Accreditations
Programme Structure for 2024/2025
Curricular Courses  Credits  

Linear Algebra and Applications
6.0 ECTS

Mandatory Courses  6.0 
Single Variable Calculus
6.0 ECTS

Mandatory Courses  6.0 
Principles of Data Analysis
6.0 ECTS

Mandatory Courses  6.0 
Programming Fundamentals
6.0 ECTS

Mandatory Courses  6.0 
Work, Organizations and Technology
6.0 ECTS

Mandatory Courses  6.0 
Numerical Linear Algebra
6.0 ECTS

Mandatory Courses  6.0 
Algorithms and Data Structures
6.0 ECTS

Mandatory Courses  6.0 
Multivariable Calculus
6.0 ECTS

Mandatory Courses  6.0 
Project Planning and Management
6.0 ECTS

Mandatory Courses  6.0 
Public Speaking with Drama Techniques
2.0 ECTS

Transversal Skills  2.0 
Introduction to Design Thinking
2.0 ECTS

Transversal Skills  2.0 
Academic Work with Artificial Intelligence
2.0 ECTS

Transversal Skills  2.0 
Numerical Analysis
6.0 ECTS

Mandatory Courses  6.0 
Entrepreneurship and Innovation I
6.0 ECTS

Mandatory Courses  6.0 
Graphs and Complex Networks
6.0 ECTS

Mandatory Courses  6.0 
Artificial Intelligence
6.0 ECTS

Mandatory Courses  6.0 
Introduction to Statistics and Probabilities
6.0 ECTS

Mandatory Courses  6.0 
Supervised Machine Learning
6.0 ECTS

Mandatory Courses  6.0 
Database and Information Management
6.0 ECTS

Mandatory Courses  6.0 
Entrepreneurship and Innovation II
6.0 ECTS

Mandatory Courses  6.0 
Financial Modelling
6.0 ECTS

Mandatory Courses  6.0 
Mathematical Optimization
6.0 ECTS

Mandatory Courses  6.0 
Computational Mathematics
6.0 ECTS

Mandatory Courses  6.0 
Project in Applied Mathematics I
6.0 ECTS

Mandatory Courses  6.0 
Technology, Economy and Society
6.0 ECTS

Mandatory Courses  6.0 
Stochastic Processes and Simulation
6.0 ECTS

Mandatory Courses  6.0 
Project in Applied Mathematics II
6.0 ECTS

Mandatory Courses  6.0 
DataDriven Decision Making
6.0 ECTS

Mandatory Courses  6.0 
Linear Algebra and Applications
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). GaussJordan 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 classification not less than 10 points (scale 120) in one of the following modalities:
 Periodic assessment: 1 midterm test (14%) + 11 weekly minitests (11x2%) + weekly autonomous work (AW) activities (12%) + construction of a glossary in group work (12%) + final test (40%); a minimum score of 7 values (scale 120) is required in each of the midterm and final tests
 Assessment by Exam (100%), in any of the exam periods, with individual written test.
Title: H. Anton and C. Rorres (2010) Elementary Linear Algebra  Applications Version, John Wiley and Sons
Blyth T.S., Robertson E.F. (2002). Basic Linear Algebra. Springer.
Lages E.L. (2015). Geometria Analítica e Álgebra Linear. Coleção Matemática Universitária. IMPA.
The Mathworks, Inc.  The Student Edition of Matlab , PrenticeHall, 5th Version
Materiais científicopedagógicos (slides, notas de desenvolvimento, código e pseudo código, fichas de exercícios e problemas) disponibilizados pela equipa docente.
Authors:
Reference:
Year:
Title: David C. Lay (2015) Linear Algebra and its Applications, Addison Wesley, Pearson
Cabral I., Perdigão C., Saiago C. (2018). Álgebra Linear Teoria, Exercícios Resolvidos e Exercícios Propostos com Soluções, Escolar Editora.
Marc Peter Deisenroth, A. Aldo Faisal, and Cheng Soon Ong (2020) Mathematics for Machine Learning, Cambridge University Press [electronic resource: https://mmlbook.github.io/book/mmlbook.pdf]
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Single Variable Calculus
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. Riemann definite integral. Antiderivatives. The fundamental theorem of calculus. Change of variables. Improper integrals. Criteria of integrability
Approval with classification not less than 10 points (120 scale) in one of the following modalities:
 Periodic assessment: 2 minitests (MT) on classes of 30 minutes duration (15% each) + Test on the first examination period (40%) + weekly tasks on Moodle (20%) + work done in groups of 23 students (10%).
