
39 (1) Fundamentals (construction of simple models and basic calculus)
40 (2) Probability theory (handling stochastic phenomena, groundwork for statistics)
41 (3) Vectors and matrices (applied to population dynamics, quantitative genetics and statistics)
42 (4) Dynamical systems (techniques to analyse models of population growth, reaction kinetics, etc.)
43
44 Parts 1 & 2 are given in the fall semester of 2007, parts 3 & 4 in spring 2008. Each part takes one study period (seven weeks), 2 h interactive lectures and 2 h exercises per week.
45
46 The course is specifically tailored for biology students and assumes no background in mathematics. Both undergraduates and graduate students are welcome. Prior registration is not necessary.
47
48 === Exams ===
49
50 Problem-solving (in writing), the problems are similar to homework exercises. Everything may be used (books, notes, dictionary) but may not be shared during the exam. There is no need for laptops; nevertheless laptops can be used if so desired, but the internet connection must be switched off (download necessary files in advance). Exercise class activity decides marginal grades.
51
52 === Bibliography ===
53
54 There is no single textbook the course would follow closely. The books listed below are useful reference books also for later use, but you need not possess them to participate in this course successfully.
55
56 L. Edelstein-Keshet (1988) Mathematical models in biology. McGraw-Hill Education, ISBN 0075549506.
57 C. Neuhauser (2003) Calculus for biology and medicine. Prentice Hall, ISBN 0131234412.
58 D. W. Jordan & P. Smith (2002) Mathematical techniques. Oxford University Press, ISBN 0199249725.
59 S. P. Ellner & J. Guckenheimer (2006) Dynamic models in biology. Princeton University Press, ISBN-10: 0691125899.
60
61 === Feedback ===
62
63 You are very welcome to give feedback in person or via email. You can give feedback also anonymously via a departmental [[webform>>url:http://mathstat.helsinki.fi/kurssit/kysely/jatkuvat/mathbiolen.html||shape="rect"]] any time during the course.
64
65 At the end of the semester, PLEASE fill in the anonymous standard [[course questionnary>>url:http://mathstat.helsinki.fi/kurssit/kysely/index.en.html||shape="rect"]]. THANKS!
66
67 ----
68
69 === Part 1 ===
70
71 ==== Exercises and projects ====
72
73 The solutions of projects will be read and commented by a fellow student in the exercise classes. Hence, please write down the logic, methods and results in such a way that others can understand it. For the exercises, it is enough if you can present the solution on the blackboard.
74
75 |(((
76 [[Exercises 1-4>>url:http://mathstat.helsinki.fi/~~kisdi/mathmet/hw1-4.pdf||shape="rect"]]
77 )))|(((
78 [[solution>>url:http://mathstat.helsinki.fi/~~kisdi/mathmet/sol1-4.pdf||shape="rect"]]
79 )))|(((
80 discussed on 13 Sept
81 )))
82 |(((
83 [[Exercises 5-8>>url:http://mathstat.helsinki.fi/~~kisdi/mathmet/hw5-8.pdf||shape="rect"]]
84 )))|(((
85 [[solution>>url:http://mathstat.helsinki.fi/~~kisdi/mathmet/sol5-8.pdf||shape="rect"]]
86 )))|(((
87 discussed on 20 Sept
88 )))
89 |(((
90 [[Exercises 9-12>>url:http://mathstat.helsinki.fi/~~kisdi/mathmet/hw9-12.pdf||shape="rect"]]
91 )))|(((
92 [[solution>>url:http://mathstat.helsinki.fi/~~kisdi/mathmet/sol9-12.pdf||shape="rect"]]
