LO1: Understand the main theories, concepts, and issues related to Work, Organizations, and Technology;
LO2: Understand the main processes of the digital transition directly related to the world of work and its organizations;
LO3: Analyze the multiple social, economic, and political implications brought by the digital transition;
LO4: Explore cases, strategies, and application methods to understand the real impacts of the digital transition on professions, companies, and organizations.

PC1. Is work different today than it was in the past?
PC2. What rights and duties in the world of work?
PC3. How has theory looked at technology?
PC4. What digital technologies are changing work?
PC5. What future for work?
PC6. Is artificial intelligence really that intelligent?
PC7. Where does precariousness begin and end?
PC8. Who is to blame when the machine makes a mistake?
PC9. Do digital technologies change the relationship between unions and companies?
PC10. What digital transformation in Portugal?

Continuous assessment throughout the semester:
Each student will conduct a Flipped Classroom session, which represents 20% of the final grade.

Individual work accounting for 35% of the final grade.

Group work accounting for a total of 35% of the final grade (10% for the group presentation and 25% for the written work).

Attendance and participation in classes represent 10% of the final grade. A minimum attendance of no less than 2/3 of the classes is required.

Each assessment element must have a minimum grade of 8. The final average of the various elements must be equal to or greater than 9.5.

Examination evaluation (1st Period if chosen by the student, 2nd Period, and Special Period): in-person exam representing 100% of the final grade with a minimum grade of 9.5.

LG1 Represent geometric elements
LG2 Classify in terms of parallelism and ortogonality
LG3 Master the language of vectors and matrices and perform operations
LG4 Classify sets of vectors according to their linear dependency
LG5 Calculate determinants, interpret their value and apply properties
LG6 Solve systems of linear equations using matrices and to identify dependent variables
LG7 Understand and calculate eigenvalues and eigenvectors
LG8 Comprehend the concept of real vector space
LG9 Understand the definition of product of complex numbers as the operation between vectors leading to the structure of C as a body and as a vector space over R
LG10 Comprehend the identification of the imaginary constant with the vector (0,1)
LG11 Construct, identify, analyze and interpret linear transformations
LG12 Use Python as a tool for exploratory work
LG13 Apply knowledge and techniques to problems with context and acquire adequate skills and reasoning to formulate and solve them

PC1 Vectors in R^2 and R^3. Euclidean distance
PC2 Scalar product. Line and parameterization of segments
PC3 Vector product. Orthogonality. Projections. Vector normal to a plane
PC4 Systems of linear equations (SLEs). Gauss-Jordan elimination method
PC5 Matrix writing of SLEs. Algebra of matrices. Transpose of a matrix
PC6 Linear combination of vectors. Linear dependence. Rank of a matrix and Gauss condensation. Rouché's theorem and dependence of variables
PC7 Inverse matrix. Elementary matrices. Permutations and signal. Determinant and propertie
PC8 Minor complementary and adjoint matrix. Laplace's formula
PC9 Inverse matrix method and Cramer's rule in SLEs
PC10 Markov chains and eigenvectors and eigenvalues of a matrix. Characteristic polynomial.
PC10 Fields. R and C
PC11 Real vector spaces. R^2, R^3 and C
PC12 Linear transformations (LTs) and operators. Image and kernel
PC13 Compose of LTs. Geometric changes: uniform expansion and contraction, reflection and rotation

Approval with an overall grade of at least 10 points (scale 1-20) in one of the following modes:
- Assessment Throughout the Semester: Test 1 (35%) + Test 2 (35%) + practical group work (15%) + exercises solved on Moodle and/or in class (15%). A minimum score of 8 out of 20 is required for each assessment component.
- Exam Assessment: In any exam period, with an individual written exam (100%).

There is the possibility of conducting oral examinations.

By the end of this course unit, the student should be able to:
LO1: Apply fundamental programming concepts.
LO2: Create procedures and functions with parameters.
LO3: Understanding the syntax of the Python programming language.
LO4: Develop programming solutions for problems of intermediate complexity.
LO5: Explain, execute and debug code fragments developed in Python.
LO6: Interpret the results obtained from executing code developed in Python.
LO7: Develop programming projects.

PC1. Integrated development environments. Introduction to programming: Logical sequence and instructions, Data input and output.
PC2. Constants, variables and data types. Logical, arithmetic and relational operations.
PC3. Control structures.
PC4. Lists and Lists of Lists
PC5. Procedures and functions. References and parameters.
PC6. Objects and object classes.
PC7. File Manipulation.

This course follows a semester-long project-based assessment model due to its predominantly practical nature, and does not include a final exam.

Students are assessed based on the following components (A1 + A2):
A1: Learning Tasks with teacher validation (30%)
Five learning tasks will be completed throughout the semester.
The A1 grade corresponds to the average of the grades for the five tasks. To pass A1, the student must meet one of the following requirements:
- obtain at least 7 points in each of the five tasks
or
- obtain a minimum average of 8 points across the five tasks.

A2: Mandatory Group Project (3) with theoretical-practical discussion (70%)
Minimum grade of 9.5 points.
Late submissions will result in penalties.

Remediation:
Students who do not achieve the minimum overall grade may complete an individual Practical Project (100%) with oral discussion.
If a student misses an exam due to absence, or does not achieve the minimum grade of 7 points, they may take a make-up exam at the end of the semester.

Attendance:
A minimum attendance of 2/3 of classes is required.

LG1. Understand the concepts of vector space and vector subspace;
LG2. Understand the concept of orthogonality and apply orthogonalization methods;
LG3. Expand and apply the knowledge of eigenvalues and eigenvectors;
LG4. Classify quadratic forms and apply them to solve problems;
LG5. Understand the applications of the concepts discussed;
LG6. Apply iterative methods to approximate the solution of systems of linear equations (linear systems);
LG7. Understand how matrix decompositions facilitate algebraic approaches and the efficient application of theory in computational approaches;
LG8. Build computational algorithms.

PC1 Euclidean vector spaces. Orthogonality. Projections. Orthogonal basis. Matrix norms.
PC2 Gram-Schmidt orthogonalization.
PC3 Complex matrices. Eigenvalues and eigenvectors of skew-Hermiteanas. Schur's decomposition. Spectral theorem.
PC4 Linear and bilinear forms. Quadratic forms. Sylvester's theorem. Identification of conics.
PC5 Finite arithmetic. Rounding error. Storing.
PC6 Direct and direct methods for linear systems.
PC7 Consistency, convergence and stability of the numerical methods studied.

