By the end of the course, the student should be able to:
LG1: Understand and apply the concepts of limits and continuity for functions of multiple variables.
LG2: Compute directional and partial derivatives of various orders, interpret the gradient, and understand differentiability.
LG3: Apply the main techniques of differential calculus, including the chain rule and the inverse and implicit function theorems.
LG4: Analyze and represent curves and surfaces, understanding their parametrization.
LG5: Compute multiple integrals and interpret their geometric applications.
LG6: Understand and apply the concepts of line and surface integrals, including the main associated theorems.
LG7: Construct and present elementary mathematical proofs with rigor.

PC1 - Euclidean Spaces
Review of vector spaces. Norm and inner product. Cauchy-Schwarz inequality. Basic topology concepts in R^n.

PC2 - Limits and Continuity
Definition of limits in R^n. Limit properties. Continuity for functions of multiple variables.

PC3 - Differential Calculus in R^n
Directional and partial derivatives. Gradient and differentiability. Chain rule. Inverse and implicit function theorems. Higher-order derivatives. Hessian matrix and Schwarz’s theorem.

PC4 - Integral Calculus in R^n
Introduction to measure theory and the Riemann integral. Fubini’s theorem and change of variables. Polar, cylindrical, and spherical coordinates. Multiple integrals and their geometric applications.

PC5 - Line and Surface Integrals
Definition and properties of line and surface integrals. Parametrization of curves and surfaces. Applications to the fundamental theorems of vector calculus.

1- Assessment throughout the semester: 2 tests, each with a weight of 50%. Each test has a minimum passing grade of 7.5 points. The final grade is the arithmetic average of the two tests.
2- Exam assessment (1st Period if chosen by the student, 2nd Period, and Special Period): In-person exam (100% of the final grade).

The instructors reserve the right to, after grading the test, hold a discussion with the student to confirm that they possess the knowledge demonstrated in the exam. Whenever relevant, the provisions of the Code of Academic Conduct are also applicable.

At the end of the course the student should be able to:
LO1: To know and apply the algebraic and geometric structures of the vector spaces R^2 and R^3.
LO2: Use matrix language to solve systems of linear equations.
LO3. Calculate and interpret determinants and apply them to solving systems of linear equations.
LO4. Interpret abstract finite-dimensional vector spaces as subspaces of R^n or C^n.
LO5. Identify linear maps as the natural maps between vector spaces; use the matrix form of a linear map; relate linear maps with plane geometry.
LO6. Calculate and interpret eigenvalues ​​and eigenvectors; apply eigenvectors to the diagonalization of matrices and computation of matrix powers.
LO7. Classify quadratic forms.

PC1. The vector spaces R^2 and R^3.
1.1 Base, dimension and coordinates of a vector.
1.2 Dot product and norm.
PC2. Matrices and systems of linear equations.
2.1 Gauss-Jordan elimination. Application to systems of linear equations.
2.2 Matrix operations.
2.3 Elementary and permutation matrices. LU decomposition.
CP3. Determinants
3.1. Definition and properties.
3.2. Adjoint matrix.
3.3. Cramer systems.
PC4. Vector spaces.
4.1 Vector space. R^n and C^n. Linear span.
4.2 Base and dimension.
4.3 Sum and direct sum of vector subspaces. Product space and quotient space.
PC5. Linear maps
5.1 Definition, kernel and image.
5.2 Matrix of a linear map.
5.3 Vector subspaces associated with a matrix and dimension Theorem.
5.4 Base Change.
PC6. Eigenvalues ​​and eigenvectors
6.1 Invariant subspaces, eigenvalues ​​and eigenvectors.
6.2 Diagonalization of matrices and powers of matrices.
6.3 Introduction to quadratic forms.

Assessment throughout the semester:
- Six Mini-Tests completed individually throughout the semester, not mandatory, accounting the 5 best grades for 25% of the final grade.
- Final in-person test accounting for 75% of the final grade, with a minimum grade of 7.5.

Exam assessment (1st Exam Period if chosen by the student, 2nd Exam Period, and Special Period): In-person exam (100% of the final grade).

The minimum grade to complete the course is 10 points.

The instructors reserve the right to, after grading the test, hold a discussion with the student to confirm that they possess the knowledge demonstrated in the exam. Whenever relevant, the provisions of the Code of Academic Conduct are also applicable.

LG1. Know and be able to apply the economic way of thinking.

LG2. Know the optimal consumer choice and how this choice changes with variations in prices and income.

LG3. Know how to characterize the production function of firms using an economic approach and the different measures of costs.

LG4. Know and understand the main market structures.

LG5. Be able to use and apply the concepts, principles and theoretical models to real world situations and problems.

PC1. PART A: Microeconomics - Introdutory concepts
- Basic concepts
- Demand, Supply and Market Equilibrium
- Surplus, Eficiency and Market Failures
- Elasticities
- Government interventions in markets (taxes and price constrols)


PC2. PART B: Consumer Theory
- Preferences and Utility
- Budget Constraint
- Choice
- Individual Demand and Market Demand

PC3. PART C: Producer Theory
- Production
- Costs

PC4. PART D: Market Structures
- Perfect Competition
- Monopoly
- Imperfect competition models

Student must choose one of the following assessment methods:

Method A:
- Group assignment (50%)
- Final Exam (50%)

In order to get a positive grade in the course, the mark of the two written exams cannot be below 7,5.

Method B:

- Final Exam (100%)

LO1: Understand and apply the concept of inner product and orthogonality in complex vector spaces.
LO2: Apply the least squares method to solve problems.
LO3. Apply matrix decompositions (SVD and QR).
LO4. Identify Jordan blocks and implement the Jordan canonical form of a matrix.
LO5. Know fundamental results of metric and normed spaces.
LO6. Understand the notions of completeness and separability.
LO7. Identify infinite-dimensional vector spaces.
LO8. Know the structure of Hilbert space.
LO9. Compute Fourier bases of certain Hilbert spaces L^2.

PC1. Euclidean Spaces
1.1. Inner product, orthogonal bases and Gram-Schmidt orthonormalization.
1.2. Orthogonal complement of a subspace.
1.3. Least squares method.
1.4. Orthogonal and unitary matrices.
1.5. Symmetric and Hermitian matrices.
1.6. Spectral theorems for Hermitian and normal matrices.
1.7. Singular Values Decomposition and QR decomposition.
PC2. Jordan canonical form
2.1. Generalized eigenvectors.
2.2. Nilpotent endomorphisms.
2.3. Jordan canonical form of a matrix.
PC3. Metric and normed spaces
3.1. Metric spaces.
3.2. Normed spaces.
3.3. Completeness and Separability.
3.4 The Banach contraction theorem.
PC4. Introduction to Hilbert spaces
4.1. Definition and existence of Orthonormal bases.
4.2. The best approximation problem in Hilbert spaces.
4.3. Duality: Riesz representation Theorem.
4.4. The Fourier basis in the Hilbert space L^2.

The teaching and learning methodologies (TLM) of this course allow students to acquire both the theoretical knowledge and the practical skills necessary to achieve the established learning objectives.
Classes are divided into theoretical-practical and practical sessions with Python programming. TLM1 (Exposition and discussion) allows students to acquire theoretical knowledge through detailed explanations and debates on the topics studied, facilitating the understanding of fundamental concepts. This methodology is complemented by TLM2 (Exercise Solving), which offers students the opportunity to apply theoretical knowledge in practical situations, promoting problem solving and consolidating the concepts learned.
Furthermore, TLM3 (Autonomous work) is crucial for developing students' autonomy and responsibility in their learning process. Students are expected to dedicate 4 to 6 hours a week to independent work, which includes consulting the indicated bibliography and reviewing the material, as well as solving exercises and problems. This time is also allocated to carrying out computational experiments using Python, an essential tool for the practical application of Linear Algebra concepts. This pedagogical model, which integrates lectures, solving exercises and independent work with programming in Python, ensures active and contextualized learning, preparing students to face real and complex challenges in the field of applied mathematics, economics and finance.

At the end of this learning unit's term, the student must be able:

1. To explain the concept of time value of money, discounting and compounding and to be able to compare cash flows with different timetables;
2. To compute cash flows from applications and financing operations;
3. To characterize the organization of the main financial markets;
4. To compute currency and interest rate operations;
5. To describe the concept of business profitability and to compute and analyze the more relevant profitability ratios linking profitability with the firm's capital structure;
6. To analyze the financial condition of a firm and to compute and analyze the more relevant financial ratios;
7. To describe and compute de concept of working capital and to link it with the firm's financial condition;
8. To describe and compute the concept of cash flow in capital investment valuation;
9. To describe and compute the main valuation criteria used in capital investment analysis.