93 )))|(((
94 discussed on 27 Sept
95 )))
96 |(((
97 [[Exercises 13-16>>url:http://mathstat.helsinki.fi/~~kisdi/mathmet/hw13-16.pdf||shape="rect"]]
98 )))|(((
99 [[solution>>url:http://mathstat.helsinki.fi/~~kisdi/mathmet/sol13-16.pdf||shape="rect"]]
100 )))|(((
101 discussed on 27 Sept
102 )))
103 |(((
104 [[Exercises 17-20>>url:http://mathstat.helsinki.fi/~~kisdi/mathmet/hw17-20.pdf||shape="rect"]]
105 )))|(((
106 [[solution>>url:http://mathstat.helsinki.fi/~~kisdi/mathmet/sol17-20.pdf||shape="rect"]]
107 )))|(((
108 discussed on 4 Oct
109 )))
110 |(((
111 [[Exercises 21-24>>url:http://mathstat.helsinki.fi/~~kisdi/mathmet/hw21-24.pdf||shape="rect"]]
112 )))|(((
113 [[solution>>url:http://mathstat.helsinki.fi/~~kisdi/mathmet/sol21-24.pdf||shape="rect"]]
114 )))|(((
115 discussed on 11 Oct
116 )))
117 |(((
118 [[Exercises 25-26>>url:http://mathstat.helsinki.fi/~~kisdi/mathmet/hw25-26.pdf||shape="rect"]]
119 )))|(((
120 [[solution>>url:http://mathstat.helsinki.fi/~~kisdi/mathmet/sol25-26.pdf||shape="rect"]]
121 )))|(((
122 discussed on 18 Oct
123 )))
124
125 |(((
126 [[Project 1>>url:http://mathstat.helsinki.fi/~~kisdi/mathmet/proj1.pdf||shape="rect"]]
127 )))|(((
128 [[solution>>url:http://mathstat.helsinki.fi/~~kisdi/mathmet/proj1_sol.pdf||shape="rect"]]
129 )))|(((
130 discussed on 20 Sept
131 )))
132 |(((
133 [[Project 2>>url:http://mathstat.helsinki.fi/~~kisdi/mathmet/proj2.pdf||shape="rect"]]
134 )))|(((
135 [[solution>>url:http://mathstat.helsinki.fi/~~kisdi/mathmet/proj1_so2.pdf||shape="rect"]]
136 )))|(((
137 discussed on 11 Oct
138 )))
139 |(((
140 [[Project 3>>url:http://mathstat.helsinki.fi/~~kisdi/mathmet/proj3.pdf||shape="rect"]]
141 )))|(((
142 [[solution>>url:http://mathstat.helsinki.fi/~~kisdi/mathmet/proj1_so3.pdf||shape="rect"]]
143 )))|(((
144 discussed on 18 Oct
145 )))
146
147 ==== Handouts ====
148
149 |(((
150 Note #1: Powers, exponents and logarithms
151 )))
152 |(((
153 Note #2: [[Radioactive decay and the number e>>url:http://mathstat.helsinki.fi/~~kisdi/mathmet/note2.pdf||shape="rect"]]
154 )))
155 |(((
156 Note #3: [[Rules of differentiation>>url:http://mathstat.helsinki.fi/~~kisdi/mathmet/note3.pdf||shape="rect"]]
157 )))
158 |(((
159 Note #4: [[Bimolecular reactions>>url:http://mathstat.helsinki.fi/~~kisdi/mathmet/note4.pdf||shape="rect"]]
160 )))
161
162 ==== Figures ====
163
164 |(((
165 [[A genetic switch: Phase plane analysis>>url:http://mathstat.helsinki.fi/~~kisdi/mathmet/switch.pdf||shape="rect"]]
166 )))
167 |(((
168 [[Circular repression in a 3-gene system>>url:http://mathstat.helsinki.fi/~~kisdi/mathmet/circ_repr.pdf||shape="rect"]]
169 )))
170 |(((
171 [[Logistic growth with diffusion>>url:http://mathstat.helsinki.fi/~~kisdi/mathmet/logistic_diff.pdf||shape="rect"]] (Fisher's equation)
172 )))
173 |(((
174 [[Pattern formation via Turing instability>>url:http://mathstat.helsinki.fi/~~kisdi/mathmet/Turing.pdf||shape="rect"]]
175 )))
176
177 === Part 2 ===
178
179 ==== Exercises and projects ====
180
181 The solutions of projects will be read and commented by a fellow student in the exercise classes. Hence, please write down the logic, methods and results in such a way that others can understand it. For the exercises, it is enough if you can present the solution on the blackboard.