Approval with classification not less than 10 points (scale 1-20) in one of the following modalities:
- Assessment throughout the Semester:
* 2 practical works in Python (20% each) with a minimum grade of 7 points
* Test 1 during the semester (30%) with a minimum grade of 7 points
* Test 2 in the date of the first exam (30%) with a minimum grade of 7 points.
or
- Assessment by Exam (100%).

There is the possibility of conducting oral exams.

Minimum attendance of no less than 2/3 of classes is required.

LG1 Apprehend the generalization of limit, continuity and differentiability in multivariable functions
LG2 Calculate partial and second derivatives of any non-null vector
LG3 Interpret the gradient vector as the direction of maximum growth of the function
LG4 Decide about the existence of tangent plane
LG5 Obtain the Taylor development in several orders and explore numerically
LG6 Deepen the knowledge on sequences and series with the approach of functions
LG7 Apply Taylor formulas to determine free extrema, namely using eigenvalues
LG8 Write double integrals in different orders of integration and choose one of them to perform the calculation
LG9 Deepen the integral calculus with one variable by using integrals in this course
LG10 Apply the contents of the course in real life problems
LG11 Articulate the different approaches of the contents: graphical, numerical and algebraic

PC1. Topology of Rn. Neighborhood and accumulation point
PC2. Real and vectorial multivariable functions. Level curves and graphical transformations. Directional limits and continuity
PC3. Partial derivatives and gradient vector. Linear approximation and differentiability. Chain rule. Directional derivatives
PC4. Higher order Taylor approximations. Implicit and inverse function theorems and application.
PC5. Hessian matrices and unrestricted extrema. Optimality conditions.
PC6. Exact differential equations.
PC7. Double and triple integrals. Fubini's theorem. Change of coordinates. Polar and spherical coordinates.
PC8. Vector fields and differential forms. Relation between shapes and fields. Properties
PC9. Parameterized curves and surfaces. Tangent and normal vectors. Regularity
PC10. Line and surface integrals. Green's, Stokes' and Gauss' theorems. Conservative field
PC11. Applications of concepts in real context problems

Approval with classification not less than 10 points (1-20 scale) in one of the following modalities:
- Periodic assessment: Test 1 (15%) + Test 2 (15%) + Practical Python work (15%) + 5 online Mini Tests (15%) + Final Test (40%); minimum score of 7 points (1-20 scale) is required on the average Tests 1 and 2, and also in the Final Test
- Assessment by Exam (100%), in any of the exam periods, with individual written test

LO1. Formulate and solve problems in a structured manner.
LO2. Understand the importance of modelling in representing phenomena.
LO3. Acquire basic knowledge of mathematical algorithms.
LO4. Perform logical operations and determine the truth value of propositions.
LO5. Apply the principles of logic and quantifiers in argument formulation.
LO6. Understand the language of set theory.
LO7. Perform operations on sets and generalise them to indexed families.
LO8. Identify mathematical proof methods.
LO9. Apply mathematical induction.
LO10. Construct and interpret mathematical proofs.
LO11. Communicate mathematical reasoning with clarity and rigour.
LO12. Identify equivalence and order relations on sets.
LO13. Classify sets according to cardinality.
LO14. Understand the fundamental concepts of groups, rings, and fields.
LO15. Identify homomorphisms and isomorphisms between algebraic structures.
LO16. Apply concepts of divisibility and modular arithmetic.

PC1. Mathematical Thinking: Algorithmics, Modelling, and Problem Solving
PC2. Mathematical Logic
- Designation, Proposition, and Condition
- Connectives and Semantics
- Quantifiers
- Numerical Systems in Different Bases
PC3. Set Theory
- Definition by Extension and Comprehension, Power Set
- Operations on Sets and Generalisation to Indexed Families
PC4. Proof Methods
- Direct and Indirect Proofs
- Constructive (e.g., Algorithmic Proof) and Non-Constructive Proofs
- Mathematical Induction
PC5. Relations, Partitions, and Recursion
- Cartesian Product and Equivalence and Order Relations
- Partitions and the Equivalence Class Theorem
- Recursive Functions, Sequences, Recurrence Relations, and Summation
PC6. Cardinality, Equipotent Sets, and the Continuum Hypothesis
PC7. Algebraic Structures and Morphisms
PC8. Congruences and Modular Arithmetic
PC9. Divisibility of Integers, Euclidean Algorithm, Prime Numbers, and the Fundamental Theorem of Arithmetic

Pass with a mark of not less than 10 in one of the following ways:
- Assessment throughout the semester: 4 mini-test taken in class (20%) + 4 group works (20%) + Final written test taken on the date of the 1st period (60%); all assessment elements are compulsory and have a minimum mark of 7,0.
or
- Assessment by Exam (100%).

At the end of the course, students should be able to:
LO1: Create and Manipulate Data Structures
LO2: Apply the most appropriate sorting and search algorithms for a specific problem
LO3: Analyze the complexity and performance of an algorithm
LO4. Identify, implement, and analyze the most appropriate data structures and algorithms for a certain problem

S1. The Union-Find data structure
S2. Algorithm analysis
S3: Data structures: stacks, queues, lists, bags
S4: Elementary sorting: selectionsort, insertionsort, shellsort
S5: Advanced sorting: mergesort, quicksort, heapsort
S6. Complexity of sorting problems
S7: Priority Queues
S8. Elementary symbol tables
S9. Binary search trees
S10. Balanced search trees
S11. Hash tables

Period 1: Assessment throughout the semester or Final Exam
Assessment throughout the semester, requiring attendance at least 3/4 of the classes:
- 2 practical tests (60%), with a minimum grade of 7.5 in each.
- 2 theoretical tests (40%), with a minimum grade of 7.5 in each.
The final weighted average between the theoretical and practical tests must be equal to or higher than 9.5.
Assessment by Exam:
- (100%) Final Exam with theoretical and practical components
Students have access to the assessment by Exam in Period 1 if they choose it at the beginning of the semester or if they fail the assessment throughout the semester.
Period 2: Final Exam
- (100%) Final Exam with theoretical and practical components
Special Period: Final Exam
- (100%) Final Exam with theoretical and practical components

