Mathematical methods in biology

Contents:

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.

The full course consists of four parts (each can be taken separately):

(1) Fundamentals (construction of simple models and basic calculus)
(2) Probability (handling stochastic phenomena, groundwork for statistics)
(3) Vectors and matrices (applied to population dynamics, quantitative genetics and statistics)
(4) Dynamic models (techniques to analyse models of population growth, reaction kinetics, etc.)

Parts 1 & 2 are given in the fall semester, parts 3 & 4 in spring. Each part takes one study period (seven weeks), 2 h interactive lectures and 2 h exercises per week.

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.

Prerequisites:

You will need to use Excel or any other software capable of simple calculations and plotting.

Time and place (spring 2016):

Part 3: weeks 3 - 9 ( = first study period). First lecture: 19 January (Tue) 10.15. The lecture of 26 January is cancelled.
Part 4: weeks 11 - 18 ( = second study period).

Part 3 Tuesday 10.15 - 12.00, Biokeskus 3, room 1401; Thursday 10.15 - 12.00, Biokeskus 1, room 3106
Part 4 Tuesday 10.15 - 12.00 and Thursday 10.15 - 12.00, Biokeskus 3, room 1401

Easter break: 24 and 29 March
Classes on week 16 (19 and 21 April) are cancelled. The lecture of 26 April had to be cancelled for sickness. The material is not cancelled but replaced with self-study: see instructions below at Part 4. Sorry for the late notice!

Exam, course codes and credits:

Each part of the course gives separate credits (3 op per part).

Exam: problem-solving (in writing), the problems are similar to the 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.

Exam of Part 4: Friday 6 May 14.15-16.00 in Kumpula, Exactum C129. Contact me if this time is not good for you.

Course codes:

Part 1: 57381
Part 2: 57382
Part 3: 57383
Part 4: 57384

Lecture notes and course books:

The lecture notes of Parts 1, 3 and 4 can be downloaded in pdf from the link under the respective parts below.

The books listed below are useful reference books also for later use, but you need not have them to participate in this course successfully:

S. Otto & T. Day (2007) A biologist's guide to mathematical modeling in ecology and evolution. Princeton University Press, ISBN 0691123446.
L. Edelstein-Keshet (1988) Mathematical models in biology. McGraw-Hill Education, ISBN 0075549506.
C. Neuhauser (2003) Calculus for biology and medicine. Prentice Hall, ISBN 0131234412.
D. W. Jordan & P. Smith (2002) Mathematical techniques. Oxford University Press, ISBN 0199249725.
S. P. Ellner & J. Guckenheimer (2006) Dynamic models in biology. Princeton University Press, ISBN-10: 0691125899.

Lecturer:

Eva Kisdi (PhD in Biology). Office: Kumpula campus, EXACTUM, room A420

Further information:

eva.kisdi [at] helsinki.fi

Feedback:

You can leave comments anonymously and at any time using this feedback form. These comments will be read only by Eva Kisdi. Feedback is very important for improving courses, and your time giving feedback is much appreciated!

Part 1

Lecture notes

Lecture notes can be downloaded in pdf.

Homework exercises

This pdf contains the homework exercises and their solutions. This file will be updated regularly with new exercises.

Assignments (exercises marked with *: write down the solution as carefully as for an exam, these will be read by a fellow student. The marked exercises are not more difficult than others.)

Set 1:	1, 2, 4, 5*	discussed on 10 September
Set 2:	7, 9, 10*, 12	discussed on 17 September
Set 3:	14, 16*, 17	discussed on 24 September
Set 4:	18, 19, 20, 21*	discussed on 1 October
Set 5:	23, 24*, 25, 26	discussed on 8 October
Set 5:	27, 28*	discussed on 15 October

Handouts and supporting files

Introductory info

Note #1:	Powers, exponents and logarithms
Note #2:	Rules of differentiation
Note #3:	Practice differentiation

Part 2

Homework exercises

This pdf contains the homework exercises and their solutions (UPDATED on 17 November; exercise numbers changed!).

Assignments (exercises marked with *: write down the solution as carefully as for an exam, these will be read by a fellow student. The marked exercises are not more difficult than others.)

Set 1:	1, 2*, 3, 5, 6	discussed on 5 November
Set 2:	4, 8, 11, 12*, 13	discussed on 12 November
Set 3:	16, 17*, 19, 20, 21	discussed on 26 November
Set 4:	7*, 9, 22, 24, 25	discussed on 3 December
Set 5:	10, 18, 23, 27, 29, 30	discussed on 10 December (#30 optional)

Handouts and supporting files

Expectation and variance

Normal distribution calculators: onlinestratbook, stattrek

Part 3

Lecture notes

Lecture notes can be downloaded in pdf.

Homework exercises

This pdf contains the homework exercises and their solutions. This file will be updated regularly with new exercises.

Assignments (exercises marked with *: write down the solution as carefully as for an exam, these will be read by a fellow student. The marked exercises are not more difficult than others.)

Set 1:	1, 2, 3, 8, 10	discussed on 28 January
Set 2:	4, 6*, 9	discussed on 4 February
Set 3:	5, 11, 12*(!!), 13	discussed on 11 February. For #5, read Chapter 3 of the lecture notes.
Set 4:	7*, 14, 16, 17, 18	discussed on 25 February
Set 5:	20, 21, 23, 24, 28	discussed on 3 March (do #28 after the last lecture)

Handouts and supporting files

Introductory info

Part 4

Lecture notes

Lecture notes can be downloaded in pdf.

For the missed lecture of 26 April, study the following 3 sections of the lecture notes: 4.6 (the Brusselator), 5.1 up to Figure 13 on page 52 (limit cycles and the Poincare-Bendixson theorem; you can skip the method of Bendixson´s negative criterion from page 53 onwards); 6.1 with Box 2 (Hopf bifurcation through the example of the Brusselator and in general). The last lecture will assume you are familiar with this material. I am sorry for not being able to lecture it. The 28 April exercise class is on!

Homework exercises

The exercises are in the lecture notes, with weekly assignments below and solutions in this pdf (updated regularly). Exercises marked with *: write down the solution as carefully as for an exam, these will be read by a fellow student. The marked exercises are not more difficult than others.

Set 1:	2, 3, 5, 8*, 9	discussed on 31 March
Set 2:	18, 19, 22, 24*	discussed on 7 April
Set 3:	21, 23, 36*, 37	discussed on 14 April
Set 4:	25, 40, 41, 44, 46	discussed on 28 April (note: the last assignment below is discussed on the same day. Save work by using the shortcut in section 4.5 of the lecture notes.)

Set 5: Read section 6.3 of the lecture notes and do all its exercises (76-79), discussed on 28 April

Handouts and supporting files

Introductory info