182
183 |(((
184 [[Exercises 1-8>>url:http://mathstat.helsinki.fi/~~kisdi/mathmet/hw2_1-8.pdf||shape="rect"]]
185 )))|(((
186 [[solution>>url:http://mathstat.helsinki.fi/~~kisdi/mathmet/sol2_1-8.pdf||shape="rect"]]
187 )))|(((
188 discussed on 8 Nov
189 )))
190 |(((
191 [[Exercises 9-12>>url:http://mathstat.helsinki.fi/~~kisdi/mathmet/hw2_9-12.pdf||shape="rect"]]
192 )))|(((
193 [[solution>>url:http://mathstat.helsinki.fi/~~kisdi/mathmet/sol2_9-12.pdf||shape="rect"]]
194 )))|(((
195 discussed on 22 Nov
196 )))
197 |(((
198 [[Exercises 13-17>>url:http://mathstat.helsinki.fi/~~kisdi/mathmet/hw2_13-17.pdf||shape="rect"]]
199 )))|(((
200 [[solution>>url:http://mathstat.helsinki.fi/~~kisdi/mathmet/sol2_13-17.pdf||shape="rect"]]
201 )))|(((
202 discussed on 29 Nov
203 )))
204 |(((
205 [[Exercises 18-22>>url:http://mathstat.helsinki.fi/~~kisdi/mathmet/hw2_18-22.pdf||shape="rect"]]
206 )))|(((
207 [[solution>>url:http://mathstat.helsinki.fi/~~kisdi/mathmet/sol2_18-22.pdf||shape="rect"]]
208 )))|(((
209 discussed on 11 Dec
210 )))
211 |(((
212 [[Exercises 23-26>>url:http://mathstat.helsinki.fi/~~kisdi/mathmet/hw2_23-26.pdf||shape="rect"]]
213 )))|(((
214 [[solution>>url:http://mathstat.helsinki.fi/~~kisdi/mathmet/sol2_23-26.pdf||shape="rect"]]
215 )))|(((
216 discussed on 13 Dec
217 )))
218
219 |(((
220 [[Project 1>>url:http://mathstat.helsinki.fi/~~kisdi/mathmet/proj2_1.pdf||shape="rect"]]
221 )))|(((
222 [[solution>>url:http://mathstat.helsinki.fi/~~kisdi/mathmet/proj2_1_sol.pdf||shape="rect"]]
223 )))|(((
224 discussed on 29 Nov
225 )))
226 |(((
227 [[Project 2>>url:http://mathstat.helsinki.fi/~~kisdi/mathmet/proj2_2.pdf||shape="rect"]]
228 )))|(((
229 [[solution>>url:http://mathstat.helsinki.fi/~~kisdi/mathmet/proj2_2_sol.pdf||shape="rect"]]
230 )))|(((
231 discussed on 13 Dec
232 )))
233
234 ==== Handouts ====
235
236 Note #5: [[Geometric series: How to compute the sum of infinitely many terms>>url:http://mathstat.helsinki.fi/~~kisdi/mathmet/note5.pdf||shape="rect"]]
237 Note #6: The cumulative distribution function of the standard normal distribution
238
239 ==== Figures ====
240
241 [[Membrane channels: dwell times>>url:http://mathstat.helsinki.fi/~~kisdi/mathmet/dwell_times.pdf||shape="rect"]]
242 [[Binomial distribution: approaching normal>>url:http://mathstat.helsinki.fi/~~kisdi/mathmet/binom_limit.pdf||shape="rect"]]
243
244 === Part 3 ===
245
246 ==== Exercises and projects ====
247
248 The solutions of projects will be read and commented by a fellow student in the exercise classes. Hence, please write down the logic, methods and results in such a way that others can understand it. For the exercises, it is enough if you can present the solution on the blackboard.
