Basic knowledge of ordinary and partial differential equations
This subject addresses topics in cellular motility and cellular population dynamics, specifically in the context of tumor growth from a mathematical perspective. Cancer is one of the major health problems in industrialized societies and there is a global perception that mathematical models will play a relevant role in the design of efficient therapeutical strategies. This subject introduces this field of knowledge and uses techiques related to other master' topics in the field of cancer modelling such as partial differential equations, dynamics systems and numerical methods.
Course competences | |
---|---|
Code | Description |
CB06 | Possess and understand knowledge that provides a basis or opportunity to be original in the development and / or application of ideas, often in a research context. |
CB07 | Apply the achieved knowledge and ability to solve problems in new or unfamiliar environments within broader (or multidisciplinary) contexts related to the area of study |
CB08 | Be able to integrate knowledge and face the complexity of making judgments based on information that, being incomplete or limited, includes reflections on social and ethical responsibilities linked to the application of knowledge and judgments |
CB09 | Know how to communicate the conclusions and their supported knowledge and ultimate reasons to specialized and non-specialized audiences in a clear and unambiguous way |
CB10 | Have the learning skills which allow to continue studying in a self-directed or autonomous way |
CE02 | Develop the ability to decide the appropriate techniques to solve a specific problem with special emphasis on those problems associated with the Modeling in Science and Engineering, Astrophysics, Physics, and Mathematics |
CE06 | Prove the necessary capacity to perform a critical analysis, evaluation and synthesis of new and complex results and ideas in the field of astrophysics, physics, mathematics and biomathematics |
CE07 | Ability to understand and apply advanced knowledge of mathematics and numerical or computational methods to problems of biology, physics and astrophysics, as well as to build and develop mathematical models in science, biology and engineering |
CE08 | Ability to model, interpret and predict from experimental observations and numerical data |
CG02 | Ability to generate and independently develop innovative and competitive proposals in research and professional activity in the scientific field of Physics and Mathematics |
CG03 | Present publicly the research results or technical reports, to communicate the conclusions to a specialized court, interested persons or organizations, and discuss with their members any aspect related to them |
CG05 | Gain the ability to develop a scientific research work independently and in its entirety. Be able to search and assimilate scientific literature, formulate hypotheses, raise and develop problems and draw conclusions from the obtained results |
CT01 | Promote the innovative, creative and enterprising spirit |
CT04 | Understand and reinforce the ethical and deontological responsibility and commitment in the performance of the professional and research activity and as a citizen |
CT05 | Autonomous learning and responsibility (analysis, synthesis, initiative and teamwork) |
Course learning outcomes | |
---|---|
Description | |
Public exhibition and critical analysis of a research article related to the subject of the course. | |
Interpretation of phenomenological results and ability to model them | |
Modeling in biological processes. Active particles | |
Treatment of biological data | |
Critical analysis of classic models based on linear diffusion | |
Understanding of a scientific article on topics related to the course | |
Understanding of individual behavior versus collective behavior in biomedical and social sciences | |
Additional outcomes | |
Description | |
Training Activity | Methodology | Related Competences (only degrees before RD 822/2021) | ECTS | Hours | As | Com | Description | |
Class Attendance (theory) [ON-SITE] | Lectures | CB10 CE02 | 0.92 | 23 | N | N | ||
Class Attendance (practical) [ON-SITE] | project-based learning | CB07 CB08 | 0.24 | 6 | N | N | ||
Problem solving and/or case studies [ON-SITE] | Project/Problem Based Learning (PBL) | CE06 CE07 | 0.36 | 9 | N | N | ||
Writing of reports or projects [OFF-SITE] | Reading and Analysis of Reviews and Articles | CT05 | 0.72 | 18 | Y | Y | ||
Study and Exam Preparation [OFF-SITE] | CG05 | 0.96 | 24 | N | N | |||
Practicum and practical activities report writing or preparation [OFF-SITE] | Project/Problem Based Learning (PBL) | CB06 CB07 | 0.56 | 14 | Y | Y | ||
Writing of reports or projects [OFF-SITE] | project-based learning | CE06 | 1.56 | 39 | Y | Y | ||
Workshops or seminars [ON-SITE] | Lectures | CE02 | 0.16 | 4 | N | N | ||
Writing of reports or projects [OFF-SITE] | CG02 CG03 | 0.16 | 4 | Y | N | |||
Project or Topic Presentations [ON-SITE] | Individual presentation of projects and reports | CB08 CB09 | 0.16 | 4 | Y | Y | ||
Writing of reports or projects [OFF-SITE] | Individual presentation of projects and reports | CT01 CT04 | 0.2 | 5 | Y | N | ||
Total: | 6 | 150 | ||||||
Total credits of in-class work: 1.84 | Total class time hours: 46 | |||||||
Total credits of out of class work: 4.16 | Total hours of out of class work: 104 |
As: Assessable training activity Com: Training activity of compulsory overcoming (It will be essential to overcome both continuous and non-continuous assessment).