LG1 Understand the completeness of R and consequences
LG2 Apprehend the concepts of succession and series in order to obtain Taylor formulas and Riemann sums
LG3 Obtain the sum function and convergence domain in power series
LG4 Apprehend the concept of function and importance in modelling
LG5 Understand the concept of limit and the characterization of continuous functions through successions
LG6 Analyze the asymptotic behavior of functions and the evolution of sequences regarding monotonicity, limitation and convergence
LG7 Obtain Taylor approximations (several orders) and apply them in real context problems
LG8 Understand the notion of partition and integral as the limit of Riemann sums, and apply the fundamental theorem
LG9 Apply derivatives, successions, series and integrals to solve problems with context
LG10 Articulate different approaches to the contents: graphical, numerical and algebraic

PC1 Real lines and algebra in R. Completeness. Absolute value
PC2 Sequences of real numbers. Recursive definition. Monotonicity. Supreme and infinity. Convergence and framing.
PC3 Notion of numerical series, partial sums and sum. Arithmetic, geometric and harmonic series
PC4 Power series. Convergence
PC5 Functions of R in R. Elementary functions. Parity and transformations to the graph. Period and frequencies.
PC6 Compound and inverse. Asymptotic behavior.
PC7 Logarithm function. Inverse trigonometric. Identities and trigonometric algebra.
PC8 Limits. Continuity. Weierstrass and intermediate value theorems.
PC9 Derivative at a point and its meaning. Mean value theorem. Chain rule and inverse derivative. Implicit derivation
PC10 Taylor approximations. Local and/or global extremes.
PC11 Partitions. Antiderivatives. Riemann definite integral. The fundamental theorem of calculus. Change of variables. Improper integrals. Criteria of integrability

The assessment is aligned with the four components of the 4C/ID model, combining part-task practice, learning tasks, project work, and summative assessment.

General Criteria:
• Minimum passing grade: 10 out of 20
• Minimum attendance requirement: two-thirds of in-person sessions
• Oral defense is mandatory for final grades ≥17 out of 20
• Two assessment options: “Continuous Assessment” or “Final Exam” (100% exam)

Continuous Assessment (CA):
1. Formative Assessment (40% of final grade)
a) Part-Task Practice – Quizzes or Forums (5%)
* Frequency: weekly, via the online platform
* Immediate feedback and unlimited repetition until mastery
* Success criterion: score ≥16 out of 20 on each task
b) In-Class Learning Tasks (30%)
* Total of 9 tasks (3 per topic: sequences and series, differential calculus, integral calculus), with the 7 highest scores considered
* Tasks completed during class
* One task per topic may be repeated
* Minimum score to qualify for the summative exam: 8 out of 20
* Each task assesses:
- Mathematical accuracy
- Integration of concepts (graphical, numerical, algebraic)
- Clarity of scientific reasoning
c) Reflective Journal and Independent Work (5%)
* Biweekly entries (2–3 paragraphs) on difficulties and problem-solving strategies
* Assesses: self-regulation and content ownership
2. Pair Project – 10%
a) Task: Model a real-world phenomenon by integrating:
* Power series (LO3, LO7)
* Derivatives and asymptotic analysis (LO6, LO9)
* Definite/improper integrals (LO8, LO9)
b) Format: written report (max. 5 pages) + computational demonstration
3. Summative Assessment (Final Test) – 50%
a) Mixed Format:
* Part A: Part-task practice questions
- Short exercises on limits, derivatives, and basic integrals
* Part B: Integrated learning task
- Contextualized problem
b) Minimum passing grade for the test: 8 out of 20

Assessment by Final Exam Only:
a) Global Exam (100% of final grade)
b) Minimum passing grade: 10 out of 20

Oral Defense:
a) Mandatory for students with a final grade ≥17 out of 20
b) Duration: 15 minutes per student
c) Purpose: to confirm understanding of concepts, reasoning, and scientific communication skills

At the end of this UC, the student should be able to:
OA.1 Define requirements for a technology project
OA.2. Elaborate the schedule according to the proposed objectives for the project
OA.3. Develop the project according to requirements
OA.4. Develop test plan
OA.5. Test the project (partial and integrated)
OA.6. make the adaptations
OA.7. Techniques for presenting technological projects
OA.8. Preparation of demonstration of its features
OA9: Standards for the preparation of technical reports

I. Introduction to technological innovation along the lines of Europe
II. Planning a technological project and its phases
III. Essential aspects for the development of a project
IV. Definition of material resources
V. Budget of a project
VI. Partial and joint Test Plan
VII. Presentation of a technological project
VIII. Technological project demonstration
IX. Preparation of Technical Report

Periodic grading system:
- Group project: first presentation: 30%; second presentation and exhibition: 40%; final report: 30%. The presentations, demonstrations and defence are in group.

OA1 - To be trained in the ethical and responsible use of Generative Artificial Intelligence (AI) tools
OA2 - To acquire critical analysis skills on the results produced by Generative AI tools
OA3 - To be able to identify and develop creative solutions in solving ethically and socially complex problems with Generative AI
OA4 - To be able to apply Generative AI tools in the preparation of academic work, in particular in the application of academic writing and in the use of normative citation and referencing procedures.

CP1 - Introduction to AI and Generative AI:
* Theoretical exposition on the historical context, evolution and important concepts about Artificial Intelligence (AI) and Generative AI
CP2 - Prompt Engineering:
* Explanation of good practices for interacting with generative language models
CP3 - Generative AI Tools:
* Exploration of multiple Generative AI tools, based on text, images and videos
CP4 - Formation of argumentative content:
* Development of creative solutions using argumentation practices and Generative AI tools
CP5 - Rules for scientific writing:
* Application of citation and referencing standards (APA standards) in academic writing

The Semester-Long Assessment includes the following activities:
1. Individual Activities (50%)
1.1 Prompt Simulations with AI Tools in an Academic Context (20%):
* Description: The student must create a clear/justified, well-structured prompt, according to the script proposed by the instructor in class.
* Assessment: (submit in Moodle), communication and teamwork skills based on the quality of the prompt simulations performed.
1.2 Oral Defense - Group Presentation - 5 min. Discussion - 5 min. (30%):
* Description: Each student must present their contributions to the work completed to the class.
* Assessment: After the student's presentation, there will be a question-and-answer session.
2. Group Activities (50%) [students are organized into groups of up to 5 students, randomly selected], which include:
* Group presentations, reviews, edits, and validations of AI-generated content. The assessment (to be submitted in Moodle) includes gathering relevant information, assessing the clarity and innovative nature of the use of structured prompts.
* Development of strategies for reviewing, editing, and validating AI-generated content. Students will be asked to critically evaluate and reflect on the ethical challenges of integrating AI into an academic environment. The assessment (to be submitted in Moodle) will consist of correcting the work based on the accuracy and quality of the reviews and edits, as well as student participation in providing feedback to their peers.
* Final Project Presentation Simulations, where groups choose a topic and create a fictitious project following the structure of a technical report or scientific text. They present their project in class (5 min.) and discuss the topic (5 min.). The assessment (to be submitted in Moodle) will consider the organization, content, correct use of the structure, and procedures of the academic work.

