
Foundations of Mathematics
Code: 104342Credits: 6
| Degree programme | Type | Course |
|---|---|---|
| Data Engineering | FB | 1 |
Contact lecturer
- Name :
- Joan Orobitg Huguet
- Email :
- joan.orobitg@uab.cat
Teaching staff
- Marina Segura Broncano
Group languages
You can consult this information at the end of the document.
Prerequisites
The mathematics content of high school
Objectives
The Fundamentals of Mathematics course aims to provide students with a solid foundation in differential and integral calculus, both single-variable and multivariable, ensuring rigorous and fluent operational competence in these areas.
This is a basic and cross-disciplinary course designed to equip students with the necessary mathematical tools for the formulation, analysis, and accurate modeling of problems specific to data engineering, with particular emphasis on data processing and interpretation.
Learning outcomes
- Search, select and manage information and knowledge responsibly.
- Students must have and understand knowledge of an area of study built on the basis of general secondary education, and while it relies on some advanced textbooks it also includes some aspects coming from the forefront of its field of study.
- Make a critical evaluation of work carried out.
- Demonstrate sensitivity towards ethical, social and environmental topics.
- Identify and apply the basic theorems of the continuous functions of a variable.
- Perform derivatives, partial derivatives and integrals.
- Identify when differential and integral calculus is needed.
Contents
1. Sequences of Real Numbers
1.1 Real Numbers. Sequences of Real Numbers. Calculating Limits
1.2 Cauchy Sequences
2. Functions of One Variable
2.1 Domains. Inequalities. Limits and Continuity. Main Theorems
2.2 Differentiation. Absolute and Relative Extrema
2.3 Concavity and Convexity. Graphing Functions
2.4 Taylor's Formula and Applications
2.5 Zeros of Functions of One Variable. Bisection and Newton's Methods
2. Integration of Functions of One Variable
2.1 The Definite Integral. Properties. Fundamental Theorem of Calculus
2.2 Antiderivatives of a Function. Techniques for Calculating Antiderivatives: Integration by Parts, Substitution, and Rational Integrals
2.3 Applications of Integral Calculus
3. Functions of Several Variables
3.1. Level Curves and Surfaces. Continuity
3.2. Gradients and Directional Derivatives
3.3. Partial Derivatives. Differentiable Functions. Chain Rule. Tangent Lines and Planes
3.4. Relative and Absolute Extrema
3.5. Optimization. Gradient and Lagrange Methods
4. Integration of Functions of Two or Three Variables
4.1. Iterated Integrals. Fubini's Theorem
4.2. Changes of Variables. Polar, Cylindrical, and Spherical Coordinates
Each of these topics will begin with a theoretical summary of the fundamental concepts and techniques, followed immediately by practical examples of their application.
Learning activities and methodology
| Title | Hours | ECTS | Learning outcomes |
|---|---|---|---|
| Resolution of problems and delivery of evaluable problems | 35 | 1.4 | 1, 2, 3, 4, 5, 6, 7 |
| Preparation of partial tests | 16 | 0.64 | 1, 2, 3, 4, 5, 6, 7 |
| Theory Classes | 26 | 1.04 | 1, 2, 3, 4, 5, 6, 7 |
| Problem Classes | 24 | 0.96 | 1, 2, 3, 4, 5, 6, 7 |
| Theory study | 35 | 1.4 | 1, 2, 3, 4, 5, 6, 7 |
The course will be structured around the following activities:
Theory classes. The scientific and technical knowledge specific to the subject and necessary for problem-solving will be presented in lectures. These lectures will introduce students to the basic concepts outlined in the syllabus and provide clear guidance on how to expand upon and deepen their understanding of this material.
Problem-solving sessions. To assimilate the various mathematical concepts and effective calculation methods introduced in the theory classes, it is crucial that students dedicate a significant portion of their study time to repeatedly practicing the examples and exercises presented in the problem-solving sessions. Therefore, we encourage students to attend these sessions regularly.
It should also be noted that students benefit greatly from these sessions when they have formulated and/or solved the problems before they are reviewed in class.
Practical sessions. These classes will introduce the use of an algebraic manipulative to perform routine calculations and to create graphical representations that help students visualize more geometric concepts.
Throughout the course, the Virtual Campus will be used primarily as the main communication channel between faculty and students.
It is recommended that students use their professors' institutional email addresses, which are listed in this guide.
Students who wish to contact professors by email should use the institutional address provided by the University (@autonoma.cat). Of course, students have access to tutoring hours (by appointment) in the professors' offices.