I - Time Value of Money
1. The concept of interest rate, consumption and saving
2. Nominal and real interest rate
3. Financial intermediation and risk
4. Simple and compounding interest
5. Discounting and compounding factors
6. Periodic/regular flows: rents
7. Applications and financing operations

II - Markets, Instruments and Financial Institutions
1. Foreign exchange market: the currency rate
2. Monetary market: the interest rate
3. Capital markets: primary and secondary markets
4. Financial Institutions
5. Financial information: sources and analysis

III - Financial Analysis
1. Economic and financial flows
2. Income and profitability ratios
3. Financial leverage
4. Sources and application of funds
5. Working capital
6. Solvency
7. Cash flow analysis

IV - Capital Investments
1. Typology of investments
2. The concept of the project's cash flow map
3. Valuation methodology
4. The discount rate
5. Valuation criteria: NPV, IRR, PI and PAYBACK

Assessment throughout the Semester:
There is no mandatory attendance.

There are 2 Tests:
1. Intermediate Test - worth 40% of the final grade, in person, and with no minimum grade. It covers points I and II of the Syllabus.
2. Final Test - worth 60% of the final grade, in person (at the same time as the First Period Exam), and with no minimum grade. It covers points III and IV of the Syllabus.

For the Intermediate Test and the Final Test, prior registration may be mandatory.

Assessment by exam:
Both the First Period and the Second Period Exams are each worth 100% of the final grade and are performed in person. Each one covers all the points on the Syllabus.

After obtaining approval in the course, students should be able to:
OA1. Develop functions/procedures that implement simple algorithms.
OA2. Develop code that manipulates arrays and objects.
OA3. Develop simple object classes, considering the notion of encapsulation.
OA4. Write and understand Python code.

CP1. Functions and parameters
CP2. Variables and control structures
CP3. Invocation and recursion
CP4. Procedures and input/output
CP5. Objects and references
CP6. Object classes
CP7. Composite objects
CP8. Composite object classes
CP9. Arrays
CP10. Matrices

This course is done only by assessment throughout the semester, not considering the modality of assessment by exam. Evaluation components:
a) TPCs (15%): 6 online mini-tests, to do at home;
b) TEST1 (20%): Intermediate written test;
c) PROJECT (25%): Individual project;
d) TEST2 (40%): Written test to be done in 1st season, 2nd season or special season (Art. 14 RGACC)
Approval requirement: TPCs + PROJECT >= 8 points (in 20 points).
The final grade for the PROJECT is determined for each student by an oral test and will depend on the code, the report, and the student's performance in the oral.
Attendance is not an essential requirement for approval

Other relevant information:
- Questions asked in the written tests may involve aspects related to the project.
- It is not possible to pass only by taking the final exam.
- in case of failure in the 1st season, the student can take TEST2 in the 2nd season, keeping the grade of the other components
- When the grade improvement occurs in a school year different from the one in which the work was done, the grade of the components PROJECT, TPCs and TEST1 is replaced by a practical exam, to be performed on a computer before or after the written exam. Students under these conditions who wish to improve their grades should contact the UC coordinator in advance, at least 2 days before the 1st season.

By the end of the course, the student should be able to:
OA1: Understand and apply the concepts of limits and continuity of real functions.
OA2: Compute derivatives and interpret their geometric and analytical implications.
OA3: Analyze the properties of a real function and represent it graphically.
OA4: Understand and apply the main methods of antiderivation.
OA5: Compute definite and indefinite integrals and interpret their meanings.
OA6: Understand the convergence of numerical series and represent functions as power series.
OA7: Construct and present elementary mathematical proofs with rigor.

CP1-The Field of Real Numbers
Properties. Supremum axiom. Finite induction.
CP2-Limits and Continuity
Definition of limit. Properties. Continuity and types of discontinuity.
CP3-Real Sequences
Bounded sequences. Monotonicity. Subsequences. Convergent sequences and limits. Cauchy criterion. Limit calculation.
CP4-Numerical and Power Series
Convergence. Geometric and Mengoli series. Convergence criteria. Simple and absolute convergence. Power series.
CP5-Differential Calculus
Definition and interpretation of the derivative. Derivative calculation, differentiation rules. Taylor’s theorem. Monotonicity, concavity, and inflection points. Graphical representation of functions.
CP6-Integral Calculus
Immediate antiderivatives, integration by parts and substitution. Antiderivatives of rational functions. Definition and properties of the Riemann integral. Fundamental Theorem of Calculus. Integral calculation. Applications to computing areas of geometric figures.

1- Assessment throughout the semester: 2 tests, each with a weight of 50%. Each test has a minimum passing grade of 7.5 points. The final grade is the arithmetic average of the two tests.
2- Exam assessment (1st Period if chosen by the student, 2nd Period, and Special Period): In-person exam (100% of the final grade).

The instructors reserve the right to, after grading the test, hold a discussion with the student to confirm that they possess the knowledge demonstrated in the exam. Whenever relevant, the provisions of the Code of Academic Conduct are also applicable.

At the end of the curricular period of this UC, the student must:
1. Know and use the main concepts used in describing qualitative and quantitative data.
2. Understand and use fundamental concepts of probabilities and random variables. Know the most important theoretical probability distributions for discrete and continuous variables, and apply this knowledge to calculate probabilities in real contexts.
3. Know the most important theoretical sampling distributions and know how to choose the appropriate ones for different types of problems. Carry out spot estimation; know how to distinguish parameters, statistics, estimators and estimates.

PC1.Descriptive Statistics(Types of variables. Frequency tables and graphs. Measures of location, dispersion and shape)
PC2. Probabilities (Concept review. Total probability theory and Bayes formula)
PC3. Discrete univariate random variables (VA) and most relevant distributions (VA concept. Probability and distribution functions. Parameters. Most relevant distributions)
PC4. Continuous univariate random variables and most relevant distributions (VA concept. Probability and distribution density functions. Parameters. Most important distributions)
PC5.Discrete two-dimensional random variables (Joint probability and distribution function, marginal probability. Covariance and correlation coefficient. Independence of VA)
PC6. Sampling Distributions (Central Limit Theorem. Distributions derived from Normal)
PC7. Parameter estimation (Point estimation. Properties of estimators. Maximum likelihood estimators)

Assessment throughout the semester: a weekly assignment in class (45%) and a final test (55%); minimum mark in each of the tests of 8 points; minimum final average of 10 points (mark rounded to the nearest integer). Oral defense for grades of 17 or higher; students who do not attend the oral defense will receive a final grade of 16.
Assessment by exam: individual exam that includes all the material (theoretical 55%; practical 45%) with a minimum mark of 10 (rounded to the nearest integer). Grades higher than or equal to 17 will be subject to an oral exam; students who do not attend the oral exam will receive a final grade of 16.
The test and exam are conducted without consultation, and the use of graphing calculators or cell phones is not permitted.

1- Being able to determine interest (and the respective interest rate), the present value and the future value involved in a financial operation for any given time period, according to several calendar basis.
2- Knowing how to convert an annual interest rate into a periodic one, either on nominal or effective terms.
3- Being able to determine the periodic payments of an instalment credit contract, a leasing contract, or any other form of loan and knowing how to calculate the respective APR
4- Knowing how to divide any payment into its capital/principal and interest components and to present the respective loan schedule table
5- Being able to use EXCEL financial functions and financial calculators (or financial calculator modules) in solving the above mentioned calculations.

1.- Simple and Compound Interest, Present Value and Future Value; Discounting; Annual and Periodic Interest Rates; Equation of Value, Common Value and Term; Excel Financial Functions NPV and IRR; Inflation , Nominal and Real Interest Rates; Spot and Forward Interest Rates, Average Interest Rate
2.- Business Calculations: Interest on Overdrafts and current accounts; Discounting operations;Instalment Payment Calculations; APR (Excel functions XNPV and XIRR).
3. Annuities: Present Value, Future Value, Term and Interest Rate of Constant Annuities (Excel functions); Annuities payable pthly; Varying annuities; Perpetuities; Leasing; Income present value on real estate evaluation
4.- Loan Calculations:Basic Calculations, Loan Schedule tables; Contract Revisions and Special Contractual Arrangements

During the semester students will provide the following evaluation items:Individual Exercise (5%); Mid Term Exam(35%); and Team Work(10%). Teams should be composed of aminimum of 3 and up to a maximum of 5.
Final Exam: 50% for the students that presented the above mentioned evaluation items,100% for the other students.
Students with a final grade above 16 may be subjected to a special exam.