General Considerations:
Feedback on student performance in each activity will be provided during the Semester Assessment.
To be assessed throughout the semester, students must attend 80% of classes and achieve a score of at least 7 points in each assessment.
If there are questions about participation in the activities, the instructor may request an oral discussion.
The group must ensure that at least one computer is available for each group to allow for classroom activities.
There will be no final exam assessment; passing will be determined by the weighted average of the assessments throughout the semester. Assessments in the second and special assessment periods will have an alternative assessment method, so any students wishing to take the assessment in these assessment periods should contact their instructor in advance to learn about the assessment procedure.

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. 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 the learning unit, the student must be able to: LG.1. Understand entrepreneurship; LG.2. Create new innovative ideas, using ideation techniques and design thinking; LG.3. Create value propositions, business models, and business plans; LG.5. Develop, test and demonstrate technology-based products, processes and services; LG.6. Analyse business scalability; LG.7. Prepare internationalization and commercialization plans; LG.8. Search and analyse funding sources

I. Introduction to Entrepreneurship; II. Generation and discussion of business ideas; III. Value Proposition Design; IV. Business Ideas Communication; V. Business Models Creation; VI. Business Plans Generation; VII. Minimum viable product (products, processes and services) test and evaluation; VIII. Scalability analysis; IX. Internationalization and commercialization; X. Funding sources

Periodic grading system: - Group project: first presentation: 30%; second presentation: 30%; final report: 40%.

At the end of this UC, the student should be able to:
LG.1. Present the image of the product/service in a website
OA.2. Present the image of the product/service in social networks
OA.3. Describe functionalities of the product/service
OA.4. Describe phases of the development plan
OA.5. Develop a prototype
OA.6. Test the prototype in laboratory
OA.7. Correct the product/service according to tests
OA.8. Optimize the product/service considering economic, social, and environmental aspects
OA.9. Adjust the business plan after development and tests, including commercialization and image
OA.10. Define product/service management and maintenance plan

I. Development of the product/service image
II. Functionalities of the product/service
III. Development plan
IV. Development of the product/service (web/mobile or other)
V. Revision of the business plan
VI. Management and maintenance of the product/service
VII. Certification plan
VIII. Intellectual property, patents, and support documentation
IX. Main aspects for the creation of a startup - juridical, account, registry, contracts, social capital, obligations, taxes

Periodic grading system:
- Group project: first presentation: 30%; second presentation: 30%; final report: 40%. The presentations, demonstrations and Defence are in group.

By the end of the course, students should have acquired the following skills:
LO1 - understand the fundamental concepts of inferential statistics;
LO2 - calculate the size of a sample;
LO3 - estimate and interpret a confidence interval;
LO4 - choose the test to use in each situation;
LO5 - apply and interpret statistical tests;
LO6 - carry out the chosen test using statistical software;
LO7 - know how to report statistical results in a report;
LO8 - analyze bivariate data.

S1. Basic concepts of descriptive statistics, inferential statistics, probabilities and normal distribution
S2. Estimation
S2.1 Confidence intervals for the mean and proportion
S2.2 Determining sample size
S3. Hypothesis tests: parametric and non-parametric tests
S3.1 One-sample t-test
S3.2 t/Mann-Whitney test for two independent samples
S3.3 One-factor ANOVA/Kruskal-Wallis
S3.4 Chi-squared test of independence
S4: Correlation and Regression Line

Pass with a mark of not less than 10 in one of the following ways:
- Assessment throughout the semester: 1 mini-test taken in class (20%) + Final written test taken on the date of the 1st period (60%) + group project (20%),
All assessment elements are compulsory and have a minimum mark of 8.
or
- Assessment by Exam (100%).

Notes:
1) A complementary oral assessment may be conducted after any evaluation moment to validate the final grade.
2) For this Course Unit, students must consult the Iscte Academic Code of Conduct, available on the institutional platforms, to ensure compliance with the established ethical and behavioral standards.

The learning outcomes (LO) of this course are:
LO1. Understand the relevance and challenges that exist in the field of analytical and numerical solutions for nonlinear models;
LO2. Identify the main methodologies for solving static nonlinear models;
LO3. Identify the main methodologies for solving dynamic linear and nonlinear models;
LO4. Gain ability to use numerical approximations methods for solving nonlinear models, when analytical methods fail;
LO5. Understand why it is necessary to employ numerical methods to obtain an approximate solution and the consequences of an inexact approximation;
LO6. Recognize the importance of numerical approximation methods and the variety of applications in real life problems.
LO7. Communicate the results of numerical computation, with appropriate and clear explanations supported by graphical material.

PC1. Introduction to numerical methods with Python
PC2. Convergence and stability. Error and loss of meaning of numerical approximation
PC3. Numerical derivation. Analytical solution of ordinary differential equations (ODE) of order 1 and 2. Numerical solution of ODE of order 1 (Runge-Kutta method); existence and uniqueness of solutions
PC4. Surface parameterisation and calculation of surface integrals. Spherical coordinates. Numerical integration: Newton-Cotes formulae and Gauss-Legendre quadrature for different numbers of points; graphical interpretation of the quadrature; integration error
PC5. Zeros of a function and finding extremes of functions (with and without differentiability, with and without continuity); bisection and Newton methods, secant method. Introduction to the solution of non-linear systems (Newton's method for systems)
PC6. Difference equations and iterative methods
PC7. Solving higher-order ODEs (Euler finite difference approximations)

Approval with classification not less than 10 points (0-20 scale) in one of the following modalities:
- Assessment Throughout the Semester: one midterm test (25%) + autonomous work exercises submitted in Moodle (5%) + one project with Python in group work (20%) + final individual written test (50%). A minimum score of 7,5 out of 20 is required in each of the midterm test and the final test. Attendance of at least 2/3 of the classes is required. There may be an oral test whenever this clarifies the teacher's opinion of the student's classification.
- Assessment by Exam (100%), in any of the exam periods, with an individual written test.

