MM554: Mathematics for Biology (5 ECTS)

STADS: 13015701

Level
Bachelor course

Teaching period
The course is offered in the autumn semester.

Teacher responsible
Email: colchero@imada.sdu.dk

Timetable
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Comment:
Ubegrænset deltagerantal. Fælles forelæsninger med MM556 enkelte uger.

Prerequisites:
The course cannot be chosen by students, who have passed FF506, FF502 and MM536.

However, this course can only be taken if it:

1. is a constituent part of your programme 
2. is a specified recommendation for elective ECTS in your programme
3. is part of a specified transitional arrangement ('overgangsordning') for a course you have not yet passed

Academic preconditions:
Students taking the course are expected to:

• be able to solve simple arithmetic and algebra problems (e.g. calculate proportions and percentages, combining like terms, solving linear equations with a single unknown, etc.)
• be able to handle special functions (i.e. linear, exponential, logarithmic, polynomials, trigonometric) 
• be able to solve problems involving differentiation and integration.
• know multiplying and dividing monomials, binomials, and polynomials.

Course introduction
Today students and practitioners in all areas of biology, from molecular biology to population ecology, require a good understanding of mathematics and their applications. As a result, most biological systems are explored and explained using mathematical models. For instance, differential equations are fundamental tools in population ecology, biochemistry or molecular biology, while statistics (i.e. applied mathematics) are keys to test hypotheses commonly represented as mathematical models. Therefore, the purpose of the course is to provide the students with the fundamental tools to understand and solve mathematical problems with emphasis on biological systems. The course will provide the necessary analytical skills for differentiation, integration and to solve differential equations, while the students will also learn the application of numerical methods to common biological processes, such as linear and Taylor approximations, Riemann sums and Euler’s method to solve differential equations. These numerical techniques are particularly important since many of the models relevant for biology cannot be solved with analytical methods. To apply these numerical methods, the students will become familiar with the free-open source software R. This package has become a fundamental analytical tool for biologists around the world, and thus its knowledge will expose the students to the latest developments in mathematical biology.

The course gives an academic basis for studying topics relevant to ecology, population and evolution, molecular biology and applied statistics, all of which are part of the degree. It will also provide the basis for those students interested in following a minor in mathematics.

In relation to the competence profile of the degree it is the explicit focus of the course to:

• Provide knowledge on the different methods relevant to mathematical biology.
• Develop skills on applying the appropriate mathematical methods to describe biological systems.
• Give the competence to work in groups to explore problems in biology through the use of mathematical models.
• Develop skills to present their work in a structured manner and with the appropriate mathematical notation.
• Expose the students to the use of mathematical models in scientific articles/book chapters in the biological literature.
• Provide expert knowledge of a selected area of study, based on the highest level of international research within the field of mathematical biology based on the background of the teacher’s active role in the research field.

Expected learning outcome
The learning objectives of the course are that the student demonstrates the ability to:

• identify the appropriate functions to describe simple biological processes.
• judge which methods are appropriate to solve mathematical problems (differentiation, integration, differential equations) applied to biological systems (either analytically or using numerical methods).
• understand and consequently disseminate both in written form and orally scientific articles/book chapters from the research area.
• apply and transfer methods from the presented applications to new problems, also in the context of other subjects.
• implement solutions based on the analytical and numerical methods learned in class using the programming language R.

Subject overview
The following main topics are contained in the course:

• Sets, properties of elementary and special functions (linear, logarithmic, exponential, polynomials, rational, trigonometric)
• Real and complex numbers
• Differentiation and applications of differentiation
• Linear approximations and Taylor polynomials
• Integrals and integration methods
• First and second order differential equations
• Analytical and numerical methods to solve differential equations (variable separation, Euler’s method)
• Linear differential equations (LDEs) and methods to solve them (variation of constant),
• Functions of several variables and partial derivatives.

Literature

Meddeles ved kursets start.

Website
This course uses e-learn (blackboard).

Prerequisites for participating in the exam
None

Assessment and marking:
The exam is evaluated by the Danish 7-mark scale and internal marking based on three parts:

1. Three mandatory tests. Count 60 % of the total evaluation.
   Allowed exam aids: Open book, only R as software
2. Eight quizzes. Count 20 % of the total evaluation.
3. Four group exercises. Count 20 % of the total evaluation

Expected working hours
The teaching method is based on three phase model.
Intro phase: 28 hours
Skills training phase: 38 hours, hereof:
 - Tutorials: 28 hours
 - Laboratory exercises: 10 hours

Educational activities Study phase: 14 hours
Educational form
Activities during the study phase:

• Solving practice exercises.
• Reading handouts and other material.
• Answering graded quizzes on the material they have read.
• Investigating and discussing the terms and concepts they are struggling with and then constructing a wiki.

Language
This course is taught in Danish or English, depending on the lecturer. However, if international students participate, the teaching language will always be English.

Course enrollment
See deadline of enrolment.

Tuition fees for single courses
See fees for single courses.