On completion of this course, students should be able to:
OA1.Recognize the fundamental principles of ethics and professional deontology in the field of engineering and technology.
LO2. Apply ethical decision-making models - such as consequentialism, virtue ethics and deontology - to solve professional dilemmas in engineering and technology.
LO3. Identify and critically analyze ethical dilemmas in complex technological contexts, with an emphasis on analyzing the social, legal and environmental impacts of technical decisions.
LO4. Develop proposals for professional conduct in line with national and international codes of ethics (OE, IEEE, ITU).

CP1: Fundaments of Ethics and Deontology
- Code of Ethics of the Order of Engineers
- Professional principles, values and duties

CP2: Introduction to ethical decision-making
- Ethical frameworks: deontology, consequentialism, virtue ethics
- Applicability in professional and organizational practice

CP3: Technological dilemmas and social impacts
- AI and decision-making algorithms: impartiality, algorithmic justice or non-discrimination
- Big Data, surveillance and privacy (briefly includes GDPR and ePrivacy)
- Innovating responsibly: legal framework and ethical principles

CP4: Ethics, social responsibility and sustainability
- Technological citizenship, environmental impact, social justice
- The engineer as an ethical agent of change

The course includes two assessment methods: continuous assessment and assessment by exam.

Continuous Assessment (CA):

This is based on the combination of collaborative learning and individual evaluation of ethical analysis skills, critical thinking, and understanding of key concepts. It includes two complementary components:

Group Presentation (50%) – Students are organized into 5 groups to prepare and deliver a reflective exercise, based on work proposals provided by the instructor related to the previous class topic. Each group gives an oral presentation during one of the sessions throughout the module. Evaluation focuses on the content, clarity, and coherence of the presentation, as well as the quality of participation in the discussion.

Individual Written Assignment (50%) – Each student writes an individual paper on the topic addressed by their group’s presentation, or on another topic agreed upon with the instructor, demonstrating critical understanding of the concepts and personal ethical reflection.

Assessment by Exam:

This method consists of an individual written exam (100%), to be taken during the official examination period, and covers all the course content. If necessary, it may include an additional oral examination. This mode is available to students who choose it or who did not pass through continuous assessment.

LO1. Develop specific oral communication skills for public presentations.
LO2. Know and identify strategies for effective use of the vocal apparatus.
LO3. Identify and improve body expression. LO4. Learn performance techniques.
The learning objectives will be achieved through practical and reflective activities, supported by an active and participatory teaching method that emphasizes experiential learning. The knowledge acquired involves both theatrical theory and specific oral communication techniques. Students will learn about the fundamentals of vocal expression, character interpretation and improvisation, adapting this knowledge to the context of public performances.

PC1. Preparing for a presentation.
PC2. Non-verbal communication techniques.
PC3. Voice and body communication, audience involvement. PC4. Presentation practice and feedback. The learning objectives will be achieved through practical and reflective activities, supported by the active and participatory teaching method which emphasizes experiential learning. Classes will consist of activities such as: Theatrical experiences and group discussions; Practical activities; Presentations and exhibitions of autonomous work; Individual reflection.

The assessment of the Public Presentations with Theatrical Techniques course aims to gauge the development of students' skills in essential aspects of public presentations. The assessment structure includes activities covering different aspects of the experiential learning process involving both theatrical techniques and specific communication techniques.
Assessment throughout the semester includes activities covering different aspects of the process of preparing a public presentation, including group and individual work activities:
Group activities (50%) [students are challenged to perform in groups of up to 5 elements, made up randomly according to each activity proposal].
1-Practical Presentations: Students will be assessed on the basis of their public presentations throughout the semester:
Description: each group receives a presentation proposal and must identify the elements of the activity and act in accordance with the objective.
The results of their work are presented in class to their colleagues (Time/group: presentation - 5 to 10 min.; reflection - 5 min.). Assessment (oral): based on active participation, organization of ideas and objectivity in communication, vocal and body expression, the use of theatrical techniques and performance. Presentations may be individual or group, depending on the proposed activities.
Individual activities (50%)
1-Exercises and Written Assignments (Autonomous Work):
Description: In addition to the practical presentations, students will be asked to carry out exercises and written tasks related to the content covered in each class. These activities include reflecting on techniques learned, creating a vision board, analyzing academic objectives, student self-assessment throughout the semester, answering theoretical questions and writing presentation scripts.
Assessment: (Oral component and written content), organization, content, correct use of the structure and procedures of the autonomous work proposed in each class, ability to answer questions posed by colleagues and the teacher. Communication skills and the quality of written work will be assessed, with a focus on clarity of presentation. These activities will help to gauge conceptual understanding of the content taught.
There will be no assessment by final exam, and approval will be determined by the weighted average of the assessments throughout the semester.
General considerations: in the assessment, students will be given feedback on their performance in each activity.
To complete the course in this mode, the student must attend 80% of the classes. The student must have more than 7 (seven) points in each of the assessments to be able to remain in evaluation in the course of the semester.

LO1: Develop the essential skills, knowledge, and tools to observe, describe, and understand the context and phenomena influencing communication.
LO2: Develop the skills to communicate effectively in multicultural contexts.
LO3: Use the skills in practical situations through oral and written communication.
LO4: Employ communication skills proactively, considering individual roles, behavioral types, and resources used during communication.

PC1: Multiple contexts that initiate and disrupt the communication process, implicit and explicit norms, as well as communication constraints across different contexts.
PC2: Ethnomethodology of the communication process, interpretation based on linguistic, paralinguistic, non-linguistic, and contextual information within oral communication.
PC3: Observation of verbal and non-verbal communication: analyzing gestures, posture, facial expressions, and eye contact (key elements of interactive communication that reinforce or replace oral communication).
PC4: The relevance of active listening in communication across multiple cultural contexts (interpreting and analyzing the phenomena).

Assessment throughout the semester:

Class participation: Evaluates the presence, involvement, and individual contributions of students in discussions and practical activities (20%).

Group work: Students are organised into groups of up to 4 members, randomly assigned, with the support of the lecturer.
• Description: Group activities focus on the observation, interpretation, and analysis of phenomena that encompass the rules, norms, and constraints of communicative activity in a practical study, using the learned content.

• Assessment: Quality of written productions and oral presentations of the developed work (active listening), which must necessarily incorporate comments provided by classmates and the lecturer during the presentations (40%).

Individual work (with consultation, to be carried out in person, in the classroom, according to the evaluation schedule):
• Description: According to a guide defined by the lecturer, comments made in the classroom are deepened in an individual report based on two presentations made by other colleagues.

• Assessment: According to the guide; explicit integration of elements outlined in the learning objectives (40%).

To complete the course unit through continuous assessment, students must not score less than 7 in any of the assessment components, including mandatory attendance of 75% of classes. The final assessment may involve an oral discussion of the work.

Final assessment:
Although not recommended, students may opt for final assessment through written work according to a prompt that will be provided by the lecturer. The final assessment of the work involves ants oral discussion with a panel of lecturers (100%).

Students who successfully complete this course will be able to:
LO1. Understand the inevitability of conflict and know how to manage it properly.
LO2. Recognize the various types of conflict and know how to transform dysfunctional conflicts into functional ones.
LO3. Use communication effectively to prevent conflict from escalating.
LO4. Recognize the different conflict resolution strategies, know how to use them and adapt them to different situations.
LO5. Understand interdependence and how to integrate individual contributions in a coordinated way as some of the essential characteristics of teams.
LO6. Use this knowledge and recognize the factors that increase and stimulate effective teamwork.