By the end of this course unit, the student should be able to:
LO1: Understand fundamental concepts and representation of graphs.
LO2: Analyse paths and perform searches in networks.
LO3: Calculate centrality measures and analyse network structures.
LO4: Apply distributions and algorithms to complex networks.
LO5: Model networks and adapt empirical data to network models.
LO6: Use computational tools for network representation and visualisation.

P1. Fundamentals of Graphs and Networks
1.1. Introduction to Graph Theory
1.2. Mathematics of Graphs
1.3. Search Algorithms

P2. Structure and Dynamics of Complex Networks
2.1. Metrics and Centrality Measures
2.2. Network Models
2.3. Advanced Topics

P3. Applications and Visualisation of Networks
3.1. Adapting Data to Network Models
3.2. Applications in Various Fields
3.3. Network Visualisation with Computational Tools

Approval requires a grade of no less than 10 out of 20 in one of the following modalities:
- Assessment throughout the semester: 1 group project (40% - presentation on the date of the 1st exam period) + 2 midterm tests (25% each) + autonomous work activities (10%); all assessment components require a minimum grade of 8 out of 20.
- Assessment by Exam (100%), in any of the exam periods.
- A complementary oral assessment may be conducted after any assessment moment to validate the final grade.

LO 1 Explain what databases and information systems are, characterising them in terms of both technology and their importance to organisations.
LO 2. formally represent information requirements by drawing up conceptual data models.
LO 3 Explain the Relational Model and data normalisation, highlighting their advantages and the situations in which they should be applied.
LO 4 Design relational databases that respond to requirements specified by conceptual data models.
LO 5. build and programme a relational database using the SQL language.
LO 6. manipulate data - i.e. insert, query, alter and delete - using the SQL language.
LO 7. Explain what database administration consists of, why it is necessary and how its most essential tasks are carried out.

S1. Introduction to Information Systems and their role in organisations.
S2. Introduction to Information Systems Analysis with UML: Introduction, requirements analysis, data models, schemas and UML diagrams.
S3. Database Design. Relational Model: relationships, attributes, primary keys, foreign keys, integrity rules, normalisation and optimisations.
S4. SQL Language. Tables, relational algebra, simple queries, subqueries, operators (SELECT, Insert, delete, update), views, indexes, triggers, stored procedures and transactions.
S5. Administration and Security in Database Management Systems (DBMS).

Assessment throughout the semester:

- 3 tests to be taken during the semester (70%). Minimum grade of 8 points for each tests.
- 1 modelling and implementation project (in groups of up to 3 people) (30%). The minimum project grade is 10 points. Completion of the project is mandatory for approval. The project is assessed in groups with individual oral discussion.

Assessment by exam:
- One exam, weighted 100%

The minimum passing grade for the course unit is 10 out of 20.
Attendance at 2/3 of the scheduled classes is mandatory for approval.

At the end of the course unit, students should:
LO1: Recognize the advantages and challenges of using Artificial Intelligence (AI) techniques and approaches, demonstrating critical awareness of informed and uninformed search methods.
LO2: Select and justify the most appropriate technological approaches and algorithms, including search methods, representation, and reasoning logics.
LO3: Apply the concepts and techniques discussed in the design and development of AI-based systems, as well as in the modeling of examples based on real scenarios.
LO4: Develop, implement, and evaluate solutions involving predicate logic and logic programming.
LO5: Understand the fundamentals of fuzzy logic and be able to implement fuzzy logic-based solutions to solve specific problems.
LO6: Work autonomously and in groups to develop projects that apply the acquired knowledge, demonstrating the ability to adapt and solve complex problems in the AI field.

S1: Fundamental notions of AI with emphasis on the search-based approach.
S2: Search algorithms: depth first and breadth first, A*, greedy BFS, Dijkstra.
S3: Fundamental notions relating to knowledge, representation and the architecture of knowledge-based systems.
S4: First-order predicate logic: representation and deduction.
S5: Declarative knowledge represented in Logic Programming.
S6: Fuzzy logic.

The assessment throughout the semester (ALS) consists of three assessment blocks (AB) and each AB consists of one or more assessment moments. This structure follows the following distribution:

- AB1: 2 practical mini-tests [20% each practical mini-test * 2 = 40%]
- AB2: 2 theoretical mini-tests [15% each theoretical mini-test * 2 = 30%]
- AB3: 1 final project [30%]

Exam assessment:
- 1st Epoch [100%]
- 2nd Epoch [100%]

The practical mini-tests, taken individually in class, focus on problem solving, involving the implementation, analysis, and validation of algorithms.

The theoretical mini-tests, also taken individually in class, aim to assess the theoretical knowledge underlying the syllabus content.

The project consists of a group deliverable, including individual oral discussions, which allows for the assessment of content consolidation and problem-solving skills.

In any AB, an individual oral discussion may be required to confirm authorship and/or assess knowledge mastery at any time during the semester.

All periodic assessment blocks (AB1, AB2, and AB3) have a minimum grade of 8.5.

The student's physical presence is mandatory in all assessment elements, under penalty of failure in the CU and/or assignment of 0 points to the assessment element.

To pass the course unit, students must achieve a minimum final grade of 10, resulting from the weighted sum of all assessment elements.

The exam assessment consists of a written exam covering all the knowledge included in the course unit syllabus and has a weighting of 100%.

Class attendance is not mandatory.

LO1: Identify data types and the main steps in the data analysis process.
LO2: Organize and prepare data in spreadsheets.
LO3: Understand and use the main concepts of descriptive statistics, choosing appropriate measures and graphical representations to describe the data.
LO4: Explain what a data model is and understand some predictive data modeling techniques.
LO5: Create effective visualizations with pivot tables and graphs.
LO6: Interpret results and present conclusions clearly and reasonedly.

CP1: Introduction to data analysis – types, sources, and data lifecycle.
CP2: Organizing and cleaning data in Excel – formats, filters, validation. Basic and advanced Excel functions – statistics, logic, search, and reference.
CP3: Basics of Descriptive Statistics: Types of variables. Frequency tables and graphical representations. Measures of central tendency, dispersion, skewness, and kurtosis. Exploratory data analysis.
CP4: Basics of predictive data modeling: Simple and multiple linear regression, logistic regression.
CP5: Data visualization – graphs, conditional formatting, simple dashboards.