249
250 |(((
251 [[Exercises 1-5>>url:http://mathstat.helsinki.fi/~~kisdi/mathmet/hw3_1-5.pdf||shape="rect"]]
252 )))|(((
253 [[solution>>url:http://mathstat.helsinki.fi/~~kisdi/mathmet/sol3_1-5.pdf||shape="rect"]]
254 )))|(((
255 discussed on 24 Jan
256 )))
257 |(((
258 [[Exercises 6-10>>url:http://mathstat.helsinki.fi/~~kisdi/mathmet/hw3_6-10.pdf||shape="rect"]]
259 )))|(((
260 [[solution>>url:http://mathstat.helsinki.fi/~~kisdi/mathmet/sol3_6-10.pdf||shape="rect"]]
261 )))|(((
262 discussed on 31 Jan
263 )))
264 |(((
265 [[Exercises 11-16>>url:http://mathstat.helsinki.fi/~~kisdi/mathmet/hw3_11-16.pdf||shape="rect"]]
266 )))|(((
267 [[solution>>url:http://mathstat.helsinki.fi/~~kisdi/mathmet/sol3_11-16.pdf||shape="rect"]]
268 )))|(((
269 discussed on 7 Feb
270 )))
271 |(((
272 [[Exercises 17-20>>url:http://mathstat.helsinki.fi/~~kisdi/mathmet/hw3_17-20.pdf||shape="rect"]]
273 )))|(((
274 [[solution>>url:http://mathstat.helsinki.fi/~~kisdi/mathmet/sol3_17-20.pdf||shape="rect"]]
275 )))|(((
276 discussed on 14 Feb
277 )))
278 |(((
279 [[Exercises 21-25>>url:http://mathstat.helsinki.fi/~~kisdi/mathmet/hw3_21-25.pdf||shape="rect"]]
280 )))|(((
281 [[solution>>url:http://mathstat.helsinki.fi/~~kisdi/mathmet/sol3_21-25.pdf||shape="rect"]]
282 )))|(((
283 discussed on 21 Feb
284 )))
285 |(((
286 [[Exercises 26-28>>url:http://mathstat.helsinki.fi/~~kisdi/mathmet/hw3_26-28.pdf||shape="rect"]]
287 )))|(((
288 [[solution>>url:http://mathstat.helsinki.fi/~~kisdi/mathmet/sol3_26-28.pdf||shape="rect"]]
289 )))|(((
290 discussed on 28 Feb
291 )))
292
293 |(((
294 [[Project 1>>url:http://mathstat.helsinki.fi/~~kisdi/mathmet/proj3_1.pdf||shape="rect"]]
295 )))|(((
296 Leslie model in [[Excel>>url:http://mathstat.helsinki.fi/~~kisdi/mathmet/Leslie.xls||shape="rect"]] / [[pdf>>url:http://mathstat.helsinki.fi/~~kisdi/mathmet/Leslie.pdf||shape="rect"]]
297 )))|(((
298 discussed on 31 Jan
299 )))
300 |(((
301 [[Project 2>>url:http://mathstat.helsinki.fi/~~kisdi/mathmet/proj3_2.pdf||shape="rect"]]
302 )))|(((
303
304 )))|(((
305 discussed on 28 Feb
306 )))
307
308 ==== Handouts ====
309
310 Note #7: [[Lagrange multiplier method>>url:http://mathstat.helsinki.fi/~~kisdi/mathmet/note7.pdf||shape="rect"]]
311
312 === Part 4 ===
313
314 ==== Exercises and projects ====
315
316 The solutions of projects will be read and commented by a fellow student in the exercise classes. Hence, please write down the logic, methods and results in such a way that others can understand it. For the exercises, it is enough if you can present the solution on the blackboard.
