Undergraduate dissertation

Descriptive data of the subject.
Character: Compulsory education.
Semester: second semester
Credits: 12 ECTS.
Language: Galician / Spanish / English
Participating departments: All the departments with teaching in the Degree of Mathematics.

Coordinator: Mercedes Conde Amboage, (881813217; email: mercedes.amboage@usc.es)

Descripción: The work consists in the preparation by the student of a project, work, memory or original study in which the knowledge, abilities, competences and skills acquired during the studies carried out in the degree in Mathematics are integrated and developed. It will include, as a minimum, tasks of bibliographic search and review, reading and integration of information, preparation of relevant results, writing, and presentation and defense of the work. They will be oriented to the evaluation of the competences associated with the degree such as: training for the search, management, organization and interpretation of relevant data, normally from its area of study; making judgments that include a reflection on outstanding issues of a social, scientific, technological or ethical nature, and that they facilitate the development of critical, logical and creative thinking and judgment.

OFFER OF “TRABAJOS FIN DE GRADO”
ACADEMIC YEAR 2024-2025 – FACULTADE DE MATEMÁTICAS
See Annex I Offer of TFG and tutors (and co-tutors) for the academic year 2024/25 (propiciated and non propiciated)
https://www.usc.gal/gl/centro/facultade-matematicas/tfg

The bibliography is specified in each proposal of TFG presented at Annex I.

COMPETENCES OF THE SUBJECT

General competences
CG2 Collect and interpret data, information and relevant results, obtain conclusions and issue reports on scientific, technological or other problems that require the use of mathematical tools.
CG3 Apply the theoretical and practical knowledge acquired and the capacity for analysis and abstraction in the definition and formulation of problems and in the search for solutions in both academic and professional contexts.
CG4 Communicate, both in writing and orally, knowledge, procedures, results and ideas in Mathematics to a specialized and non-specialized audience.
CG5 Study and learn autonomously, with organization of time and resources, new knowledge and techniques in any scientific or technological discipline.

Specific competences
CE1 Understand and use mathematical language.
CE2 Know rigorous demonstrations of some classical theorems in different areas of Mathematics.
CE3 Think demonstrations of mathematical results, formulate conjectures and imagine strategies to confirm or deny them.
CE4 Identify the errors in the incorrect reasoning by proposing demonstrations or counterexamples.
CE5 Assimilate the definition of a new mathematical object, relate it to others already known and be able to use it in different contexts.
CE6 Know how to abstract the properties and substantial facts of a problem, distinguishing them from those that are purely occasional or circumstantial.
CE7 Propose, analyze, validate and interpret models of simple real situations, using the most appropriate mathematical tools for the purposes pursued.
CE8 Plan and execute algorithms and mathematical methods to solve problems in the academic, technical, financial or social field.
CE9 Use computer applications for statistical analysis, numerical and symbolic calculation, graphical visualization, optimization and scientific software, in general, to experiment in Mathematics and solve problems.

Transversal competences
CT1 Use bibliography and search tools for general and specific of Mathematics bibliographic resources, including Internet access
CT2 Manage work time optimally and organize available resources, establishing priorities, alternative routes and identifying logical errors in decision making
CT3 Verify or reasonably disprove the arguments of other people.
CT5 Read scientific texts in their own language and in others of relevance in the scientific field, especially in English.

Modalities of TFG

There will be a double procedure for the offer of TFG:
a) Ordinary offer by the Commission of the Degree (CT).
b) Propitiated offer by proposal of a project in agreement between student and tutor, and co-tutor, if applicable. In this case, the assignment to the student will be conditioned to the fulfillment of the requirements indicated in article 4 of the Regulation at the time of definite assignation.

See Annex I for the list of TFG and tutors (and co-tutors) for the academic year 2024/2025 (Propitiated offer and non propitiated offer). Once the offer of TFG has been approved, any proposal for modification (title, tutor and/or co-tutor) must be submitted to the approval of the CT sufficiently in advance before the request of defense.

Procedure for the assignation of TFG

There will be an assignation period for each ordinary enrollment period, in the two types of offer, according to the following procedure:
a) The assignment corresponding to the propiciated offer will be made, verifying that the student who proposed it is enrolled in the TFG within the period established for this purpose.
b) The students enrolled in the TFG who opted for the ordinary offer will be called for the assignment. In each of the assignation periods, this will be done by order of simple average mark of the academic records. In the event of a tie, the provisions of the regulations of the USC on the evaluation of academic records will apply.