Assessment throughout the semester includes:

- Practical data analysis project completed in a group (maximum 3 students), including a report (15%), with mandatory midterm submission (15%) and oral defense with individual grading (20%). Minimum grade of 8 points.
- Individual exam (30%) to assess theoretical knowledge.
- In-class exercises and weekly assignments (20%).

The use of AI tools (e.g., ChatGPT) is permitted for technical support and must be clearly referenced with the prompts used.

The Final Exam is a written, individual, closed-book exam covering all material.

Those who do not opt ​​for assessment throughout the semester take the final exam in Period 1.

Those who did not successfully complete the assessment throughout the semester, or the exam in Period 1, with a score greater than or equal to 9.5 (out of 20), take the final exam in Period 2.

LO1. Understand mathematical modelling (MM) and identify the stages of the process.
LO2. Distinguish between different types of mathematical models.
LO3. Understand the challenges in creating models for real-world phenomena.
LO4. Formulate models using ordinary differential equations (ODEs) or systems of ODEs.
LO5. Solve ODEs and systems of ODEs using analytical techniques and computational support.
LO6. Apply the Laplace transform to ODEs.
LO7. Analyse systems of ODEs in various contexts.
LO8. Identify and classify equilibrium points of dynamical systems (DS).
LO9. Study the qualitative behaviour of DS using phase diagrams.
LO10. Implement mathematical models in Python.
LO11. Computationally simulate physical phenomena and biological systems.
LO12. Evaluate models through parameter adjustment and numerical error analysis.
LO13. Apply MM techniques in engineering, physics, biology, economics, and finance.
LO14. Communicate model analysis and conclusions clearly and rigorously.

PC1. Introduction to Mathematical Modelling (MM)
- MM cycle: formulation, analysis, validation, and interpretation
- Deterministic vs stochastic and continuous vs discrete models
PC2. Ordinary Differential Equations (ODE)
- ODE-based models: populations, radioactive decay, fluid dynamics, epidemiology, harmonic oscillator, and electrical circuits
- First-order ODE: separation of variables, integrating factor, exact and linear equations.
- Second-order ODE: linear equation with constant coefficients and the Laplace transform
- Systems of ODE
PC3. Introduction to Dynamical Systems (DS)
- Equilibrium points and stability
- Phase diagrams and qualitative analysis of DS
- Attractors, bifurcations, and chaotic behaviour
PC4. MM and Computational Simulation
- Examples of MM in enginnering, physics, biology and economics
- Computational implementation of models
- Simulation of physical phenomena and biological systems
- Model validation: parameter adjustment and error analysis

Approval requires a grade of no less than 10 out of 20 in one of the following modalities:
- Assessment throughout the semester: 1 final test (40% - on the date of the 1st exam period) + 2 midterm tests (25% each) + autonomous work activities (10%); the average of the two midterm assessments must be at least 8 out of 20.
- Assessment by Exam (100%), in any of the exam periods.
- A complementary oral assessment may be conducted after any assessment moment to validate the final grade.

LO1. Know the history of machine learning; know and understand the different types of machine learning: concepts, foundations and applications.
LO2. Know the concepts that enable Exploratory Data Analysis (EDA) to be carried out, as well as understanding its importance in problem-solving and decision-making.
LO3. Learn Data Wrangling mechanisms - preparing data for input to a supervised algorithm.
LO4. Know how to use continuous and categorical variables; distinguish between classification and regression
LO5. Know and analyze the results by applying performance evaluation metrics
LO6. Understand supervised algorithms: decision trees, linear and logistic regression, SVMs, Naive-Bayes and k-NN.
LO7. Understand ensemble algorithms: bagging and boosting
LO8. Know and understand hyperparameter optimization

S1. Introduction to Machine Learning: The history, foundations and basic concepts
S2. Exploratory Data Analysis (EDA): Data Wrangling and Data Visualization
S3. Classification and Regression; Continuous and categorical / discrete variables; performance evaluation metrics
S4. Supervised Learning: SVM, Decision Trees, Linear and Logistic Regression, Naive-Bayes and k-NN.
S5. Bagging and Boosting in supervised algorithms
S6. Hyperparameter optimization

This course unit (CU), due to its highly practical and applied nature, follows a 100% project-based continuous assessment model throughout the semester; therefore, it does not include a final exam. The assessment consists of 3 assessment blocks (AB), and each AB includes one or more assessment moments. The distribution is as follows:

- AB1: 1st tutorial + 1st mini-test [20% for the 1st tutorial + 10% for the 1st mini-test = 30%]
- AB2: 2nd tutorial + 2nd mini-test [20% for the 2nd tutorial + 10% for the 2nd mini-test = 30%]
- AB3: 3rd tutorial + 3rd mini-test [30% for the 3rd tutorial + 10% for the 3rd mini-test = 40%]

Tutorials consist of projects to be developed in groups, which also include individual oral discussions, allowing for the assessment of students' performance in these same projects.

Mini-tests, taken individually, allow for the assessment of theoretical knowledge applied to each of the projects evaluated in tutorials.

In any AB, there may be a need to conduct an individual oral discussion to assess knowledge.

All periodic assessment blocks (AB1, AB2, and AB3) have a minimum grade of 8.5.

The student's physical presence is mandatory in all assessment elements, under penalty of failure in the curricular unit and/or assignment of 0 points to the assessment element.

This CU may include the participation of external organizations or companies, which may propose projects that are properly framed within the curriculum and aligned with the learning objectives of the CU.

The 1st and 2nd Epochs may be used for assessment.

Class attendance is not mandatory.

