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Basics of Mathematics

Code: 106747
Credits: 6
2026/2027
Degree programme Type Course
Environmental Sciences FB 1

Contact lecturer

Name :
Joaquin Martín Pedret
Email :
joaquin.martin@uab.cat

Group languages

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

Prerequisites

Although there are no official prerequisites, it is essential that students have a very good command of the most basic concepts of mathematics. They must have a solid understanding of the calculus taught in upper secondary school: limits, continuity and derivability of real functions of a real variable; concepts of integral calculus, which will enable them to pass the PAU mathematics exam without any problems. Students who do not have a minimum background in mathematics will have to make an effort to address these deficiencies.

Objectives

On one hand, we will review all fundamental concepts that have been worked at high school. On the other hand, we will introduce some new concepts  (as differential equations o calcules in seeral variables). But the most important point will be the emphasis in the use of these techniques in the mathematical modelization of several areas of interest.

Learning outcomes

  • CM01 (Work on basic real mathematical problem resolution applied to the environmental field.) Work on basic real mathematical problem resolution applied to the environmental field.
  • CM02 (Transmit the basic mathematical and statistics information related to an environmental problem to the general public correctly.) Transmit the basic mathematical and statistics information related to an environmental problem to the general public correctly.
  • KM01 (Identify the basic relationships between the principles and foundations of Mathematics and environmental processes.) Identify the basic relationships between the principles and foundations of Mathematics and environmental processes.
  • KM02 (Recognise the tools and basic concepts of calculus and algebra.) Recognise the tools and basic concepts of calculus and algebra.
  • KM03 (Recognise basic flat and spatial geometry problems, as well as basic maths statistics and optimisation problems.) Recognise basic flat and spatial geometry problems, as well as basic maths statistics and optimisation problems.
  • KM04 (Identify the rules for re-routing and taking on functions, as well as the basic results of differential calculus using various real variables.) Identify the rules for re-routing and taking on functions, as well as the basic results of differential calculus using various real variables.
  • SM01 (Set out the resolution of basic mathematical problems associated with the environment.) Set out the resolution of basic mathematical problems associated with the environment.
  • SM02 (Resolve basic flat and spatial geometry problems, as well as basic maths statistics and optimisation problems.) Resolve basic flat and spatial geometry problems, as well as basic maths statistics and optimisation problems.
  • SM03 (Outline the derivation and incorporation of simple functions, as well as the resolution of basic differential calculus problems.) Outline the derivation and incorporation of simple functions, as well as the resolution of basic differential calculus problems.
  • SM04 (Express yourself correctly using basic mathematical language.) Express yourself correctly using basic mathematical language.

Contents

1. Elementary functions


2. Limits and continuity


3. The derivative and its applications


4. The integral and its applications


5. Introduction to differential equations


6. Matrices, vectors and 3D geometry


7. Functions of several variables


In each of these topics, a theoretical summary of the fundamental concepts and techniques will be presented and immediately followed by examples of the application of these concepts and techniques to relevant topics in Environmental Sciences. For example: population growth, decline and extinction, biodiversity, allometry, logistic curve and sustainability, equilibria, predator/take models, half-life, seasonal pollution models, social inequality index, natural selection models, disease transmission, the Allee effect, stratified population matrix models, social mobility matrix, etc.


 

Learning activities and methodology

Title Hours ECTS Learning outcomes
Practical tests and / or delivery of problems 17 0.68
Theory 44 1.76
Theory 38 1.52
Classroom Practices (problem solving classes) 12 0.48
To prepare partial exams and to realize partial exams. 15 0.6

The course will be given in person.

The students will receive a list of exercises on which they will work, trying to solve them. During your non-classroom activity, you will have read and worked the proposed exercises and problems, as well as the theoretical notions necessary for the resolution of the exercises. This will guarantee your participation in the classroom and will facilitate the assimilation of the procedural contents.

The teaching of the course will use the virtual campus as a means of communication, as well as virtual teaching media. It is recommended to use the institutional e-mail of the professors that appears in this guide. Students who wish to communicate with professors by e-mail should do so from the institutional address provided by the university (@autonoma.cat). Naturally, students will have tutoring hours (to be arranged) in the professors' offices.

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
Resolution of problems and/or delivery of evaluable problems 20% 20 0.8 CM01, CM02, KM01, KM02, KM03, KM04, SM01, SM02, SM03, SM04
Partial exam 2 40% 2 0.08 KM01, KM02, KM03, KM04, SM01, SM02, SM03, SM04
Partial exam 1 40% 2 0.08 KM01, KM02, KM03, KM04, SM01, SM02, SM03, SM04

a) Assessment process and scheduled assessment activities

The course consists of the following assessment activities:

Recoverable activities:

Two midterm exams, E1 and E2, with a weight of 80% of the final grade: 40% for the first exam and 40% for the second exam.

