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Mathematics

Code: 100872
Credits: 6
2026/2027
Degree programme Type Course
Biochemistry FB 1

Contact lecturer

Name :
Bogdan Vasile Crintea
Email :
bogdanvasile.crintea@uab.cat

Group languages

You can consult this information at the end of the document.

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

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.

Learning outcomes

  • CM03 (Interpret the specific terminology used in the field of mathematics and statistics, or proposed by specialists in this field.) Interpret the specific terminology used in the field of mathematics and statistics, or proposed by specialists in this field.
  • KM08 (Perform calculations and make graphical representations that can be used to process biochemical data.) Perform calculations and make graphical representations that can be used to process biochemical data.
  • SM05 (Use digital resources in calculations, graphic representations, simple mathematical models and statistical tests.) Use digital resources in calculations, graphic representations, simple mathematical models and statistical tests.

Contents

1 Real functions of a real variable.


1.1 Numbers, functions and graphs, elementary functions, equations.


1.2 Limits. Continuous functions.


1.3 Derivatives. Applications of the derivative.


1.4 The integral. Applications of the integral.


1.5 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 Diagonalization of a matrix.


2.4 Systems of linear differential equations with constant coefficients. Applications.


 


 

Learning activities and methodology

Title Hours ECTS Learning outcomes
Problems 15 0.6 CM03, KM08, SM05
Theory 30 1.2 CM03, KM08, SM05
Exercises 45 1.8 CM03, KM08, SM05
Study 40 1.6 CM03, KM08, SM05
Tutorials 10 0.4 CM03, KM08, SM05

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.

Assessment

Continuous assessment activities

Title Weight Hours ECTS Learning outcomes
First midterm exam 40% 2 0.08 CM03, KM08, SM05
Assignment submission 10% 3 0.12 CM03, KM08, SM05
Recovery exam 90% 3 0.12 CM03, KM08, SM05
Second midterm exam 50% 2 0.08 CM03, KM08, SM05

The course will be evaluated continuously through the following activities:

  • one first midterm exam, whose score is denoted by MT1
  • two assignment submission, whose score is denoted by AS
  • one second midterm exam, whose score is denoted by MT2

The score by continuous assessment, S, will be obtained from:


S = 0.40 MT1 + 0.50 MT2 + 0.10 AS


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= 0.90 R + 0.10 AS

We remark that the score of the assignment submission, AS, can not be recovered. The repeating students will have to do the same assessment activities as new entry students. Those students who desire to increase their grades will have to take the recovery exam.


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.


Any irregularity committed during an assessment activity (academic misconduct, plagiarism, or improper use of AI, unless such use is expressly authorized in the course syllabus) that may lead to a significant alteration of the grade will result in that activity being graded as 0. If the course syllabus stipulates that obtaining a minimum mark in this assessment is an essential requirement to pass the course, or if multiple irregularities occur in the assessment activities of the same course, the final grade for the course will be 0. Furthermore, disciplinary proceedings may be initiated against any student who incurs any of these irregularities.

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

Course groups and languages

The information provided is provisional until November 30. After this date, you will be able to consult the language of each group through this link. To access the information, you will need to enter the course CODE

Type of teaching Group Language Semester Shift
(TE) Theory 31 Catalan first semester afternoon
(PAUL) Classroom practices 311 Catalan first semester afternoon
(PAUL) Classroom practices 312 Catalan first semester morning-mixed