The learning goals (LGs) of this Course Unit (CU) are:
LG1. Becoming familiar with the concepts and results in complex analysis.
LG2. Understand the inner product and the concept of orthogonality through the study of orthogonal functions.
LG3. Understand the concept of series of functions, namely passing from power series to trigonometric harmonic and harmonic exponential series.
LG4. Obtain solutions for initial value problems based on Fourier analysis.
LG5. Apply the Fourier transform, mainly based on its properties.
LG6. To obtain the characteristics of a signal, both in time and frequency domain.
LG7. Apply Python in the exploration of the contents, signal analysis and description of the analysis of experimental or simulated data

PC1. Polynomials and complex numbers. Elementary complex functions. Laplace equation. Laurent series. Pointwise and uniform convergence. Euler formula.
PC2. Complex variable method for numerical derivation of real functions. Cauchy integral formulas.
PC3. Discrete and continuous signals. Periodicity and generalized function.
PC4. Orthogonality of functions. Fourier series: trigonometric and complex exponential form. Convergence
PC5. Series in solution of differential equations (DEs). Separation of variables. Heat equation. Semi-linear DE. Wave Equation.
PC6. Fourier Transform. Convolution. Partial Black-Scholes Partial DE
PC7. Diagrams (amplitude and phase) of signals in time and frequency domains.
PC8. Discrete Fourier methods. Discrete Fourier Transform: aliasing and the sample theorem.
PC9. Fast Fourier Transform (FFT) and spectral methods. Power spectrum and Parseval's theorem
PC10. Applications to experimental and simulation data

Approval with a grade not lower than 10 points (scale 1-20) in one of the following modalities:
- Assessment Throughout the Semester:
* 3 group practical assignments (20% each) with a minimum grade of 7 points.
* 2 tests (20% each) with a minimum grade of 7 points.

or

- Examination Assessment (100%).

There is the possibility of oral examination.

After completing this UC, the student will be able to:

LO1. Identify the main themes and debates relating to the impact of digital technologies on contemporary societies;
LO2. Describe, explain and analyze these themes and debates in a reasoned manner;
LO3. Identify the implications of digital technological change in economic, social, cultural, environmental and scientific terms;
LO4. Predict some of the consequences and impacts on the social fabric resulting from the implementation of a digital technological solution;
LO5. Explore the boundaries between technological knowledge and knowledge of the social sciences;
LO6. Develop forms of interdisciplinary learning and critical thinking, debating with interlocutors from different scientific and social areas.

S1. The digital transformation as a new civilizational paradigm.
S2. The impact of digital technologies on the economy.
S3. The impacts of digital technologies on work.
S4. The impact of digital technologies on inequalities.
S5. The impacts of digital technologies on democracy.
S6. The impacts of digital technologies on art.
S7. The impacts of digital technologies on individual rights.
S8. The impacts of digital technologies on human relations.
S9. The impacts of digital technologies on the future of humanity.
S10. Responsible Artificial Intelligence.
S11. The impact of quantum computing on future technologies.
S12. The impact of digital technologies on geopolitics.

The assessment process includes the following elements:

A) Ongoing assessment throughout the semester
A1. Group debates on issues and problems related to each of the program contents. Each group will participate in three debates throughout the semester. The performance evaluation of each group per debate will account for 15% of each student's final grade within the group, resulting in a total of 3 x 15% = 45% of each student's final grade.
A2. Participation assessment accounting for 5% of each student's final grade.
A3. Final test covering part of the content from the group debates and part from the lectures given by the instructor, representing 50% of each student's final grade.
A minimum score of 9.5 out of 20 is required in each assessment and attendance at a minimum of 3/4 of the classes is mandatory.

B) Final exam assessment Individual written exam, representing 100% of the final grade.

At the end of the course, the student should be able to:
LO1: Apply co-creation methodologies in the development of innovative triple sustainable projects (with economic, social and environmental value) in organizations.
LO2: Create empathy with the user and his organization (define needs, obstacles, goals, opportunities, current and desired tasks), define the problem and raise the issues addressed by the project.
LO3: Conduct a systematic literature review and competitive landscape analysis (if applicable), related to the identified problem and the issues raised.
LO4: Identify the digital (including data collection), computational and other resources needed to address the problem.
LO5: Apply already consolidated knowledge of project planning, agile management and project development, within the framework of group work.
LO6: Participate in collaborative and co-creation dynamics and make written and oral presentations, in the context of group work.

S1 Co-creation methodologies based on Design Thinking and Design Sprint
C2 Sustainable Development Goals (SDGs) of the United Nations. Creation of value propositions
S3 Presentation of case studies and digital technologies project topics of applied mathematics (product, service or process)
S4 Selecting the project topic and framing it in the organization
S5 Problem space: creating empathy with the user and his organization, defining the problem and its related issues, considering business requirements, customer and user needs, and technology challenges
S6 Application of a systematic literature review methodology and its critical analysis. Competition analysis (if applicable)
S7 Identification of digital resources (including data collection), computational, and other resources required for project development.
S8 Application of agile project management methodologies, appropriate to the group work to be developed by the students of applied mathematics. Communication of results.

Course in periodic assessment, not contemplating final exam, given the adoption of the project-based teaching-learning method applied to real situations. Presentations, demonstrations and discussion will be carried out in groups.
Assessment weights:
R1 Report: Project Topic Definition: 5%.
R2 Report: Empathy with the User and the Organization and Definition of the Problem. Its presentation and group discussion: 40%
R3 Report: Systematic Literature Review and Project Development Planning. Its presentation and group discussion: 55%.

The learning goals (LGs) of this CU are:
LG1. Understand the correlation between variables, the simple and multiple linear regression model.
LG2. Understand and apply parameter estimation methods (OLS-Ordinary Least Squares and ML-Maximum Likelihood).
LG3. Know how to analyse regression model assumptions, hypothesis tests and diagnostics.
LG4. Understand the extensions to the linear regression model: non-linear models.
LG5. Obtain skills in forecasting, forecast performance and decision-making.
LG6. Apply logistic regression, classification, confusion matrix and ROC curve (Receiver Operating Characteristic) and QCA (Qualitative Comparative Analysis).
LG7. Acquire practice in basic programming and computing.
LG8. Apply the concepts studied to real data/cases.

PC1. Regression models: correlation and causality, simple linear regression, multiple regression. Multicollinearity
PC2. Estimation and inference, OLS (Ordinary Least Squares) and ML (Maximum Likelihood).
PC3. Residual assumptions: hypothesis tests and diagnostics
PC4. Polynomial regression and regression with categorical variables. Dummy variables
PC5. Forecasting (in-sample and out-of-sample). Training and test sets. Metrics for assessing forecasting performance (RMSE-Root Mean Squared Error, MAPE-Mean Absolute Percentage Error, MAE-Mean Absolute Error). Predictive analysis
PC6. Logistic regression. Classification problems. Confidence matrix and ROC (Receiver Operating Characteristic) curve.
PC7. Fuzzy sets. QCA (Qualitative Comparative Analysis) on dichotomous variables (csQCA) and on fuzzy sets (fsQCA). Stepwise and temporal QCA (mvQCA and tQCA)
PC8. Other multivariate statistical models: cluster analysis, discriminant analysis and principal components

Pass with a mark of not less than 10 (scale 1-20) in one of the following ways:
- Assessment throughout the semester: a test taken on the date of the 1st term (60%) + practical assignment(s) (30%) + autonomous work (10%).
All assessment elements are compulsory and have a minimum mark of 8.
A complementary oral assessment may be carried out after any assessment moment to validate the final grade.
or
- Assessment by Exam (100%).