Non-recoverable activities:

Two assessment tests, with a weight of 10% each and 20% overall of the final grade. The content of these tests will be based on several quizzes that students will have to complete throughout the course through the Virtual Campus. These tests will give rise to a grade P.

Course grade:

Continuous assessment.

If NE=(E1+E2)/2<2.5, the course is failed with final grade NE.

If 2.5<=NE<3.5, the student must take the reassessment exam.

If NE>=3.5, then the final grade F is calculated as follows:

F=0.4E1+0.4E2+0.2P

If F>=5, the course is passed with grade F; otherwise, the student must take the reassessment exam.

b) Reassessment process:

To be eligible for the reassessment exam, it will be necessary that NE=(E1+E2)/2>=2.5.

There will be a reassessment exam that will give rise to a grade R. Then:

If R<2.5, the course is failed with final grade R.

If R>=2.5, the course grade is

F=min(0.8R+0.2P;6)

c) Grade improvement

It is not possible to take the reassessment exam with the aim of improving the grade.

d) Scheduling of assessment activities:

The calendar of assessment activities will be provided on the first day of the course and will be made public through the Virtual Campus and on the Faculty of Sciences website, in the exams section.

e) Procedure for reviewing grades:

For each recoverable assessment activity, we will indicate a place, date, and time for review, during which students may review the activity with the teaching staff.

In this context, students may submit claims regarding the grade of the activity, which will be assessed by the teaching staff responsible for the course.

Students who do not attend the review on the scheduled day and at the scheduled place will not be able to review this activity afterwards.

f) Grades:

Honours grades. Awarding an honours grade is a decision of the teaching staff responsible for the course.

UAB regulations state that honours grades may only be awarded to students who have obtained a final grade equal to or higher than 9.00.

Up to 5% of the total number of enrolled students may be awarded an honours grade.

A student will be considered to have taken the course if they have taken at least one recoverable activity and/or one non-recoverable activity.

g) Consequences of irregularities committed by students: copying, plagiarism, etc.

Without prejudice to any other disciplinary measures deemed appropriate, and in accordance with current academic regulations, any irregularities committed by a student that may lead to a variation in the grade of an assessable activity will be graded with a zero (0).

Assessment activities graded in this way and through this procedure will not be recoverable.

If it is necessary to pass any of these assessment activities in order to pass the course, the course will be failed directly, with no possibility of reassessment during the same academic year.

These irregularities include, among others:

  • total or partial copying of a practical assignment, report, or any other assessment activity;
  • allowing others to copy;
  • submitting group work that has not been completed entirely by the members of the group. This applies to all members, not only to those who have not worked;
  • unauthorised use of AI, such as Copilot, ChatGPT or equivalent tools, to solve exercises, practical assignments and/or any other assessable activity;
  • submitting as one’s own materials produced by a third party, even if they are translations or adaptations, and, in general, submitting work containing elements that are not original and exclusive to the student;
  • having communication devices, such as mobile phones, smart watches, pens with cameras, etc., accessible during individual theoretical-practical assessment tests, that is, exams;
  • talking to classmates during individual theoretical-practical assessment tests, that is, exams;
  • copying or attempting to copy from other students during theoretical-practical assessment tests, that is, exams.

h) Single assessment:

Students who have chosen the single assessment modality must take a final test consisting of a theory exam in which they will have to develop a topic and/or answer a series of short questions.

They will then have to take a problems/practical test in which they will have to solve a series of exercises similar to those worked on in the Practical/Problem-solving classroom sessions.

The grade will be the weighted average of the two previous activities, with the theory exam accounting for 30% of the grade and the problems/practical exam accounting for 70%.

If the final grade does not reach 5, students who have failed will have another opportunity to pass the course by means of the reassessment exam, which will take place on the date set by the degree coordination.

To be eligible for the reassessment exam, students must have obtained a minimum grade of 3.5.

The review of the final grade follows the same procedure as for continuous assessment.


This English version of the guide is a translation of the Catalan version. If there's any discrepancy between the two, the Catalan version is the correct one for all purposes.

Bibliography

Basic

\"Matemàtiques i modelització per a les Ciències Ambientals\" de J. Aguadé

(This is a digital book of free access that can be download from the UAB Library webpages).

 

Supplementary

\"Matemáticas para ciencias\" . 2a, edición, Pearson, Prentice Hall. Neuhauser, C.

(Students will found many examples, solved problems resolts and exercises that will help to study the subject).

 

 

Software

We will use (if is necessary) the free SAGE Software.

 

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 1 Catalan first semester afternoon
(PAUL) Classroom practices 1 Catalan first semester afternoon
(PAUL) Classroom practices 2 Catalan first semester afternoon