Mathematics
Code: 101001 ECTS Credits: 6| Degree | Type | Year | Semester |
|---|---|---|---|
| 2500502 Microbiology | FB | 1 | 2 |
Contact
- Name:
- Joaquim Bruna Floris
- Email:
- joaquim.bruna@uab.cat
Teaching groups languages
You can check it through this link. To consult the language you will need to enter the CODE of the subject. Please note that this information is provisional until 30 November 2023.
Teachers
- Marti Prats Soler
Prerequisites
We do not need any prerequisites for this subject, but we recommend to follow the propedèutic course in mathematics, if the student does not have a good level in mathematics.
Objectives and Contextualisation
In the context of microbiology studies, a solid mathematical training is essential, especially to be able to understand and use the function graphs, the differential calculus and the understanding of the models of growth, as well as basic statistical inference tools. Like in any university degree, It is essential that students reach a critical reasoning and respect for diversity and plurality of ideas, people and situations. In order to include a gender perspective in the subject, we include written bibliography for women and we will make special mention of scientific contributions from women related to the agenda of the subject, as well as we will include more women as protagonists of the statements of the problems that consider timely. Obviously, and something we already do, we will use non-sexist and androcentric language in all Written and visual or other documents of the subject.
The specific objectives of the subject are:
1. Understanding of the basic tools to draw and interpret graphs of functions.
2. Study of the growth of biological populations. The exponential growth and the logistic growth. use and interpretation of logarithmic graphs.
3. Acquisition of notions about interpretation of data, application of tests of hypothesis contrasts and calculation of confidence intervals. Use of computer tools for the statistical treatment of data.
Competences
- Apply knowledge of theory to practice
- Communicate orally and in writing.
- Design experiments and interpret the results
- Know, interpret and use basic tools of mathematical calculus and statistics.
Learning Outcomes
- Apply knowledge of theory to practice
- Communicate orally and in writing.
- Design experiments and interpret the results
- Know, interpret and use basic tools of mathematical calculus and statistics.
Content
Program
1. The derivative as a growth rate. Derivation rules. Growth and decline. Maxima, minima, convexity, concavity
2. Functions of one variable: graphical representation, parameter dependence, polynomial functions and rational functions. The exponential function. The number e. The logarithm function. experimentation Dimensional analysis. Logarithmic graphs.
3. The definite integral and the indefinite integral, primitives. Primitive calculation rules.
4.. Exponential growth and decline. Logistics growth. Differential equations as mathematical models of the change of magnitudes.
5.. Introduction to probability. Randomvariables and more frequent distributions. Binomial and normal law.
6. Descriptive statistics. Descriptive study of a variable: mean, deviation, bar diagrams. Samples, statistics.
7.. Introduction to statistical inference. Confidence intervals and hypothesis testing.
Methodology
The subject consists of three main activities, plus complementary ones.*
There will be theory classes called "magistrals", which will only be "magistrals" in the form.
From the point of view of the content it is very difficult to distinguish between theory and problems and in fact the theory classes will be full of examples and exercises, and its theoretical part will be very limited. There will also be problem sessions, complementary to theory classes and where exercises will be solved without introducing new concepts. Finally sessions of two hours of practices will be held in the computer room, where specific software will be used for the mathematical calculation (Maple / Sage / Maxima) and possibly another more generic one (Excel) that will also be used for the Statistical practices. These activities will be tutorials in which doubts that have not been solved yet, will be clarified in the class.
The communication with the professors will preferably be face-to-face, although they can also be answer specific questions by email or through the Virtual Campus.
Annotation: Within the schedule set by the centre or degree programme, 15 minutes of one class will be reserved for students to evaluate their lecturers and their courses or modules through questionnaires.
Activities
| Title | Hours | ECTS | Learning Outcomes |
|---|---|---|---|
| Type: Directed | |||
| Computer practice | 8 | 0.32 | 1, 4, 3, 2 |
| Problem sessions | 14 | 0.56 | 1, 4, 2 |
| Theory sessions | 30 | 1.2 | 1, 4 |
| Type: Supervised | |||
| Doubt clearing sessions student-professor | 4 | 0.16 | 1, 4, 2 |
| Type: Autonomous | |||
| At home work | 40 | 1.6 | 1, 4 |
| Problem solving | 37 | 1.48 | 1, 4, 3 |
| Writing mathematics | 12 | 0.48 | 1, 4, 3, 2 |
Assessment
Assessment Activities
| Title | Weighting | Hours | ECTS | Learning Outcomes |
|---|---|---|---|---|
| First partial exam | 35% | 2.5 | 0.1 | 1, 4, 2 |
| Problem deliveries | 15% | 0 | 0 | 1, 4, 2 |
| Second partial exam | 35% | 2.5 | 0.1 | 1, 4, 2 |
| computer exercises | 15% | 0 | 0 | 1, 4, 3, 2 |
Bibliography
Batschelet, E., Matemáticas básicas para biocientíficos, Dossat, Madrid
Bardina, X., Farré, M., Estadística : un curs introductori per a estudiants de ciències socials i humanes Colecció Materials, Universitat Autònoma de Barcelona
Delgado de la Torre, R. Apuntes de probabilidad y estadística. Colecció Materials, Universitat Autònoma de Barcelona
Neuhauser, C. Matemáticas para ciencias, Prentice Hall Newby,
J.C. Mathematics for the Biological Sciences, Clarendon Press
Software
Maxima
Microsoft Excel