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

### Teaching Plan Information

2024/25
Subject:
68451 - Introduction to Mathematical and Physical methods in Biology
Faculty / School:
Degree:
626 - Máster Universitario en Biofísica y Biotecnología Cuantitativa / Master in Biophysics and Quantitative Biotechnology
ECTS:
6.0
Year:
01
Semester:
First semester
Subject type:
ENG/Complementos de Formación
Module:
---

### 1. General information

The aim of this course is to give an overview of the main mathematical and physical tools  required to develop an abstract thinking and have a proper understanding of concepts that will be used in other subjects of this master's degree. The subject is introduced from basics concepts in other to help those students who haven´t had previous math or physics knowledge.

### 2. Learning results

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

### 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

1. Classical Mechanics
• Newton's laws
• Hamiltonian mechanics
2. Introduction to Thermodynamics and Statistical Mechanics
• Basic thermodynamical functions: energy and entropy
• The concept of ensemble
• Microcanonical and canonical ensembles. The concept of temperature.
3. Introduction to Quantum Mechanics
• The wave function
• Schrödinger equation
• The hydrogen atom

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.

### 5. Assessment system

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.

### 6. Sustainable Development Goals

4 - Quality Education

## 68451 - Introducción a los Métodos Físicos y Matemáticos en Biología

### Información del Plan Docente

2024/25
Asignatura:
68451 - Introducción a los Métodos Físicos y Matemáticos en Biología
Titulación:
626 - Máster Universitario en Biofísica y Biotecnología Cuantitativa / Master in Biophysics and Quantitative Biotechnology
Créditos:
6.0
Curso:
01
Periodo de impartición:
Primer semestre
Clase de asignatura:
Complementos de Formación
Materia:
---

### 1. Información básica de la asignatura

The aim of this course is to give an overview of the main mathematical and physical tools  required to develop an abstract thinking and have a proper understanding of concepts that will be used in other subjects of this master's degree. The subject is introduced from basics concepts in other to help those students who haven´t had previous math or physics knowledge.

The 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

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

### 3. Programa de la asignatura

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

1. Classical Mechanics
• Newton's laws
• Hamiltonian mechanics
2. Introduction to Thermodynamics and Statistical Mechanics
• Basic thermodynamical functions: energy and entropy
• The concept of ensemble
• Microcanonical and canonical ensembles. The concept of temperature.
3. Introduction to Quantum Mechanics
• The wave function
• Schrödinger equation
• The hydrogen atom

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.

### 5. Sistema de evaluación

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.