S1. Is conflict inevitable?
Factors that lead to conflict.
Elements of divergence in conflict situations.
S2. The different types of conflict in work teams: task, process and relationship.
S3. The escalation of conflict
S3.1 Situations that lead to conflict escalation.
S3.2 Using communication to prevent or stop conflict escalation.
S4. Conflict management skills
S4.1 Knowing conflict resolution skills.
Individual strategies for managing conflicts and adapting to the situation
S5. Advantages of teamwork
S5.1 Ways of strengthening interdependence, relational roles and participation styles
S6. Team decision-making
S6.1 Particularities of virtual teams; how to use online interaction tools

Lectures, in-class exercises (or online), in-class discussions (or online), readings, case discussions (in small groups), group dynamics, self-diagnostic surveys.
Pedagogical approach: Instruction, self-exploration, and process-based experiential learning
The evaluation process is carried out throughout the class period and by a final evaluation.
1.Throughout the classes, the following will be assessed
- Attendance (5%): this point presupposes 80% attendance.
- Participation in class exercises (10%)
Individual work (5) - 5%/each (25%)
2. Final individual work:
- Analysis of a practical case with compulsory passage through key points to be indicated (60%)
Assessment by examination - 1st and 2nd season - 100%

- To successfully complete the assessment throughout the semester, students must not score less than 7 in any of the assessment components listed;
- In the case of UCs in which the Final Assessment includes an assignment: the awarding of the final assessment may involve a discussion of the final assignment submitted within the previously defined assessment deadlines.

Students who complete this Unit will be able to:
OA1. Distinguish the concepts of sex and gender
OA2. Participate in research projects using the gender perspective for the analysis of social inequalities and the obstacles against equality.
OA3. Participate in intervention projects aiming at countering discrimination based on gender or intersected with gender.
OA4- Understanding the diversity of the gender spectrum

CP1 - Gender and diversity: basic concepts

CP2 -Social and experiential meaning of gender. Gender and democracy.

CP3- Intersections with gender

CP4 - Politics for Gender Equality and Diversity
Portugal
European Union
United Nations

Knowledge will be assessed throughout the semester, and attendance at 75% of classes is required. Assessment will be based on a mark for: 1 individual assignment (presentation and argumentation skills 80%) and participation throughout the semester in class exercises (assessment of presentation and oral argumentation skills 20%). The assignment consists of a review of an article or chapter chosen from a list of texts selected by the teaching team. The weighted average of these assessments must be higher than 9.5 to guarantee a pass.
A minimum mark of 7 is required at all assessment points.
Assessment by exam will involve the submission of an individual assignment (100%). The assignment will be made available on moodle 3 days before the due date. To pass the final exam, the minimum mark is 9.5.
The assessment criteria for the assignment and the exam will be: quality of the presentation of arguments and conceptual and methodological proposals, critical reflexivity and quality of form.
The teacher may request evaluation by oral examination as a complement, whenever justified (i.e. in case of doubt regarding plagiarism).

LO1. Acquiring knowledge about the fundamentals and stages of the Design Thinking process
LO2. Develop skills such as critical thinking, collaboration, empathy and creativity.
LO3. To apply Design Thinking in problem solving in several areas, promoting innovation and continuous improvement.

S1. Introduction to Design Thinking and Stage 1: Empathy (3h)
S2. Steps 2 and 3: Problem Definition and Ideation (3h)
S3. Step 4: Prototyping (3h)
S4. Step 5: Testing and application of Design Thinking in different areas (3h)

Semester-long Assessment Mode:

• Class participation (20%): Evaluates students' presence, involvement, and contribution in class discussions and activities.

• Individual work (40%): Students will develop an individual project applying Design Thinking to solve a specific problem. They will be evaluated on the application of the stages of Design Thinking, the quality of the proposed solutions, and creativity.

• Group work (40%): Students will form groups to develop a joint project, applying Design Thinking to solve a real challenge. Evaluation will be based on the application of the steps of Design Thinking, the quality of the solutions, and collaboration among group members.

To complete the course in the Semester-long Assessment mode, the student must attend at least 75% of the classes and must not score less than 7 marks in any of the assessment components. The strong focus on learning through practical and project activities means that this course does not include a final assessment mode.

At the end of this Course students will be able to:
- Understand personal branding as a tool for impressions creation and managing
- Practice and develop skills of self-awareness
- Identify and develop personal identity
- Identify communication skills and image management
- Understand the process of creating a personal brand

1. Introduction to Personal Branding
- What is personal branding
- Importance of personal branding in impression creation and management
- The process of auto-branding
2. The Personal Branding
- Self-concept and self-awareness
- Personal Identity
- Skills / Communiation
- Image management
3. Develop the Personal Branding
- Create the 'self' brand
- Implement the 'self' brand

Assessment throught out the semester: Lectures, classroom or online exercises, classroom discussions, readings, case discussions (in small groups), group dynamics, self-diagnosis questionnaires, in person or online via platform.
The pedagogical approach: instruction, self-exploration and experimental based on a learning process.
The assessment modality of this UC is according to the following elements: Attendance - minimum 2/3 classes
Home work, participation / exercises (25%)
Individual work:
Personal Branding Portfolio (75%)
Examination times - Written Work - 100%
- To successfully complete the assessment throughout the semester students must not score less than 7 in any of the assessment components listed;
- In the case of UC in which the Final Assessment includes an assignment, the awarding of the final assessment may involve a discussion of the final assignment submitted within the previously defined assessment deadlines.

LO1: By the end of this course unit, each student should understand the importance of study methods and techniques for their future academic and professional careers.
LO2: Students should acquire the necessary skills to recognise learning habits, challenges, and styles/profiles.
LO3: Analyse barriers to study and apply different strategies to mitigate them.
LO4: Reflect on the importance of teamwork and implement strategies to enhance communication, conflict management, and the effectiveness of collaborative study.
LO5: Plan and organise study time.
LO6: Test different individual and team study strategies.
LO7: Identify and apply different strategies for dealing with academic tasks and optimising assessment preparation.

PC1. Study methods and techniques: their relevance in academic and professional life.
PC2. Self-awareness in learning: learning habits, styles and profiles (e.g. self-regulation and motivational profiles).
PC3 – Barriers to studying, such as procrastination, lack of motivation and anxiety: their causes, impacts and strategies for overcoming them, including the Pomodoro technique and SMART goals.
PC4. Collaborative methodologies (e.g. Scrum, TBL and DT) and teamwork skills (e.g. effective communication, active listening, understanding roles and rules, and conflict mediation).
PC5- Time management and organisation: analysing actual time use; long, medium and short-term planning; organising tasks using digital and/or analogue tools.
PC6- Individual and team study profiles and techniques.
PC7 – Individual study plans and preparation for assessments.

I – Assessment throughout the semester
Your class participation (60%) will be assessed through the completion and submission of the following individual and team exercises throughout the semester:
1. Individual activities (20%)
1.1 Completion of self-assessment exercises (student profile; learning styles; study strategies; barriers to study). – 10%
1.2 Preparation and implementation of a weekly study plan. – 5%
1.3 Preparation of an individual improvement plan: – 5%

2. Team activities (40%). Teams will be formed randomly with a maximum of five members and will include:
2.2. Discussion of real cases, participation in role play, the World Café and moments of collective reflection. – 10%
2.3. Preparation, facilitation and participation in individual and team study strategy workshops – 30%. – 30%

3. Individual reflective portfolio – 40%.
To complete the semester-long assessment, students must achieve a minimum of 7 points in each of the indicated assessment components. They must also attend at least 70% of classes and complete the UC online course.

II – Final assessment (exam period):
There will be no final exam, and approval will be determined by the weighted average of assessments throughout the semester.
Students who wish to take the assessment in the second or special periods should contact the teacher in advance to find out about the alternative assessment method.

The student who successfully completes this Course Unit will be able to:
LG1. Distinguish the different types of stress and the impact it has on the individual.
LG2.Distinguish Stress, Anxiety and Depression
recognize the different signs and symptoms of stress.
LG3. Identify the main sources of stress in different contexts and recognize the impact at individual level) CP3
LG4. Recognize "unhealthy" stress management strategies and adjust effectively to prevent a dysfunctional situation.
LG5. Recognize the need to adjust lifestyle and incorporate some habits in order to more effectively manage stress situations.
LG6. Perform breathing exercises and mindfulness as one of the stress management strategies.

LG1
Stress definition
What is stress.
Types of stress.
LG2
Distinguish Stress, Anxiety and Depression
Identify signs and symptoms of stress
LG3
Sources of stress
Identify main sources of stress
Identify stress reactions
Identify psychological, physical, social and performance
LG4
Prevent and manage stress (I)
Understand the importance of preventing and managing stress in different contexts (sociofamiliar, academic, work)
Unhealthy strategies for stress Management
LG5
Prevent and manage stress (II)
Healthy Strategies for Stress Management:
Resilience (Definition and importance)
Mindset (Definition and Importance
Healthy lifestyles (food/ economic and healthy food recipes, sleep, physical exercise, social life)
Relaxation techniques (Knowing the different relaxation techniques, e.g. mindfulness, yoga, pilates, etc.)
LG6
Stop, breathe, reflect, choose
Practical exercise Mindfulness (aim to learn to breathe and relax)

Throughout the course, the following components will be assessed:
Attendance (5%): This criterion requires attendance (and punctuality) of at least 9 hours.
Class participation (15%)
Group project development (30%) – a single grade will be assigned to all group members.
Group project presentation (20%) – individual grade.
Final individual assignment (30%): Case study analysis, with mandatory coverage of key points to be indicated.