The average of the classifications of the minitests ( (MT1+MT2)/2 ) must be greater or equal to 7 points.
The classification in the final test must be greater or equal to 7 points.
There is the possibility of oral assessment.
or
 Assessment by Examination (100%), in any of the examination periods.
Title: Campos Ferreira J. (2018). Introdução à Análise Matemática. Fundação Calouste Gulbenkian.
Stewart J. (2013). Cálculo. Vol I, 7ª Edição [tradução EZ2 Translate, São Paulo]. Cengage Learning [recurso eletrónico: https://aedmoodle.ufpa.br/pluginfile.php/311602/mod_resource/content/1/Calculo%20%20James%20Stewart%20%207%20Edição%20%20Volume%201.pdf]
Strang, G. (2007). Computational Science and Engineering, WellesleyCambridge Press
Materiais científicopedagógicos (Jupyter noteboos, slides, notas de desenvolvimento, código e pseudo código, fichas de exercícios e problemas) disponibilizados pela equipa docente Scientificpedagogical materials (Jupiter notebooks, slides, lectures, code and pseudo code, exercise sheets, problems) provided by the teaching team.
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Title: Lima E.L. (2001). Análise real. Vol 1. Coleção Matemática Universitária,SBM. Rio de Janeiro.
Ávila G. (2006). Análise Matemática para a Licenciatura. Ed.Edgard Blucher. São Paulo.
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Principles of Data Analysis
After successfully attending the curricular unit, students should be able to:
OA1. Know the different data formats.
OA2. Know the complete data cycle.
OA3. Know how to perform exploratory data analysis using R.
OA4. Know how to model a set of data.
OA5. Implement a data analysis solution for a given problem.
CP1. Introduction to Data Analysis
CP2. Introduction to R and RStudio
CP3. Knowledge of problems in data analysis with examples
CP4. The complete cycle of data analysis
CP5. Data and data format
CP6. Data preparation
CP7. Odds; Descriptive Statistics and Exploratory Analysis
CP8. Data visualization
CP9. Modeling and different types of machine learning problems
CP10. Model evaluation methods
CP11. Reporting and publishing results
PERIODIC assessment results from: online exercises, without a minimum grade, after each class (20%); two individual tests  a midterm test and another at the end of the semester (30%); and a group work (maximum of 3 students) in R with preparation of a report and oral presentation (50%).
Students who obtain a final grade above 9.5 are approved.
Title: Torgo Luís; Data mining with R. ISBN: 9781439810187
C. O'Neil, R. Schutt. 'Doing Data Science: Straight Talk from the Frontline'. O'Reilly. 2013
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Title: Wickham, Hadley, and Garrett Grolemund. 2017. R for Data Science. O?Reilly Media.
Wilke, Claus O. 2019. Fundamentals of Data Visualization. O?Reilly Media.
P. Mathur, Machine Learning Applications Using Python: Cases Studies from Healthcare, Retail, and Finance. Apress. 2018.
I. Foster, R. Ghani, R. S. Jarmin, F. Kreuter, J. Lane, Big Data and Social Science: A Practical Guide to Methods and Tools, 1st Edition. CRC Press, Chapman & Hall. 2016
T. W. Miller, Marketing Data Science: Modeling Techniques in Predictive Analytics with R and Python?. O'Reilly. 2015
M. N. Jones, Big Data in Cognitive Science (Frontiers of Cognitive Psychology), Taylor & Francis, 2016
F. Provost. Data Science for Business: What You Need to Know about Data Mining and DataAnalytic Thinking. O'Reilly. 2013
L. M. Chen, Z. Su, B. Jiang. Mathematical Problems in Data Science: Theoretical and Practical Method
Aggarwal, C. C. 2015. Data mining: the textbook (Vol. 1). New York: Springer.
Han, J., Pei, J., & Tong, H. 2022. Data mining: concepts and techniques. Morgan Kaufmann.
P. Tattar, T. Ojeda, S. P. Murphy B. Bengfort, A. Dasgupta, Practical Data Science Cookbook, Second Edition. Packt Publishing. 2017.
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Programming Fundamentals