Evaluation System | Continuous assessment | Non-continuous evaluation * | Description |
Projects | 25.00% | 0.00% | |
Practicum and practical activities reports assessment | 65.00% | 50.00% | |
Theoretical exam | 0.00% | 50.00% | |
Oral presentations assessment | 10.00% | 0.00% | |
Total: | 100.00% | 100.00% |
Not related to the syllabus/contents | |
---|---|
Hours | hours |
Unit 1 (de 8): Introduction to cancer for mathematicians. | |
---|---|
Activities | Hours |
Class Attendance (theory) [PRESENCIAL][Lectures] | 6 |
Writing of reports or projects [AUTÓNOMA][Reading and Analysis of Reviews and Articles] | 4 |
Study and Exam Preparation [AUTÓNOMA][] | 3 |
Practicum and practical activities report writing or preparation [AUTÓNOMA][Project/Problem Based Learning (PBL)] | 4 |
Unit 2 (de 8): Elementary mathematical models of tumor growth. | |
---|---|
Activities | Hours |
Class Attendance (theory) [PRESENCIAL][Lectures] | 3 |
Problem solving and/or case studies [PRESENCIAL][Project/Problem Based Learning (PBL)] | 1 |
Writing of reports or projects [AUTÓNOMA][Reading and Analysis of Reviews and Articles] | 2 |
Study and Exam Preparation [AUTÓNOMA][] | 3 |
Practicum and practical activities report writing or preparation [AUTÓNOMA][Project/Problem Based Learning (PBL)] | 6 |
Unit 3 (de 8): Radiotherapy and its mathematical modelling | |
---|---|
Activities | Hours |
Class Attendance (theory) [PRESENCIAL][Lectures] | 3 |
Problem solving and/or case studies [PRESENCIAL][Project/Problem Based Learning (PBL)] | 1 |
Writing of reports or projects [AUTÓNOMA][Reading and Analysis of Reviews and Articles] | 6 |
Study and Exam Preparation [AUTÓNOMA][] | 3 |
Practicum and practical activities report writing or preparation [AUTÓNOMA][Project/Problem Based Learning (PBL)] | 4 |
Unit 4 (de 8): Chemotherapy and its mathematical modelling. | |
---|---|
Activities | Hours |
Class Attendance (theory) [PRESENCIAL][Lectures] | 3 |
Problem solving and/or case studies [PRESENCIAL][Project/Problem Based Learning (PBL)] | 1 |
Writing of reports or projects [AUTÓNOMA][Reading and Analysis of Reviews and Articles] | 6 |
Study and Exam Preparation [AUTÓNOMA][] | 3 |
Practicum and practical activities report writing or preparation [AUTÓNOMA][Project/Problem Based Learning (PBL)] | 7 |
Workshops or seminars [PRESENCIAL][Lectures] | 1 |
Writing of reports or projects [AUTÓNOMA][] | 1 |
Unit 5 (de 8): Models with spatial dependence. | |
---|---|
Activities | Hours |
Class Attendance (theory) [PRESENCIAL][Lectures] | 2 |
Problem solving and/or case studies [PRESENCIAL][Project/Problem Based Learning (PBL)] | 1 |
Study and Exam Preparation [AUTÓNOMA][] | 3 |
Practicum and practical activities report writing or preparation [AUTÓNOMA][Project/Problem Based Learning (PBL)] | 4 |
Workshops or seminars [PRESENCIAL][Lectures] | 1 |
Writing of reports or projects [AUTÓNOMA][] | 1 |
Unit 6 (de 8): Individual-based models and mesoscopic models. | |
---|---|
Activities | Hours |
Class Attendance (theory) [PRESENCIAL][Lectures] | 3 |
Problem solving and/or case studies [PRESENCIAL][Project/Problem Based Learning (PBL)] | 3 |
Study and Exam Preparation [AUTÓNOMA][] | 3 |
Practicum and practical activities report writing or preparation [AUTÓNOMA][Project/Problem Based Learning (PBL)] | 4 |
Workshops or seminars [PRESENCIAL][Lectures] | 1 |
Writing of reports or projects [AUTÓNOMA][] | 1 |
Unit 7 (de 8): Evolutionary dynamics in cancer | |
---|---|
Activities | Hours |
Class Attendance (theory) [PRESENCIAL][Lectures] | 2 |
Problem solving and/or case studies [PRESENCIAL][Project/Problem Based Learning (PBL)] | 2 |
Study and Exam Preparation [AUTÓNOMA][] | 3 |
Practicum and practical activities report writing or preparation [AUTÓNOMA][Project/Problem Based Learning (PBL)] | 3 |
Workshops or seminars [PRESENCIAL][Lectures] | 1 |
Writing of reports or projects [AUTÓNOMA][] | 1 |
Unit 8 (de 8): Introduction to immunotherapies and their mathematical modelling. | |
---|---|
Activities | Hours |
Class Attendance (theory) [PRESENCIAL][Lectures] | 1 |
Class Attendance (practical) [PRESENCIAL][project-based learning] | 6 |
Study and Exam Preparation [AUTÓNOMA][] | 3 |
Practicum and practical activities report writing or preparation [AUTÓNOMA][Project/Problem Based Learning (PBL)] | 5 |
Writing of reports or projects [AUTÓNOMA][project-based learning] | 21 |
Workshops or seminars [PRESENCIAL][Lectures] | 4 |
Global activity | |
---|---|
Activities | hours |