(OA1) The student should be able to identify the main global challenges of humanity: climate change, inequality, resource scarcity, biodiversity loss, pollution, and population growth. Understand their evolution and how human actions influence them, as well as the opportunities that arise from these challenges.

(OA2) The student should understand the three dimensions of sustainability: environmental, social, and economic. Preservation of ecosystems, sustainable use of resources, biodiversity protection, promotion of equality, social justice, access to education and health, and overall well-being. Resilient, inclusive economic systems that promote prosperity without degrading the environment.

(OA3) The student is expected to be familiar with the SDGs 2030, understanding their goals, targets, and indicators through the study and analysis of best practices in sustainability implemented by companies, governments, and non-governmental organizations worldwide.

S1. What is sustainability?
a) Evolution of the concept
b) Current state of knowledge
c) Systems view and interdisciplinarity
S2. People, Planet, Prosperity, Peace and Partnerships: the United Nations SDG framework as a guide to 2030
S3. The contribution of citizens through personal action and through participation in institutions

The assessment throughout the semester will consist of:

Attendance in 80% of the classes - (5%)
Participation in face-to-face discussions (20%)
Autonomous work (individual and group) - (25%)
Final work (50%)
Final evaluation by exam (100%)

Although not recommended, it is possible to opt for the final evaluation through a paper. The final evaluation may also involve, at the discretion of the instructor, an oral discussion (if conducted, this oral component will account for 40% of the final grade).

To successfully complete the assessment throughout the semester, students must not score less than 7 out of 20 in any of the marked assessment components.

By the end of the course, students should be able to:
LO1: Identify argumentative structures and recognize informal fallacies.
LO2: Apply the Six Thinking Hats methodology to critical analysis and problem-solving scenarios.
LO3: Mobilize divergent and convergent thinking, integrating data, emotions, risks, opportunities, and creativity.
LO4: Collaborate in parallel thinking tasks, managing different modes of reasoning.
LO5: Critically evaluate decisions and arguments based on a structured and multidimensional thinking approach.

Course Content
CC1: Definition and importance of Critical Thinking (CT)
CC2: Basic structure of an argument: premises and conclusion
Examples of simple and complex arguments
CC3: Methods for argument analysis
CC4: Logical fallacies and common reasoning errors
CC5: Criteria for evaluating the quality of arguments
CC6: Argument construction
CC7: Practical applications of CT
CC8: Lateral thinking and the foundations of the Six Thinking Hats model
CC9: Practical applications of each hat: data (white), emotions (red), risks (black), benefits (yellow), creativity (green), thought management (blue)
CC10: Parallel thinking dynamics in academic, professional, and ethical contexts; integration of argumentative methodologies and the Six Hats in simulations, debates, and written exercises

Assessment throughout the semester includes presentations, exercises, debates, readings, and case discussions (in small groups).
Active participation in practical sessions is expected and evaluated according to the following criteria:
Attendance and participation – In-class exercises and group debates (minimum 80% attendance): 20%
Homework assignments – Two tasks: one worth 5%, the other 10%: 15%
Individual essay applying the Six Thinking Hats to a real dilemma or situation: 30%
Final critical reflection, integrating course dimensions and articulating argumentative and parallel thinking: 35%
To successfully complete the assessment throughout the semester, students cannot score less than 7 points in any of the evaluation components listed.
Exam Periods
Written Work - 100%
Although not recommended, it is possible to choose assessment by exam; this assessment may also involve, at the teacher's discretion, an oral discussion (this oral component carries a weight of 40% in the final evaluation).

LO1. Understand numerical errors and computational stability
LO2. Evaluate the computational efficiency of different numerical methods
LO3. Apply direct and iterative methods to solve linear and nonlinear systems of equations
LO4. Learn and implement techniques for approximation, differentiation, and integration
LO5. Implement the discussed algorithms in Python

I - Numerical Computation
1. Representation of numbers, approximate values, rounding, errors
2. Error propagation, condition number, numerical stability
3. Convergence and computational cost

II - Systems of Linear Equations
1. Direct methods, Gaussian elimination, and pivoting strategies
2. Factorization methods: LU and Cholesky
3. Conditioning of linear systems
4. Iterative methods: Jacobi and Gauss-Seidel

III - Approximation Theory and Interpolation
1. Polynomial interpolation: Lagrange and Hermite
2. Interpolation error theorem
3. Chebyshev polynomials and minimax approximation
4. Least squares approximation

IV - Systems of Nonlinear Equations
1. Bisection method, Newton-Raphson, and fixed-point method
2. Convergence and stability of the methods

V - Numerical Differentiation and Integration
1. Numerical differentiation formulas
2. Newton-Cotes quadrature formulas
3. Integration errors
4. Gaussian quadrature formulas

'Given the eminently practical nature of this discipline, with a significant laboratory component, this UC does not provide for the assessment method by exam and only the assessment method throughout the semester is contemplated. The evaluation will be based on two exercise sheets (worth 20% each), completed individually throughout the semester, a Python implementation project (worth 20%), carried out in groups of 2 or 3 students (with a final presentation and discussion), and an individual written test worth 40% (with a minimum grade of 8.5 out of 20).

The special period is reserved for the cases provided for in Article 14 of the General Regulation for the Assessment of Knowledge and Skills (RGACC) and will include a single exercise sheet (with an implementation component in Python worth 20%), to be carried out individually, and covering all the topics of the UC.

The instructors reserve the right to, after grading the test, hold a discussion with the student to confirm that they possess the knowledge demonstrated in the exam. Whenever relevant, the provisions of the Code of Academic Conduct are also applicable.

Students should be able to identify the main macroeconomic variables and economic policy instruments.

Students should be able to understand the mechanisms of economic policy and the consequences of policy measures for the welfare of economic agents.

Students should be able to analyze and assess the consequences of shocks to economic activity.

1. Welcome to Julia & Pluto notebook
2. Introduction to Macroeconomics
3. Measuring Macroeconomic Data
4. The IS Curve
5. Monetary Policy & Aggregate Demand
6. The Central Bank Balance Sheet & Monetary Policy Tools
7. Aggregate Supply and the Phillips Curve
8. The Aggregate Demand & Supply Model
9. Macroeconomic Policy: Aggregate Demand & Supply Analysis
10. Extreme cases: Deflation vs Rampant Inflation
11. Fiscal Policy & the Government Budget
12 . Rounding off topics & controversies

Option A:
1. Attendance at at least 75% of classes
2. Mid-term test (covering the topics up to week 6): 50%
3. Final test (covering all topics, but with more emphasis on the material from weeks 6 to 12): 50%
4. The grade in any of these tests cannot be less than 8 points out of a possible 20
5. The tests are computer-based (not paper-based). For this purpose, students must register in a UC database to receive the test by email.

Option B:
1. Final exam: 100% weight in the final grade.
2. Covers all the material taught throughout the semester.
3. The exam will be computer-based (not paper-based). For this purpose, students must register in a UC database to receive the test by email.

At the end of the course the student should be able to:
LO1. Explain the algebraic geometric and topological structures of the complex plane
LO2. Calculate the limit and continuity of complex functions, the complex derivative and identify the conditions under which a function is analytic
LO3. Define complex line integrals and calculate them, explain the theoretical and practical meaning of the Cauchy Theorem and Cauchy Integral Formula
LO4. Determine the convergence of power series and represent analytic functions locally by a power series
LO5. Calculate Laurent series for analytic functions with singularities, and classify the associated singularities
LO6 Calculate residues of analytic functions, solve complex integration problems using the Residue Theorem.

PC1. Analytic functions
Complex numbers and the complex plane. Properties. Elementary complex functions. Limits and continuous functions. Analytic functions. Cauchy-Riemann equations.
PC2. Cauchy's theorem
Contour integrals. Cauchy's theorem. Cauchy's integral formula.
PC3. Taylor and Laurent series
Convergence series of analytic functions. Power series and Taylor's theorem. Laurent series. Classification of singularities.
PC4. Residue theorem
Calculation of residues. Residue theorem. Evaluation of definite integrals.