To optimize student preferences and encourage students to consult with teachers, the ordinary assignment process will be carried out by public appeal in one or more rounds, so that in each one of them the students express their preferences among the proposals that are still available.

If they cannot attend in person, the student may previously submit a form that contains the list of available jobs, listed in order of preference.

It is the responsibility of the coordinator of TFG to organize the process so that all enrolled students can choose one of the available proposals. If a student is not present, the TFG will be assigned according to their preferences, if they submitted the form mentioned in the previous paragraph, or ex officio among those that are available at the end of that call and by order of record. in the case of not knowing their preferences.

Once the TFG proposals have been assigned, each student, regardless of the TFG modality, must contact the tutor of the TFG in order to define the work to be carried out in the TFG. Student, tutor and, if applicable, co-tutor, will sign a document to start the work, which they will send to the CT within the term established for this purpose from the final resolution of the assignment, with the following information:
a) Reference of the work.
b) Brief planning.
c) Intellectual property of the work.
d) Signature of the tutor and, if applicable, co-tutor, and the student, in addition to the date.

The student who does not request the defense of their TFG, or does not pass it in any of the periods established for the academic year, may request to the CT by a reasoned document with the approval of the tutor of the TFG, annual extensions for the continuation of the validity of the project. This application will be submitted within the period set for this purpose, which will always be prior to the assignment of the TFG of the corresponding academic year.
If the term has elapsed without the request for an extension being made, the student will lose his rights with respect to the assigned TFG project, and this will be declared expired. In this case, the student must start the procedure established in the regulations again, except in extraordinary cases that are considered by the CT.

The TFG may be developed within the framework of agreements with companies or institutions.

Requirements for the presentation of the TFG and documentation that must be submitted

Students must submit the request for the defense of the TFG and an electronic copy in PDF format through the electronic procedure that the USC establishes, within the period established for this purpose by the CT in each call. In the TFG defense request, the student will be able to choose between public defense before the tutor and public defense before tribunal.

In order to present the TFG defense request, it is an essential requirement to be registered in the TFG at the time of the request. The Faculty of Mathematics will verify that the requirements to authorize its presentation are fulfilled, specifically, that the student passed all the necessary credits to obtain the degree title, except those corresponding to the TFG. The same is applicable to students in the integral programs of dual degrees, provided that the student proceeds to the recognition of credits that he is not obliged to study according to the integral program for having taken credits in another degree. For these purposes, in the event that on the date of defense not all the evaluation reports of the subjects have been received yet, the secretary of the Faculty will request the teachers in charge of the subjects to report on the qualifications of the students to defend the works in the same call.

In the case the student opts for public defense before a tribunal, prior to the defense, the TFG tutor must deliver, by the electronic procedures defined by the USC, a mandatory signed tutoring report, and, if applicable, incorporating the valuations of the co-tutors, which will be available to the tribunal. In the above-mentioned report, the following aspects will be particularly assessed:
- Acquisition of concepts and understanding of the theoretical and practical aspects related to the TFG.
- Application of acquired knowledge (synthesizes information, justifies the decisions made, generates well-based conclusions, proposes solutions ...).
- Development and deepening of the proposed tasks.
- Use and management of bibliographic references.
- Fulfillment of with the proposed objectives.
- Creativity and initiative.
- Commitment and autonomy at work.

The presented work, with an extension of between 30 and 60 pages (excluding supplementary material such as data tables and codes), will show the work developed by the student. For information purposes, the Faculty will establish a common recommended format. In any case, it will respect the following structure:

1. Cover in which they appear: Degree in Mathematics, title of the work, full name of the author and academic year of the defense.
2. Index of the chapters and sections.
3. Summary (about 200 words) in the language used and in English.
4. Introduction.
5. Contents.
6. Bibliography consulted.
7. Format: A4 size document (21x29.7 cm) with font size of 11 points, 2.5 cm side margins and 3.5 cm top and bottom margins. In addition, the line spacing shall be 1.25 and the space before a paragraph shall be 8 points.

Titorization of the TFG

The TFG tutoring activities may be presential and/or virtual through MS Teams or other telematic tools available to teachers and students.

Presentation and defense of the TFG

The defense will be carried out by the student through an individual presentation in public session on the assigned date.
The TFG presentation will have a maximum duration of 20 minutes. At the end of the presentation, the tribunal, or the tutor, in the case of public presentation before this, may ask as many questions and issues as they deem appropriate (recommended duration 20 minutes).

The defense of the TFG will be carried out by the student in person. Notwithstanding the foregoing, for exceptional cases duly authorized by the CT, the defense may be carried out by telematic means, with the guarantees established in the authorization.