317
318 Remember that analytical solutions are not always available: Use numerical methods when necessary. Excel is sufficient.
319
320 |(((
321 [[Exercises 1-2>>url:http://mathstat.helsinki.fi/~~kisdi/mathmet/hw4_1-8.pdf||shape="rect"]]
322 )))|(((
323 [[solution>>url:http://mathstat.helsinki.fi/~~kisdi/mathmet/sol4_1-8.pdf||shape="rect"]]
324 )))|(((
325 discussed on 27 Mar
326 )))
327 |(((
328 [[Exercises 3-6>>url:http://mathstat.helsinki.fi/~~kisdi/mathmet/hw4_1-8.pdf||shape="rect"]]
329 )))|(((
330 [[solution>>url:http://mathstat.helsinki.fi/~~kisdi/mathmet/sol4_1-8.pdf||shape="rect"]]
331 )))|(((
332 discussed on 10 Apr
333 )))
334 |(((
335 [[Exercises 7-9>>url:http://mathstat.helsinki.fi/~~kisdi/mathmet/hw4_1-8.pdf||shape="rect"]]
336 )))|(((
337 [[solution>>url:http://mathstat.helsinki.fi/~~kisdi/mathmet/sol4_1-8.pdf||shape="rect"]]
338 )))|(((
339 discussed on 17 Apr
340 )))
341 |(((
342 [[Exercises 10-11>>url:http://mathstat.helsinki.fi/~~kisdi/mathmet/hw4_1-8.pdf||shape="rect"]]
343 )))|(((
344 [[solution>>url:http://mathstat.helsinki.fi/~~kisdi/mathmet/sol4_1-8.pdf||shape="rect"]]
345 )))|(((
346 discussed on 24 Apr
347 )))
348 |(((
349 [[Exercises 12-14>>url:http://mathstat.helsinki.fi/~~kisdi/mathmet/hw4_1-8.pdf||shape="rect"]]
350 )))|(((
351 [[solution>>url:http://mathstat.helsinki.fi/~~kisdi/mathmet/sol4_1-8.pdf||shape="rect"]]
352 )))|(((
353 discussed on 29 Apr
354 )))
355
356 |(((
357 [[Project 1>>url:http://mathstat.helsinki.fi/~~kisdi/mathmet/proj4_1.pdf||shape="rect"]]
358 )))|(((
359
360 )))|(((
361 discussed on 27 Mar
362 )))
363 |(((
364 [[Project 2>>url:http://mathstat.helsinki.fi/~~kisdi/mathmet/proj4_2.pdf||shape="rect"]]
365 )))|(((
366 [[solution>>url:http://mathstat.helsinki.fi/~~kisdi/mathmet/proj4_2_sol.pdf||shape="rect"]]
367 )))|(((
368 discussed on 24 April
369 )))
370
371 ==== Handouts ====
372
373 Note #8: [[Linear stability analysis in two dimensions>>url:http://mathstat.helsinki.fi/~~kisdi/mathmet/note8.pdf||shape="rect"]]
374 Note #9: [[Divergence>>url:http://mathstat.helsinki.fi/~~kisdi/mathmet/note9.pdf||shape="rect"]]
375
376 Quadratic map
377 Plots of iterated maps: [[pdf>>url:http://mathstat.helsinki.fi/~~kisdi/mathmet/logistic_itermap.pdf||shape="rect"]]
378 Cobweb diagrams: [[Java applet>>url:http://www.lboro.ac.uk/departments/ma/gallery/doubling/||shape="rect"]] by Andy Burbanks, Loughborough University
379 Bifurcation diagram: [[Java applet>>url:http://www.dallaway.com/pondlife/Bifurcation.html||shape="rect"]] by Richard Dallaway
380 Lyapunov exponents: [[pdf>>url:http://mathstat.helsinki.fi/~~kisdi/mathmet/quadratic_map_lyapunov.pdf||shape="rect"]]