LG1. Formulate problems in linear and non-linear programming, integer programming and goal programming.
LG2. Distinguish between linear and non-linear problems.
LG3. Adjust and apply the theoretical knowledge to solve concrete problems.
LG4. Solve mathematical models and interpret the solutions.
LG5. Interpret the sensitivity analysis reports.
LG6. Understand the theoretical assumptions inherent to optimality conditions.
LG7. Understand the specificity of convex optimization.
LG8. Distinguish between local and global extremes and the difficulties in their classification.
LG9. Adapt and apply iterative methods of line-search.
LG10. Distinguish the advantages and limitations of the applied methods (convergence, robustness).
LG11. Carrying out technical analysis (single objective) and making trade-off decisions (multiple objectives).
LG12. Identify the adequate approach or algorithm for a given optimization problem.

PC1. Formulation of optimization problems. Free versus constrained optimization.
PC2. Linear versus nonlinear programming
PC3. Optimality conditions. Limitations of analytical methods
PC4. Concept of convex set and convex function. Convex Optimization.
PC5. Geometric solving techniques
PC6. Linear programming methods. Simplex and big-M
PC7. Duality. Dual problem and Simplex dual algorithm
PC8. Interpretation os solutions and sensitivity analysis
PC9. Discrete optimization fundamentals. Binary, integer and mixed integer programming. Cutting plans. Hybrid Methods.
PC10. Multi-objective linear programming. Goal-oriented programming. Sequential and penalty-weight methods.
PC11. Polynomial approximations and line search methods. Convergence criteria.
PC12. Lagrangean duality. Karush-Kuhn-Tucker conditions.

Approval with classification not less than 10 points (1-20 scale) in one of the following modalities:
- Periodic assessment: Intermediate Test (20%) + 2 Group Work in Python (2x15%) + Autonomous work (10%) + Final Test (40%); minimum score of 7 points (1-20 scale) is required in the Final Test
- Assessment by Exam (100%), in any of the exam periods, with individual written test.

LO1. Study the basic concepts of the theory of stochastic processes
LO2. Understand the most important types of stochastic processes and study the properties and characteristics of processes
LO3. Understand the methods of description and analysis of complex stochastic models
LO4. Verify how stochastic processes are widely used in the analysis of complex networks, ranging from the generation of a network with particular characteristics to dynamic modeling in a network
LO5. Understand the nature of diffusion processes in a network , where information diffusion is ubiquitous
LO6. Understand the most important types of stochastic processes (Markov, Poisson, Gaussian, Wiener and other processes) and be able to find the most suitable process for numerical modelling
LO7. Understand the mathematical study and numerical simulation of branching processes that reveal the dissemination of information in a network

This CU has the following programmatic contents (PCs):

PC1. Brief review of some concepts of probability theory;
PC2. Introduction to stochastic processes. Different types of stocastic processes: discrete vs continuos descriptions of time and space variable;
PC3. Markov chain: Basic properties;
PC4. Poisson processes;
PC5. Some concepts in measure theory. Wiener processes and Brownian motion;
PC6. Basic theory of stochastic differential equations;
PC7. Numerical methods;
PC8. Study of difussion models in a graph. Applications to complex networks;
PC9. Numerical simulation of a branching process that reveals the dissemination of information in a network.

Approval with an overall grade of at least 10 points (scale 1-20) in one of the following modes:
- Assessment Throughout the Semester: Test 1 (35%) + Test 2 (35%) + practical work in Python (15%) + exercises solved on Moodle and/or in class (15%). A minimum score of 7 out of 20 is required for each assessment component.
- Exam Assessment: In any exam period, with an individual written exam (100%).

LO1: Correct the user and/or organization problem identified in the Applied Project I course of the 1st semester, developing, in an iterative way, an integrated project with all its components, including requirements gathering, solution prototyping (lo-fi, hi-fi, MVP), and evaluation and field deployment of the innovative solution, regarding product, process or service (PPS).
LO2: Produce design documentation of the PPS innovation solution, including, where applicable, architecture, hardware and software configuration, installation, operation and usage manuals.
LO3: Produce solutions with the potential to be triple sustainable in the field, taking into account the applicable legal framework.
LO4: Produce audiovisual content on the achieved results, to be exploited in several communication channels: social networks, landing page web, presentation to relevant stakeholders, demonstration workshop.

S1. Solution space: ideation of the best technological solution relative to the project, development of user requirements, storyboarding, user/costumer journey, iterative prototyping cycles (low fidelity - lo-fi, high fidelity - hi-fi, minimum viable product - MVP), heuristic evaluation of the solution with experts and evaluation with end users.
S2. Production of solution design documentation, including, where applicable, architecture, technical specifications, hardware and software configuration, installation, operation and use manuals.
S3. Experimental deployment of the solution with the potential to be triple sustainable (with economic, social and environmental value creation), safeguarding the applicable legal framework.
S4. Audiovisual communication on the Web and social networks. Communication in public and its structure. Presentation to relevant actors.
S5. Demonstration in workshop with relevant actors in the field of Applied Mathematics.

UC in periodic assessment, not contemplating final exam, given the adoption of the project-based teaching method applied to real situations. Presentations, demonstrations and discussion are carried out in groups.
Evaluation weights:
R1 Solution Ideation Report, with Storyboard, User Journey, User Requirements, Technical Specifications and its audiovisual presentation: 20%.
R2 Solution Prototyping: Lo-fi and Hi-fi Prototypes and Minimum Viable Prototype - MVP (on GitHub), its Demonstration and Evaluation Report: 40%
R3 Solution Design Report with the following elements (if applicable): Architecture (UML Package Diagram, UML Component Diagram), Hardware and Software Configuration, Installation Manual (UML Deployment Diagram, Configuration Tutorial), Operation Manual, User Manual: 20%
R4 Audio-visual presentation of the solution and its demonstration in a Workshop: 20%.