The preparation and defense of the TFG must be carried out in any of the two official languages of the Autonomic Community.


Evaluation, qualification and revision

The qualification of the works will be carried out according to the criteria indicated below, which will be linked to the achievement of the competences of the degree and the transversal competences. Specifically, the assessment of the memory delivered will take into account the following aspects:
-Structure and organization (Objectives of the work, results and critical and reasoned discussion, conclusions ...).
-Presentation and formal aspects.
-Mastery of the subject.
-Bibliography and other sources of information.
-Ability to communicate by writing knowledge, procedures, results and ideas in Mathematics to both a specialized and non-specialized audience.

In the assessment of the defense, the following will be taken into account:
-Structure and organization.
-Concision and clarity.
-Mastery of the subject.
-Use of adequate resources to facilitate presentation and understanding.
-Ability to debate and defend.
-Ability to communicate orally knowledge, procedures, results and ideas in Mathematics to both a specialized and non-specialized audience.

The members of the tribunal will deliberate on the corresponding grade according to the evaluation criteria published in this teaching guide and the provisions of the degree verification report. In particular:

-The total assessment of the tribunal (VTR) will be obtained by weighting the qualification of the document by 60% and the qualification of the defense by 40%.
-The tribunal will extract the overall assessment from the tutor's report, denoted by VTI.
-The final grade of the TFG will be obtained according to the formula max{VTR,0.3*VTI+0.7*VTR}, with expression of a decimal.

In case the student opts for public defense before the tutor, the maximum grade they can obtain will never exceed 8.

The mention of "Honors" (MH) may be granted in accordance with the provisions of the USC. This mention can only be granted once the defenses of all the TFG corresponding to the academic year have been completed. If there are two or more evaluating tribunals, each committee will send to the CT a reasoned proposal of a number of candidates for the MH, which may not exceed the maximum number of MH that can be awarded in the subject. In view of the proposals, the CT will grant the mention of MH among the students proposed by the tribunals, assigning them to the students with the best records calculated from the average mark of all the subjects taken, including that of the TFG.

The publication of the TFGs in the institutional repository of the USC (Minerva) will be done for all successfully defended works for which the corresponding authorization has been given, and in accordance with the regulations of mentioned repository.

The TFG must be original works of own elaboration and the sources that were taken into account for their realization must be duly cited. Failure to comply will involve the qualification of "fail" that academic year and the duty of the tutor and the tribunal that detects it to inform the Rectorate in order to initiate the appropriate disciplinary actions, in accordance with article 16 of the "Normativa de avaliación do rendemento académico dos estudantes e de revisión de cualificacións”.

Prior to the authorization of the defense, within the term established by the Faculty of Mathematics, the student must carry out an automated analysis on the control of the violation of intellectual property rights through the tool available at the USC for this purpose. This analysis must be delivered to the tutor and assessed together with him/her, to be taken into account for the report that the tutor prepares. From this analysis, according to the procedure to be established, if the CT considers that the aforementioned rights were violated, it may deny the defense of the work and the provisions of the preceding paragraph will apply.

The specific obligations of the students in relation to the TFG are:
a) Inform the tutor of the evolution of the TFG.
b) Attend the tutorials scheduled by the tutor.
c) Consult with the tutor if the defense of the TFG is appropriate.
d) Prepare and present an original TFG for which the student is responsible for the authorship and originality of the work, committing to perform the forementioned automated analysis.

Seminars (5 hours) dedicated to the formulation and/or formation on concepts and tools which are neccessary to achieve the objectives proposed for the TFG.
Tutorials (12.5 hours) dedicated to the orientation and follow-up of the TFG, evaluation of progress and improvement proposals, including the revision of the versions of the manuscript.
Evaluation session (1 hour) dedicated to the oral presentation and defense of the TFG before the evaluation committee or tutor.
Personal work (281.5 hours). Individual and autonomous student work.
TOTAL: 300 hours.

List of Annexes
Annex I Offer of TFG and tutors (and co-tutors) for the academic year 2024/25 (propitiated and non-propitiated offer)
Annex II Extension request form
Annex III Documentation of work initiation
Annex IV Report of the tutor
Annex V Report of evaluation by Committee
Annex VI Report of evaluation by Tutor

For more information you can consult the following page:
https://www.usc.gal/gl/centro/facultade-matematicas/tfg


For cases of fraudulent performance of exercises or tests will apply the provisions of the "Normativa de avaliación do rendemento académico dos/das estudantes e de revisión de cualificacións".