Mathematics
Code: 100872 ECTS Credits: 6| Degree | Type | Year | Semester |
|---|---|---|---|
| 2500252 Biochemistry | FB | 1 | 1 |
Contact
- Name:
- Bogdan Vasile Crintea
- Email:
- bogdanvasile.crintea@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
- Jaume Aguade Bover
Prerequisites
It is recommended that students have knowledge of the following topics
-
Rational numbers and real numbers: inequalities, absolute value.
-
Elementary functions: linear, polynomial, rational, exponential, logarithmic and trigonometric functions.
- Solution of systems of linear equations.
- The basics of differential and integral calculus.
Objectives and Contextualisation
This course will provide students the basic mathematical concepts and tools required to model and analyze problems which arise from chemistry, biology and physics. The purpose of the course is that the student not only assimilate new mathematical knowledge and techniques, but also to be able to apply them to analyze and solve properly models which arise from biosciences.
Competences
- Act with ethical responsibility and respect for fundamental rights and duties, diversity and democratic values.
- Take account of social, economic and environmental impacts when operating within one's own area of knowledge.
- Take sex- or gender-based inequalities into consideration when operating within one's own area of knowledge.
- Understand the language and proposals of other specialists.
- Use ICT for communication, information searching, data processing and calculations.
- Use the basics of mathematics, physics and chemistry that are required to understand, develop and evaluate the chemical procedures of living matter.
Learning Outcomes
- Act with ethical responsibility and respect for fundamental rights and duties, diversity and democratic values.
- Apply basic calculus tools to obtain information on simple mathematical models of physical, chemical or biological phenomena.
- Interpret graphs of the functions of a variable and relate it to the formulae.
- Interpret the formulation of simple mathematical models of physical, chemical or biological phenomena, whether discrete or continuous, described by a function or a differential equation.
- Make calculations and graphic representations using a symbolic calculus programme.
- Make simple calculations by hand or using symbolic calculus programmes.
- Take account of social, economic and environmental impacts when operating within one's own area of knowledge.
- Take sex- or gender-based inequalities into consideration when operating within one's own area of knowledge.
- Understand the language and proposals of other specialists.
- Use ICT for communication, information searching, data processing and calculations.
- Use mathematical language.
- Use symbolic calculus programmes to make small-scale simulations.
Content
1 Real functions of a real variable.
1.1 Numbers, functions and graphs.
1.2 Elementary functions.
1.3 Limits. Continuous functions.
1.4 Derivatives. Applications of the derivative.
1.5 The integral. Applications of the integral.
1.6 Introduction to differential equations. Applications to models of problems in chemistry, physics and biology.
2 Linear Algebra
2.1 Linear maps and matrix algebra.
2.2 Eigenvalues and eigenvectors.
2.3 Systems of linear differential equations with constant coefficients. Applications.
Methodology
In the theoretical lectures the teacher will develop the fundamental ideas and concepts of the subject of the course showing several illustrative examples.
Different lists of exercises will be proposed so that the student can practice and learn the contents of each topic. In the problem lectures the teacher will work on the lists of exercises, will solve the doubts of the students and will discuss and solve the exercises.
All the course material will be posted on 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 | |||
| Problems | 15 | 0.6 | 10, 2, 9, 5, 6, 3, 12 |
| Theory | 30 | 1.2 | 1, 8, 7, 9, 5, 6, 4, 3, 11 |
| Type: Supervised | |||
| Tutorials | 10 | 0.4 | 10, 2, 5, 6, 4, 3, 11, 12 |
| Type: Autonomous | |||
| Exercises | 45 | 1.8 | 10, 2, 5, 6, 4, 3, 11, 12 |
| Study | 40 | 1.6 | 10, 2, 9, 5, 6, 4, 3, 11, 12 |
Assessment
The course will be evaluated continuously through the following activities:
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one mid-term exam, whose score is denoted by MT
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control sessions, whose score is denoted by PS
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a final exam, whose score is denoted by FE
The score by continuous assessment, S, will be obtained from:
N1 = 0.50 FE + 0.30 MT + 0.20 PS
If S is greater than or equal to 5, the final score is s. Otherwise the student may attend a recovery exam if the following requirements are satisfied. To participate in the recovery, the students must have previously been evaluated in a set of activities whose weight equals to a minimum of two thirds of the total grade of the subject or module. Therefore, students will obtain the «Non evaluable» qualification when the assessment activities carried out have a weighting of less than 67% in the final grade. If R denotes the score of the recovery exam, then the final grade is
S2= 0.80 R + 0.20 PS
We remark that the score of the session problem, PS, can not be recovered. The repeating students will have to do the same assessment activities as new entry students.
This subject foresees the single assessment system. The single assessment will consist of a single test in which the contents of the entire subject program will be assessed.The grade obtained in this synthesis test will account for 100% of the final grade of the subject. The single assessment test will take place on the same day, time and place as the last continuous assessment test of the subject. The single assessment can be recovered on the day set for the recovery of the subject.
Assessment Activities
| Title | Weighting | Hours | ECTS | Learning Outcomes |
|---|---|---|---|---|
| Control sessions | 20% | 2 | 0.08 | 1, 8, 7, 10, 2, 9, 5, 4, 12 |
| Final exam | 50% | 3 | 0.12 | 2, 9, 6, 4, 3, 11 |
| Mid-term exam | 30% | 2 | 0.08 | 2, 6, 3, 11 |
| Recovery Exam | 80% | 3 | 0.12 | 2, 9, 6, 4, 3, 11 |
Bibliography
“Introduction to Mathematics for Life Scientists”, E. Batschelet, Springer, 1979.
“Cálculo con Geometria Analítica”, E. W. Swokowski, G. E. Iberoamérica, México, 1989.
“Differential Equations and Their Applications”, M. Braun, Springer, 1983.
“Linear Algebra and its Applications”, David C. Lay, Pearson, 2017.
"Matemàtiques i modelització per a les Ciències Ambientals", Jaume Aguadé. UAB, http://ddd.uab.cat/record/158385
"Matemàticas para ciencias", C. Newhauser. Prentice Hall, 2004. (e-book, UAB)
Software
There are several programs that one can use to help with the better understanding of the concepts seen in the lectures. A couple of these programs are:
- GeoGebra
- R