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: Understand the syntax of the Python programming language.
LO4: Develop programming solutions for problems of simple complexity.
LO5: Explain, execute, and debug code fragments developed in Python.
LO6: Interpret the results obtained from the execution of code developed in Python.
LO7: Develop programming projects.
S1. Introduction to Programming: Logical sequence and instructions, Input and output of data, Constants, variables, and data types, Logical, arithmetic, and relational operations, Control structures
S2. Procedures and Functions
S3. References and Parameters
S4. Integrated Development Environments
S5. Syntax of the programming language
S6. Objects and object classes
S7. Lists and Lists of Lists
S8. File Manipulation
The course unit follows a projectbased assessment model due to its highly practical nature and does not include a final exam.
Students are evaluated based on the following parameters:
A1: Programming tasks validated by the instructors (10%), with a minimum grade of 9.5 out of 20 in the average of the tasks.
A2: Individual Project with theoreticalpractical discussion (40%), with a minimum grade of 8.5 out of 20.
A3: Group Project with theoreticalpractical discussion (50%), with a minimum grade of 8.5 out of 20.
Title: Wanda Dann, Stephen Cooper, & Randy Pausch, Learning to Program with Alice!, 2011, ISBN: 9780132122474
João P. Martins, Programação em Python: Introdução à programação com múltiplos paradigmas, IST Press, 2015, ISBN: 9789898481474
Kenneth Reitz, Tanya Schlusser, The Hitchhiker's Guide to Python: Best Practices for Development, 1st Edition, 2016, ISBN13: 9781491933176, https://docs.pythonguide.org/
Eric Matthes, Python Crash Course, 2Nd Edition: A HandsOn, ProjectBased Introduction To Programming, No Starch Press,US, 2019, ISBN13 : 9781593279288
John Zelle, Python Programming: An Introduction to Computer Science, Franklin, Beedle & Associates Inc, 2016, ISBN13 : 9781590282755
Ernesto Costa, Programação em Python: Fundamentos e Resolução de Problemas, 2015, ISBN 9789727228164,
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Title: David Beazley, Brian Jones, Python Cookbook: Recipes for Mastering Python 3, O'Reilly Media, 2013, ISBN13 ? : ? 9781449340377
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Work, Organizations and Technology
LO1: Know the main theories, concepts and problematics 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 of the digital transition;
LO4: Explore cases, strategies and application methods to understand the real impacts of the digital transition on professions, companies and organizations.
S1. Is work different today than in the past? S2. How has theory looked at technology?
S3. What technologies for the future?
S4. What future for work?
S5. How intelligent is artificial intelligence?
S6. Where does precarity begin?
S7. Do platform workers need employment contracts?
S8. Who is to blame when the machine goes wrong?
S9. Are digital technologies changing the relationship between unions and companies?
S10. Does teleworking make people happier?
S11. Portugal and the digital transformation?
"Periodic evaluation:
Making of an Inverted class class. Each Inverted Class represents 20% of the final mark, with a minimum mark of 8. Weekly question and answer which represents 10% of the final mark, with a minimum mark of 8. An individual assignment, spread over 3 assessment periods, with a minimum mark of 8 in each, representing 35% of the final grade. A group assignment, representing a total of 35% (10% group presentation and 25% written assignment), with a minimum mark of 8. The average grade must be equal to or greater than 9.5.
Assessment by exam (First season 1 if the student chooses, Second Season and Special Season): Inperson exam (100% of the final grade)."
Title: Autor, David H., "Why Are There Still So Many Jobs? The History and Future of Workplace Automation.", 2015, Journal of Economic Perspectives, 29 (3): 330.
Benanav, A, Automation and the Future of Work, 2020, London: Verso
