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Academic Year/course:
2022/23
**

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**626 - Máster Universitario en Biofísica y Biotecnología Cuantitativa/Biophysics and Quantitative Biotechnology**

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**68451 - Introduction to Mathematical and Physical methods in
Biology**

__Syllabus Information__

**Academic Year:**

2022/23

**Subject:**

68451 - Introduction to Mathematical and Physical methods in
Biology

**Faculty / School:**

100 - Facultad de Ciencias

**Degree:**

626 - Máster Universitario en Biofísica y Biotecnología Cuantitativa/Biophysics and Quantitative Biotechnology

**ECTS:**

6.0

**Year:**

01

**Semester:**

First semester

**Subject Type:**

ENG/Complementos de Formación

**Module:**

---

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**1.1. Aims of the course**

The aim of this course is to present a brief summary of the main mathematical and physical tools which will be required during the master to those students whose degree does not include them.

These goals are aligned with the following Sustainable Development Goals (SDGs) of the United

Nations 2030 Agenda (https://www.un.org/sustainabledevelopment/), in such a way that the

acquisition of the learning results of this course provides training and skills to contribute to some

extent to its achievement. In particular, we focus on Goal 4: Quality education

###
**1.2. Context and importance of this course in the degree**

The contents of the course will be necessary to follow subjects such as "*Systems and synthetic biology*" and "*Simulation of Biomolecules*" also in the first semester, or "*Biological modelling*" in the second.

###
**1.3. Recommendations to take this course**

No special recommendations.

###
**2.1. Competences**

Basic and General

1. Order, analyze critically, and interpret information from different types of sources.

2. Develop the learning skills needed to continue studying autonomously new data, methods and applications.

3. Communicate results clear and unambiguously, using suitable presentation tools and with the limitations

imposed by time or space.

4. Learn to manage the resources and time available for solving a problem or developing a project.

5. Learn to apply new knowledge to solve problems in wider contexts related to the own area.

Specific

1. Identify the basic algebraic properties present in biological models

2. Understand the analytic tools necessary to formulate evolution models and how they can be solved with computational tools.

3. Understand basic statistical distributions

4. Understand how to build basic models in classical mechanics and classical statistical mechanics.

5. Understand the necessity of quantum mechanical models in Biology and the basical tools used to build them.

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**2.2. Learning goals**

At the end of the course the students should be able to understand the different mathematical tools required to construct the models of biological systems which will appear in the course of *System and synthetic biology *and the physical properties encoded in the different tools described in the course *Simulation of Biomolecules*.

###
**2.3. Importance of learning goals**

As discussed above, the contents of the course will be necessary to follow subjects such as "*Systems and synthetic biology*" and "*Simulation of Biomolecules*" also in the first semester, or "*Biological modelling*" in the second.

###
**3. Assessment (1st and 2nd call)**

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**3.1. Assessment tasks (description of tasks, marking system and assessment criteria)**

The grading system will be as follows:

1: (50% of the final grade). Continuous evaluation of the student's progress during the practical and theoretical sessions, through the correction of the practice reports, as well as through direct interaction in the classroom, rewarding active participation during the lectures and practices.

2: (50% of the final grade) Written exam, possibly including computer exercises, and/or resorting to the

Moodle platform, on the topics discussed throughout the course.

###
**4. Methodology, learning tasks, syllabus and resources**

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**4.1. Methodological overview**

The course is designed to achieve the learning objectives. Theoretical and practical

issues will be often combined in the same session. All lectures will take place in a computer room.

Students are expected to participate actively in the class throughout the semester.

Classroom materials will be available via Moodle. These include a repository of the lecture notes used in class, the course syllabus and other course-specific learning materials.

###
**4.2. Learning tasks**

This is a 6 ECTS course which will be organized in three types of sessions:

- Theory sessions.

- Problem sessions

- Computer laboratory sessions.

From the problem and laboratory sessions the students will have to prepare reports and submit them to be assessed. This part of the students work represents 50% of the final grade.

###
**4.3. Syllabus**

**Mathematical Methods:**

1. Introduction to linear algebra

- Vector spaces and linear mappings
- Matrices
- Eigenvectors and eigenvalues. Diagonalizability

2. Introduction to calculus

- Functions in one and several variables
- Continuity and differentiability. Taylor series.
- Riemann integral
- Systems of Differential equations
- Qualitative methods
- Partial differential equations

3. Introduction to Statistics and Probability

- Basic probability distributions
- Descriptive statistics
- Basis inference: estimation and basic tests

**Physical methods**

- Classical Mechanics
- Newton's laws
- Hamiltonian mechanics

- Introduction to Thermodynamics and Statistical Mechanics
- Basic thermodynamical functions: energy and entropy
- The concept of ensemble
- Microcanonical and canonical ensembles. The concept of temperature.

- Introduction to Quantum Mechanics
- The wave function
- Schrödinger equation
- The hydrogen atom

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**4.4. Course planning and calendar**

Being an introductory course required by the courses of the first semester, the course is scheduled for the first seven weeks of the academic year (end of september-beginning of november), with ten hours of lecture per week. The mathematical methods will cover the first half of the course (end of september-mid october) and the physical methods the second one.