ECTS credits ECTS credits: 3
ECTS Hours Rules/Memories Student's work ECTS: 51 Hours of tutorials: 3 Expository Class: 9 Interactive Classroom: 12 Total: 75
Use languages Spanish, Galician
Type: Ordinary subject Master’s Degree RD 1393/2007 - 822/2021
Departments: Mathematics, Statistics, Mathematical Analysis and Optimisation
Areas: Geometry and Topology, Mathematical Analysis
Center Faculty of Mathematics
Call: First Semester
Teaching: With teaching
Enrolment: Enrollable | 1st year (Yes)
Show the student the use of graph and network theory in Biology. To present the use of mathematical models in biological problems.
Unit 1. Introduction to the applications of graph and network theory in Biology.
Graph theory and genome assembly algorithms. The use of graph theory for the structural analysis of biological networks. Boolean networks for the study of the dynamics of biological networks. Introduction to evolutionary dynamics on graphs. (Dedicated time: 4.5 teaching hours, 3 interactive seminar hours and 3 interactive laboratory hours).
Unit 2. Application of ordinary differential and difference equations to the study of some mathematical models in biology and ecology. (Time estimated: 9 hours for lectures, and 3 laboratory interactive hours).
Allman, E. S., Rhodes, J.A. , Mathematical models in biology. An introduction, Cambridge University Press 2004 (reimpresión de 2007).
Bellouquid, A. Delitala, M. Mathematical Modeling of Complex Biological Systems. A Kinetic Theory Approach.
Birkhäuser, 2006.
Deonier, R. C., Tavaré, S., Waterman, M. S., Computational Genome Analysis, An introducction, Springer, 2005, USA
Gascuel, O. (ed) Mathematics of Evolution and Phylogeny Oxford University Press, 2005
Murray, J. D., Mathematical Biology, Springer-Verlag, 1989
C. de Vries, T. Hillen, M. Lewis, J. Muller, B. Schonfisch, A course in mathematical biology. Quantitaive modelling and computational methods, SIAM, 2006
Our aim is to contribute to prepare the students in the competences mentioned for the Master in Mathematics at USC: the basic competences CB6, CB7, CB8, CB9, CB10; the general competences CG01, CG02, CG03, CG04, CG05; the transversal competences CT01, CT02, CT03 and the specific competences CE01, CE02, CE03.
We combine the teachers' explanations about the main concepts and procedures to be developed in the subject with the students' presentations on the proposed tasks.
Part 1 will consist in an introduction to the mathematical and computational methods in genetics, genomics and systems biology. In particular, the use of the graphs theory in genomics, in systems biology and in the theory of evolution will be emphasized.
In part 2, the basic theory of difference equations will be exposed, providing the basic properties of their solutions and showing different discrete models for the study of the evolution of populations, with several applications in biology and ecology. The students will work on some properties of the solutions to ordinary differential equations with applications to the mentioned contexts.
The qualification of the subject will be obtained through continuous evaluation (75%) and final test (25%) in both blocks that compose it. For the continuous evaluation, the realization of works by the students will be evaluated. In case the continuous evaluation was satisfactory enough, the final test could be ignored, having in this case the continuous evaluation a weight of 100% in the grade.
The final grade of the subject will be the arithmetic average of the grades obtained in the two blocks in which the subject is divided.
Type of work in the continuous evaluation:
In relation to the first part, students will have to expose, focusing on the mathematical aspects of it, a recent research article that includes some of the topics discussed in class.
Regarding the second part, the realization and presentation by students of a work in which the application of ordinary differential equations to biological problems or other areas will be demonstrated. In this work they should analyse in detail some of the properties of their solutions in a research context and use current mathematical methodologies for their study, for which they can take as a basis any recent publication. Any suitable ICT media can be used for the presentation.
Through the proposed activities, students will be able to show the acquisition of the following skills: basic competences CB6, CB7, CB8, CB9, CB10; general competences CG01, CG02, CG03, CG04, CG05; transversal competences CT01, CT02, CT03 and specific competences CE01, CE02, CE03.
In the second opportunity, the same evaluation system will be used: presentation of works and final test.
Warning. In cases of fraudulent performance of exercises or tests (plagiarism or improper use of technologies), the provisions of the “Normativa de avaliación do rendemento académico dos estudantes e de revisión de cualificacións” will apply.
PRESENTIAL WORK IN THE CLASSROOM
Lectures: 18 hours
Seminar interactive classes: 6 hours
Laboratory interactive classes: 6 hours
Group tutorials: 3 hours
PERSONAL STUDENT WORK
Individual or group self-study: 22 hours
Resolution of exercises, writing conclusions or other work: 18 hours
Programming / experimentation or other work in computer / laboratory: 8 hours
Regular attendance to class and active participation in the development of the subject.
Maria Victoria Otero Espinar
Coordinador/a- Department
- Statistics, Mathematical Analysis and Optimisation
- Area
- Mathematical Analysis
- Phone
- 881813170
- mvictoria.otero [at] usc.es
- Category
- Professor: University Professor
Antonio M. Gómez Tato
- Department
- Mathematics
- Area
- Geometry and Topology
- Phone
- 881813151
- antonio.gomez.tato [at] usc.es
- Category
- Professor: University Lecturer
| Monday | |||
|---|---|---|---|
| 10:00-11:00 | Grupo /CLE_01 | Galician | Classroom 10 |
| Wednesday | |||
| 12:00-13:00 | Grupo /CLIL_01 | Galician | Classroom 10 |
| 01.27.2025 10:00-14:00 | Grupo /CLE_01 | Classroom 10 |
| 06.25.2025 10:00-14:00 | Grupo /CLE_01 | Classroom 10 |