The classes have a theoretical-practical nature. Three main teaching and learning methodologies are used: clarification of doubts and problem-solving (TLM1), presentation and discussion of the material (TLM2), and students' autonomous work (TLM3).
Generally, the first part of the class follows TLM1, consisting of a review of the topics covered in the previous session, clarification and discussion of doubts, and solving proposed exercises.
In the second part, the classes take on a more theoretical approach, following TLM2. The professor presents new content, always accompanied by illustrative examples.
In parallel, students are expected to engage in autonomous work (TLM3). This promotes autonomy and responsibility in the learning process and involves solving exercises recommended by the instructors, reading the suggested bibliography, and exploring additional resources such as videos or educational software.
Additionally, weekly office hours are available, where students can discuss specific difficulties and receive further guidance.

At the end of this learning unit's term, the student must be able:

1. To distinguish different economic growth models and theories; to understand their practical implications; and, to identify economic policies that can promote economic growth
2. To know and understand the effect of intertemporal decisions decision on the main macroeconomic variables in the short-run.

1. Economic growth facts
2. The Solow growth model
3. Technology in the Solow growth model
4. Convergence and growth accounting
5. Revisions of the IS-LM model
6. Financial Markets and Expectations
7. Expectations, Consumption, and Investment
8. Expectations, Output, and Policy
9. Openness in Goods and Financial Markets
10. The Goods Market in an Open Economy
11. Output, the Interest Rate and the Exchange Rate
12. Exchange Rate Regimes
13. Financial Crises

There are two types of assessment.

The first type consists of assessment throughout the semester, in which the following instruments will be used: intermediate exam (30%) and knowledge assessment exam (70%). This assessment type requires meeting a minimum attendance criterion of 60%. There is no minimum grade requirement for maintenance in assessment throughout the semester.

The second type consists of assessment by exam, in this case the assessment exam has a weight of 100%.

1 - The content of financial reports
2 - Recognition of the effect of operating, investing and financing transactions in the financial statements
3 - Using financial statement informaton to compute indicator of performance, capital structure, and liquidity
4 - Generating and analysing large datasets of financial information

1 - The content of financial reports
2 - Recognition of the effect of operating, investing and financing transactions in the financial statements
3 - Using financial statement informaton to compute indicator of performance, capital structure, and liquidity
4 - Generating and analysing large datasets of financial information

The assessment in the course is based in a scale 0 to 20 points, and has two possibilities:
1. Assessment throughout the semester: includes the resolution of a case (weight of 30% of the final grade) and an written individual test (weight of 70% of the final grade). The minimum mark for each assessment element is 7.5 points;
2. Final Exam with a weighting of 100%.

1. Understand the working of the different segments of financial markets.
2. Know how to value bonds, how to make trading decisions in the bond market, how to compute the return of a bond investment and characterize their exposure to interest rate risk.
3. Know how to analyze the efficiency, performance and risk profile of a portfolio of financial assets.
4. Identify the main sources of value for a stock and value stocks with the discounted cash-flow method.

1. Financial Markets
(a) Money market
(b) Forex market
(c) Stock market
(d) Bond market
(e) Derivatives market

2. Bonds
(a) Bond features
(b) Day count conventions
(c) Term structure of interest rates: spot and forward rates
(d) Valuation of fixed rate bonds
(e) Trading decisions on the bond market
(f) Rates of return: yield-to-maturity and realized rate of return
(g) Rating e credit risk
(h) Valuation of floating rate bonds
(i) Interest rate risk: duration and convexity

3. Asset Pricing Models
(a) Risk and return
(b) Markowitz's model
(c) Tobin's model
(d) Capital Asset Pricing Model (CAPM)
(e) Performance valuation: Jensen's alpha, Sharpe index and Treynor index

4. Stocks
(a) Gordon model
(b) Present value of growth opportunities and dividend payment policy

Students can choose between an assessment by exam or an assessment throughout the semester.

The assessment throughout the semester consists of 2 written tests. Each test has a minimum grade of 7.5 and a weight of 50% in the final grade. Passing the course depends on obtaining the minimum grade in each of the written tests and a final grade, rounded to the nearest integer, equal to or greater than 10.

In the assessment by exam passing the course depends on obtaining a grade, rounded to the nearest interest, equal to or greater than 10.

For any written test, the use of graphical calculating machines is prohibited.

By the end of the semester the student should have developed and be able to apply the following competences:
A. Knowledge and understanding
- Describe and make sense of the main concepts and ideas of microeconomic theory;
- Understand the relevant modeling techniques;
B. Application of Knowledge
- Implement theoretical results to analyze real market events;
- Choose the appropriate conceptual, mathematical and graphical approaches to provide solutions for specific problems;
C. Learning
- Development of individual studying methods, namely problem solving and understanding of models and modelling techniques.

1. Consumer theory
1.1. Axioms of revealed preferences
1.2. Slutsky equation
1.3. Consumer surplus, compensating and equivalent variation
1.4. Consumer choice with an endowment
2. Intertemporal choice
2.1. Consumer?s intertemporal choice
2.2. Asset markets
3. Decision under uncertainty
4. General equilibrium theory
4.1. General equilibrium in a pure exchange economy
4.2. General equilibrium with production
4.3. Welfare theory
5. Market failures
5.1. Externalities
5.2. Public Goods
5.3. Asymmetric Information

Assessment throughout the semester includes the following elements:
- one intermediate exam (40%)
- one written exam at the end of the term (60%).
In order to pass the course, the mark of each of the written exams cannot be below 7.5 pts.
Assessment throughout the semester requires a minimum attendance of 2/3 of all classes.
The final evaluation is carried out through a single final exam (100%).

LG1: Solve optimization problems analytically, both with and without constraints.
LG2: Understand the theoretical foundations of gradient descent methods and their variants, evaluating their applicability and limitations in different optimization contexts. Recognize the existence of alternatives when gradient-based methods are ineffective.
LG3: Implement gradient descent algorithms in Python to obtain approximate solutions to optimization problems, critically analyzing the results from a mathematical, computational, and applicability perspective.

PC1- Optimization in One Variable
(a) Necessary and sufficient conditions for the existence of extrema
(b) Unidimensional optimization algorithms
(c) Practical examples

PC2- Unconstrained Optimization in Multiple Variables
(a) Necessary and sufficient conditions for the existence of extrema
(b) Numerical methods: gradient descent and variations, Newton and Quasi-Newton methods.
(c) Implementation of numerical methods in Python
(d) Applications in economics and finance

PC3- Constrained Optimization in Multiple Variables
(a) Equality constraints: necessary and sufficient conditions for the existence of extrema
(b) Inequality constraints: KKT conditions
(c) Numerical methods for constrained optimization problems
(d) Implementation in Python with practical examples

PC4 - Limitations and Alternative Approaches
(a) Limitations of gradient-based methods
(b) Brief introduction to non-differentiable optimization
(c) Brief introduction to metaheuristics

'Two possible assessment modalities:
Assessment througout the semester: based on a project in Python in groups of 2 or 3 students, with oral presentation and discussion (weight of 30% in the final grade), and on an individual written test with minimum grade of 8.5 (weigth of 70% in the final grade).
Alternatively assessment by exam: individual written exam accounting for 100% of the grade.

The instructors reserve the right to, after grading the test, hold a discussion with the student to confirm that they possess the knowledge demonstrated in the exam. Whenever relevant, the provisions of the Code of Academic Conduct are also applicable.

At the end of this learning unit's term, the student must be able to:
LG1. Know and use the main concepts of inferential statistics.
LG2. Construct confidence intervals, define and test hypotheses, identify errors and probabilities, specify and adjust simple and multiple regression linear models.
LG3. Know how to interpret SPSS outputs from the application of descriptive and inferential statistical methods.

0. Revision of parameter estimation concepts.
S1. Confidence interval estimation. Pivotal function method.
S2. Hypotheses testing.
2.1 Hypothesis formulation.
2.2 Errors and their probabilities.
2.3 Power function.
S3. Parametric tests: hypothesis and assumptions.
3.1 One population tests: one mean, one proportion and one variance.
3.2 Tests for equality of two means with paired samples and independent samples.
3.3 Levene's test for equality of variances.
3.4 Oneway analysis of variance (ANOVA).
3.5 Multiple comparison tests.
S4. Non-parametric tests.
4.1 Tests for equality of two or more distributions: Mann-Whitney and Kruskal-Wallis
4.2 Goodness of fit tests: Chi-square, Kolmogorov-Smirnov and Shapiro-Wilk.
4.3 Chi-square test of independence.
S5. Simple and multiple linear regression models.
5.1. OLS estimation.
5.2 Assumptions and validation.
S6. Using SPSS to analyse the results.