Assessment
Continuous assessment activities
| Title | Weight | Hours | ECTS | Learning outcomes |
|---|---|---|---|---|
| Test 2 | 40% | 3 | 0.12 | 1, 2, 3, 4, 5, 6, 7 |
| Partial test 1 | 40% of the final grade | 3 | 0.12 | 1, 2, 3, 4, 5, 6, 7 |
| Delivery or evaluation of classroom practices | 10% final grade | 4 | 0.16 | 1, 2, 3, 4, 5, 6, 7 |
| Submission of solved exercises | 10% of the final note | 4 | 0.16 | 1, 2, 3, 4, 5, 6, 7 |
Continuous assessment will be conducted through:
a) A midterm exam (First Partial Exam = EP1) will be administered to assess the work completed up to that point. The grade on this exam will account for 40% of the final grade. Students who take this exam will no longer be marked as NOT EVALUABLE. Students who do not take this exam will be marked as NOT EVALUABLE for academic purposes and will not be entitled to a makeup exam (except for duly justified reasons, in which case a makeup exam will be permitted).
b) At the end of the semester, there will be a second partial exam (EP2) to assess knowledge of topics not covered in the first partial exam. The grade on this exam will account for another 40% of the final grade. Students who do not take this exam will not be entitled to a makeup exam (except for duly justified reasons, in which case a makeup exam will be permitted).
c) There will be an assessment for the practical sessions, graded PR, which will account for 10% of the final grade. This portion of the grade cannot be retaken.
d) The submission of completed exercises, as indicated by the instructors, will contribute 10% to the course assessment, graded SL. This portion of the grade cannot be retaken.
If the average (EP1+EP2)/2 is less than 3.5, the student must take the resit exam, which is a comprehensive exam covering the entire course. If the average is 3.5 or higher, a grade C1 is calculated as (0.4)EP1+(0.4)EP2+(0.1)PR+(0.1)PL. If C1 is 5 or higher, the final grade is C1. If this is not the case, the student must take the resit exam, and in this case, the final grade will be at least (0.8 R + 0.1 PR + 0.1 PL, 8), where R is the grade of the resit exam.
5% of the students may obtain the highest possible grade (MatrĂcula de Honor). They must have a grade of 9 or higher. The final decision regarding the distinction will be made by the teaching staff.
Calculators are not permitted in the midterm exams or the resit exam.
For assessment activities EP1, EP2, and PR, a date, time, and location will be provided for a review session where students can discuss their work with the teaching staff. At this session, students may submit appeals regarding their grade, which will be evaluated by the teaching staff responsible for the course. If a student does not attend this review session, the activity will not be reviewed at a later date. The dates for midterm and resit exams will be determined by the Degree Coordination Office and may be subject to scheduling changes to accommodate unforeseen circumstances. These changes will always be announced on the Virtual Campus (VC), as the VC is considered the primary means of communication between professors and students.
Without prejudice to any other disciplinary measures deemed appropriate and in accordance with current academic regulations, any irregularities committed by a student that could lead to a grade change will result in a zero (0). For example, plagiarism, copying, allowing others to copy, or using communication devices (such as mobile phones, smartwatches, etc.) during an assessment activity will result in a failing grade for that assessment activity. Assessment activities graded in this manner and by this procedure are not eligible for retake. If passing any of these assessment activities is required to pass the course, the course will be automatically failed, with no opportunity to retake it within the same academic year. The numerical grade on the transcript will be the lower of 3.0 and the weighted average of the grades if the student has committed irregularities in an assessment (and therefore, passing by compensation will not be possible).
This course acknowledges the growing use of generative artificial intelligence as a support tool, and therefore its use is permitted in a limited capacity. For all intents and purposes, the use of these tools will only be accepted to improve formal aspects of the work, such as writing, style, clarity of expression, linguistic accuracy, or translation, and for obtaining occasional assistance with technical aspects.
It is not acceptable to use generative artificial intelligence tools to generate content for the work submitted for evaluation, such as methodological approaches, designs, the execution of experiments, analysis or interpretation of results, development of ideas, or formulation of conclusions. These tasks must be carried out entirely by the student, as they constitute the essential part of the intellectual and creative work required to pass the course. Given the wide variety of assignments, please consult your tutor if you have any questions.
In any case, students must explicitly indicate in each report and deliverable whether generative artificial intelligence tools have been used, specifying which ones, their purpose, and the extent to which they were used. Irresponsible, excessive, or unnecessary use of these tools may negatively impact the final grade of the degree project. Detection of undeclared or inappropriate use of these tools may result in failing the course.
Single Assessment.
Students who have opted for the single assessment option must take a final exam covering the entire course syllabus (including practical components). This exam will be held on the same day that students taking the second midterm exam for continuous assessment. The student's grade will be the score on this exam.
If the final grade is below 5, the student has another opportunity to pass the course by taking a resit exam, which will be held on a date set by the program coordinator. The student's final grade will be the lower of 8 and the score on this resit exam.
Bibliography
Bibliografia bàsica
1. D. Pestana, J. Rodríguez, E. Romera, E. Touris, V. Alvarez, A. Portilla. Curso Práctico de Cálculo y Precálculo, Ed. Ariel, 2000.
2. S.L. Salas, E. Hille. Calculus Vol. 1, Ed. Reverte, 2002.
3. C. Neuhauser, Matemáticas para ciencias. 2a, edición Pearson, Prentice Hall.
4. J.M. Ortega, Introducció a l'Anàlisi Matemàtica. Manual UAB
Software
The free-to-use program Sage Math will be used in the practice classes.
The student can use other free programs such as Maxima or Wolfram Alfa, all the programming knowledge they have will be useful in the future.
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 | 81 | Catalan | first semester | morning-mixed |
| (PAUL) Classroom practices | 811 | Catalan | first semester | morning-mixed |
| (PAUL) Classroom practices | 812 | Catalan | first semester | morning-mixed |