Assessment throughout the semester:
An individual interim test (40%) and an individual final test (60%); test with a minimum score of 8 points; final average of at least 10 points (rounded to the nearest integer). Oral defence only for grades higher than or equal to 18; students not attending the oral defence will have a final grade of 17.

Assessment by exam:
An individual exam that includes all the syllabus content with a minimum grade of 10 (rounded to the nearest integer). Grades higher or equal to 18 will be subject to oral defence; students not attending the oral defence will have a final grade of 17.

All evaluation moments will be carried out without consulting handouts, books or other materials; the use of graphic calculators or mobile phones is not allowed; all necessary calculation formulas will be provided by the teaching team at the evaluation moment.

By the end of the course, students should be able to:
1. Understand the fundamentals of measure and probability theory, including sigma-algebras, measures, and probability spaces.
2. Interpret random variables as measurable functions and analyze their distributions.
3. Relate mathematical expectation to the Lebesgue integral.
4. Apply fundamental inequalities (Markov, Jensen, Chebyshev) in the study of mathematical expectation.
5. Establish criteria for independence and convergence, including convergence in probability and almost sure convergence, preparing for limit theorems.
6. Understand the basic principles of stochastic processes, including Markov chains and Brownian motion.

1. Fundamentals of Probability and Introduction to Measure Theory
1.1. Sample spaces, σ-algebras, and probability measure
1.2. Random variables as measurable functions and associated distributions

2. Mathematical Expectation
2.1. Definition of mathematical expectation in the context of integration
2.2. Motivation for the Lebesgue integral
2.3. Fundamental inequalities (Markov, Jensen, Chebyshev)

3. Independence and Dependence
3.1. Multidimensional random variables
3.2. Criteria for independence and transformations of random variables

4. Convergence and Limit Theorems
4.1. Notions of convergence: in probability and almost sure convergence
4.2. Central Limit Theorem and moment generating function

5. Introduction to Stochastic Processes
5.1. Fundamental concepts and classic examples
5.2. Discrete processes and Markov chains
5.3. Introduction to continuous processes: Brownian motionn

Assessment in this course follows the provisions of the RGACC and provides for two types of assessment:
Assessment throughout the semester
- Two individual written tests are carried out.
- Each test has a weighting of 50 per cent in the final grade.
- A minimum mark of 9.5 is required in each test. If one of the tests does not achieve the minimum mark, the student will not pass.
Assessment by exam
- Students who do not opt for assessment during the semester or who do not pass the tests may sit an exam.
- The exam covers all the material taught and must be written and individual, with the possibility of an oral exam if further clarification is deemed necessary.
- The final mark obtained in the exam replaces the test marks in their entirety.

The instructors reserve the right to, after grading the test, hold a discussion with the student to confirm that they possess the knowledge demonstrated in the exam. Whenever relevant, the provisions of the Code of Academic Conduct are also applicable.

At the end of the course, students should be able to:

LG1. Formally define sigma-algebra, measurability and probability measures.
LG2. Understand the construction of the Lebesgue measure and integral.
LG3. Apply the monotone and dominated convergence theorems to the integration of random variables.
LG4. Understand and apply the Law of Large Numbers and the Central Limit Theorem.
LG5. Define and calculate conditional expectation.
LG6. Explain the structure of martingales and apply fundamental properties.

1. Introduction to measure theory
1.1. Measurability and sigma-algebra in R
1.2. Lebesgue measure and integration.
1.3. Convergence theorems: monotone convergence theorem; Fatou's lemma; dominated convergence theorem.
1.4.Product measures and Fubini-Lebesgue theorem.

2. Classical probability limit theorems
2.1. Successions of independent variables
2.2. Law of large numbers
2.3. Central limit theorem
2.4. Applications.

3. Conditional Expectation and Conditional Distributions
3.1. Definition and examples
3.2. Properties and interpretations
3.3. Conditional distributions and disintegration of measures

Assessment in this course follows the provisions of the RGACC and provides for two types of assessment:
Assessment throughout the semester
- Two individual written tests are carried out.
- Each test has a weighting of 50 per cent in the final grade.
- A minimum mark of 9.5 is required in each test. If one of the tests does not achieve the minimum mark, the student will not pass.
Assessment by exam
- Students who do not opt for assessment during the semester or who do not pass the tests may sit an exam.
- The exam covers all the material taught and must be written and individual, with the possibility of an oral exam if further clarification is deemed necessary.
- The final mark obtained in the exam replaces the test marks in their entirety.
The instructors reserve the right to, after grading the test, hold a discussion with the student to confirm that they possess the knowledge demonstrated in the exam. Whenever relevant, the provisions of the Code of Academic Conduct are also applicable.

At the end of the Curricular Unit, the student is expected to be able to:
LO1. To develop linear programming, linear integer programming and mixed integer programming formulations to solve decision support problems; interpret the results obtained with a general software to determine solutions; to characterize the solutions obtained.
LO2. To do the economic interpretation and to produce managerial recommendations based on the obtained solutions and sensitivity analysis.
LO3. To distinguish network models and to choose the one that allows solving a given network problem; develop network models and to choose the appropriate methodologies to solve them.

S1. LINEAR PROGRAMMING AND INTEGER LINEAR PROGRAMMING
1.1. Linear programming formulations
1.2. Optimization software
1.3. Economic interpretation and sensitivity analysis
1.4. Linear integer and mixed integer linear programming formulations
1.5. Applications of linear and integer linear programming
S2. NETWORK MODELS
2.1 Network elements
2.2. The minimum spanning tree problem
2.3. The shortest path problem
2.4. The maximum flow problem
2.5. The minimum-cost network flow problem
2.6. Applications of network models

Assessment throughout semester or Assessment by exam.
Assessment throughout the semester:
i) Individual Intermediate Test:
• Weight of 40% in final grade.
ii) Individual Final Test:
• Weight of 60% in final grade
• Minimal grae required 8.5
iii) Weighted average for tests: at least 9.5;
v) Minimum attendance: 2/3 of classes taught
Assessment by exam: 100%

An Oral discussion may be required (for Assessment throughout semester and Assessment by exam)

Scale: 0-20 points

By the end of the UC, each student should have acquired the necessary skills to:
LO1. To know the principles of dynamic programming in discrete and continuous time, and their applications to economic growth models.
LO2. To apply fundamental concepts of optimal control, including conditions of existence and controllability, and necessary and sufficient conditions for optimality.
LO3. To develop the ability to solve optimal control problems in finite and infinite horizons, using practical examples such as optimal consumption, optimal advertising, exploitation of exhaustible and renewable resources, and investment strategies.
LO4. To know the basic concepts of stochastic control and its practical applications, such as optimal portfolio selection.
LO5. Introduce students to scientific research in the area of applying optimal and stochastic control to economics and finance.

S1. Dynamic Programming
I. Dynamic programming in discrete-time.
II. Dynamic programming in continuous-time.
III. Applications to economic growth models.
S2. Optimal Control
I. Existence and controllability.
II. Necessary and sufficient optimality conditions.
III. Optimal control in finite horizon.
IV. Optimal control in infinite horizon.
V. Examples: optimal consumption; optimal advertising; exploitation of an exhaustible resource; exploitation of a renewable resource; investment strategies.
S3. Introduction to Stochastic Control Theory
I. Introduction and motivation.
II. Basic stochastic control problem.
III. Application examples: optimal portfolio selection.

'The preferred assessment modality will be 'Assessment throughout the semester'. This assessment regime consists of: i) two practical problem sets carried out by groups of two students; ii) two individual written tests. Each assignment has a weight of 15% in the final grade, while the weight of each test is 35%. To be approved, the student must meet the following criteria: i) weighted average equal to or greater than 9.5/20; ii) grade in all assessment elements equal to or greater than 7.5/20.
Alternatively, the student can opt for the 'Assessment by exam' modality, which consists of taking an individual written test accounting for 100% of the grade.
The instructors reserve the right to, after grading the test, hold a discussion with the student to confirm that they possess the knowledge demonstrated in the exam. Whenever relevant, the provisions of the Code of Academic Conduct are also applicable.

At the end of the curricular period of this UC, the student should be able to:
1. Understand and use different stochastic calculation tools.
2. Implement hedging and speculation strategies via the financial options market.
3. Evaluate financial options using the Black-Scholes-Merton (1973) model.

1. Introduction to financial options and other derivatives
2. Hedging and speculation with options
3. Stochastic calculus
3.1. Brownian motion
3.2 Itô process
3.3. Itô’s lemma
3.4. Geometric Brownian motion
3.5 Fundamental PDE
4. Black-Scholes-Merton model
4.1 Equity options
4.2 Dividends and volatility
4.3 Index options
4.4. FX options
4.5 Futures options
4.6 Greeks

Assessment in this course provides for two types of assessment:
Regular grading system:
- One individual exam (80%)
- Individual assessment cases, attendance and active participation (20%)

Assessment by exam:
Students who do not opt for the regular grading system or fail the test may take the exam, which accounts for 100% of the final grade.

In any of the evaluation systems (regular or exam) it is considered that a student has course approval if he has a grade equal or above 9.5 points.

After completing the course, students should
(LO1) be aware of the advantages and challenges of using and developing AI based systems and models, in particular search algorithms, knowledge representation and reasoning, approaches for adaptive systems, and machine learning;
(LO2) be capable of identifying the requirements of the systems and models to create;
(LO3) be capable of choosing and the approaches more suited to the LO2 requirements
(LO4) mastering and usage of the approaches presented in the course for system development and world modelling

(CP1) Fundamental notions of AI with emphasis on the search-based approach
(CP2) Search algorithms: depth first and breadth first, A*
(CP3) The basics of machine learning: supervised, reinforcement learning and unsupervised learning
(CP4) Genetic algorithms
(CP5) Multilayer feedforward neural networks with backpropagation
(CP6) Fundamental notions relating to knowledge, representation and the architecture of knowledge-based systems
(CP7) First-order predicate logic: representation and deduction
(CP8) Declarative knowledge represented in Logic Programming
(CP9) Rule Systems based on Fuzzy Logic

Assessment throughout the semester:
- 2 Tests (35% each), minimum grade of 8.5 in each test
- 2 Project (15% each) minimum grade of 9.5 in each project


Final evaluation:
- Exam (in 3 possible dates: 1ª época, 2ª época and Special Season) 100%

The grades for the projects will result from a practical assessment conducted during an oral presentation, on the dates indicated in the respective assignment. One of the projects will be submitted mid-semester, and the other during the last week of classes. Although the projects are developed in groups, the grade assigned to each student in the group will be individualized, based on their performance in the practical assessment for each project.

The tests and the Exams may have groups of questions with a minimum grade

To access the tests and exam, it is necessary to complete all activities related to the covered topics up to this moment on Moodle.

Students may be required to explicitly enroll in any of the evaluation components

By the end of the unit, the student should have achieved the following learning goals (LG):
LG1. Know how to specify, estimate, test and interpret linear regression models based on cross-sectional data;
LG2. Recognize and solve endogeneity problems;
LG3. Know and apply panel data models;
LG4. Have the ability to choose and apply the most appropriate econometric models, methods and tests for analyzing the impact of economic policy measures and exogenous shocks.
LG5. Know how to use econometric packages in data analysis.
LG6. Have the ability to work in groups and develop theoretically-, logically- and factually-based arguments and communicate them to others.

S1. Introduction;
S2. The Simple and Multiple Linear Regression Model;
S3. Inference and Prediction;
S4. Model Specification Analysis;
S5. The Instrumental Variable Regression Model;
S6. Panel Data Linear Regression Models.

The following teaching methodologies (TM) are used:
TM1. Expositional, for presentation of models, methods and tests;
TM2. Participatory, with the analysis of empirical exercises, many of which based on real data;
TM3. Active, carrying out group work;
TM4. Experimental, with the development and estimation of models using econometric software;
TM5. Self-study, implying autonomous learning activities by the student.

By the end of this course, students should be able to:
LG1. Understand and apply classical time series models;
LG2. Assess the stationarity of a time series;
LG3. Select, apply, and evaluate ARIMA and GARCH models;
LG4. Familiarize themselves with multivariate time series models;
LG5. Work with the most important statistical software packages (R/RStudio).

P1. Classical Methods in Time Series Analysis
P1.1. Basic Concepts
P1.2. Trends and Seasonality
P1.3. Decomposition Methods
P1.4. Smoothing Methods
P2. Univariate Stochastic Models
P2.1. Models for Stationary Time Series: ARMA
P2.2. Unit Root Tests: ADF, KPSS, PP
P2.3. Models for Non-Stationary Time Series: ARIMA
P2.4. Structural Breaks: Testing and Modeling
P2.5. Diagnostics and Forecasting
P2.6. ARCH/GARCH Volatility Models: Estimation, Diagnostics, and Forecasting
P3. Introduction to Multivariate Stochastic Models
P3.1. VAR/VECM Models
P3.2. Cointegration Analysis

The assessment throughout the semester consists of:
a) An individual test, weighted at 60%.
b) A group project, weighted at 40%.

The assessment throughout the semester requires attendance in at least 80% of the classes and covers all the material taught.

Students being assessed throughout the semester who do not obtain the minimum grade of 7,5 in the individual test and 10 in the project
as well as those who do not opt for assessment during the semester, will be required to take a final exam (minimum passing grade: 10).

Upon completing the course, students should be able to:

OA1: Understand and apply structured processes to analyze, design, organize, and execute intelligent systems projects.
OA2: Develop practical skills in the critical stages of a project, from data preparation and manipulation to modeling and result evaluation.
OA3: Identify and address challenges associated with the use of real-world data.
OA4: Distinguish and select knowledge extraction algorithms appropriate for different problems, understanding their characteristics, advantages, and limitations.
OA5: Implement intelligent system solutions applied to practical problems in economic and financial contexts.

P1. Introduction to Intelligent Systems
P2. Data Manipulation and Preparation
P3. Classification and Regression Models
P4. Clustering and Cluster Analysis
P5. Unstructured Data: Computational Language Processing
P6. Ethics and Interpretability

The student must pass this course only through assessment throughout the semester modality, not contemplating the assessment by exam modality.

Assessment instruments:

- 2 written tests (20% x 2), a mid-term test and a final test, in the 1st season;
- Final Project (code, report, and presentation) with two submissions (30% x 2), one middle of the semester submission (code and report, only), which concerns the first part of the project, and another at the end of the teaching period (penultimate week, presentation in the last week) that corresponds to the complete project, including the first part (which can be improved).

Approval requirement: the final average of the tests has a minimum score of 8 points.

The Final Project must be done in group; presentation is mandatory.

In case of failure, the written tests component score can be replaced by a written test, performed during the period of the 2nd season, or special season.

LO1. Construct and analyse mathematical models based on differential equations.
LO2. Determine the analytical solution of some notable differential equations.
LO3. Obtain approximate solutions to differential equations using appropriate numerical methods.
LO4. Implement, in Python, some of the numerical methods mentioned in the previous point.
LO5. Interpret the models developed and the results obtained from them from a financial point of view.

I. Ordinary differential equations (ODEs)
1. Separable ODEs.
2. 1st and 2nd order linear ODEs.
3. Systems of linear ODEs.
4. Existence and uniqueness theorems.
5. Euler and Runge-Kutta methods.
6. Applications to natural sciences, economics and finance.
II. The heat equation.
1. introduction to partial differential equations.
2. The heat equation in physics and finance.
3. Existence and uniqueness.
4. Fundamental solution and solution in terms of Fourier series.
5. Finite differences.
6. Financial options and the Black-Scholes model.
III. Hamilton-Jacobi (HJ) equations.
1. HJ in the context of finance.
2. Fundamental properties.
3. Method of characteristics.
4. Merton's portfolio models.
5. Finite differences for HJ.
6. PINNs - Physics Informed Neural Networks.

ME1. Theoretical-practical classes: These classes will present the main concepts and techniques referred in the programme. Time will also be set aside for discussion with the students, resolution of exercises and monitoring of the project.
ME2. Laboratory classes: Development, in Pyhton, of the numerical/computational methods set out in the programme.
ME3. Project: Developed in groups throughout the semester, with the detailed analysis of a mathematical finance model, involving data and computer implementation, using PINNs - Physics Informed Neural Networks.
ME4. Self-study: Reading theoretical texts and solving exercises.