Boreham, P; Thompson, P; Parker, R; Hall, R, New Technology at Work, 2008, Londres: Routledge.
Crawford, C, The Atlas of AI. Power, Politics, and the Planetary Costs of Artificial Intelligence, 2021, Yale University Press.
Edgell, S., Gottfried, H., & Granter, E. (Eds.). (2015). The Sage Handbook of the sociology of work and employment.
Grunwald, A. (2018). Technology Assessment in Practice and Theory. London: Routledge.
Huws, U. (2019) Labour in Contemporary Capitalism, London, Palgrave.
OIT (2020), As plataformas digitais e o futuro do trabalho
Agrawal A, Gans J, Goldfarb A (2018), Prediction Machines, Boston, Massachusetts, Harvard Business Review Press.
Autor D (2022), The labour market impacts of technological change, Working Paper 30074, NBER Working Paper Series.
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Title: Berg J, Furrer M, Harmon E, Rani U, Silberman M (2020), As plataformas digitais e o futuro do trabalho, Geneva, International Labour Office.
Braun J, Archer M, Reichberg G, Sorondo M (2021), Robotics, AI and Humanity, Cham, Springer.
Degryse, Cristophe (2016), Digitalisation of the Economy and its Impact on Labour Markets, WP 2016.2, ETUI
ILO (2018), The economics of artificial intelligence: Implications for the future of work, Geneva, International Labour Office.
ILO (2019) Work for a Brighter Future – Global Commission on the Future of Work. Report. Geneva, International Labour Office.
Lane M, SaintMartin A (2021), The impact of Artificial Intelligence on the labour market: What do we know so far?, OECD.
OECD (2019b), How’s Life in the Digital Age?, OECD Publishing, Paris.
Valenduc, Gérard & Vendramin, Patricia (2019), The mirage of the end of work, FB 6/2019, ETUI
WEF (2023), Future of Jobs Report 2023, Geneva, World Economic Forum.
Zuboff S (2019), The Age of Surveillance Capitalism, PublicAffairs.
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Numerical Linear Algebra
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 GramSchmidt orthogonalization.
PC3 Complex matrices. Eigenvalues and eigenvectors of skewHermiteanas. 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 120) in one of the following modalities:
 Periodic assessment: 2 practical works in Python (20% each) + Test 1 during the semester (30%) + Test 2 in the date of the first exam (30%).
All assessment instruments are mandatory and have a minimal grade of 7 (scale 120).
 Assessment by Exam (100%).
Title: Ford W. (2015). Numerical Linear Algebra with Applications  using MATLAB. Elsevier
Burden R., Douglas Faires J. (2005). Numerical Analysis. Brooks/Cole Cengage Learning
Gupta R.K. (2019). Numerical Methods: Fundamentals and Applications. Cambridge University Press.
Kong Q., Siauw T., Bayen A.M. (2021). Python Programming and Numerical Methods: A Guide for Engineers and Scientists, Elsevier Inc..
Lay, D.C. (2015). Linear Algebra and its Applications. Addison Wesley. Pearson.
Blyth T.S., Robertson E.F. (2002). Further Linear Algebra. Springer.
Deisenroth M.P., Faisal A.A., Soon Ong C. (2020). Mathematics for Machine Learning. Cambridge University Press [electronic resource: https://mmlbook.github.io/book/mmlbook.pdf]
Rossun G. (2018). Python Tutorial Release 3.7.0. Python Software Foundation.
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Title: Lima E.L. (2015). Geometria Analítica e Álgebra Linear. Coleção Matemática Universitária, IMPA.
Cabral I., Perdigão C., Saiago C. (2018). Álgebra Linear Teoria, Exercícios Resolvidos e Exercícios Propostos com Soluções (5ª edição). Escolar Editora.
Anton H., Rorres C. (2010). Elementary Linear Algebra  Applications Version. John Wiley and Sons.
Hanselman, D., Littlefield, B. and MathWorks Inc. (1997). The Student Edition of MATLAB, 5th Version, PrenticeHall
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Algorithms and Data Structures
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 UnionFind 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
Season 1: Periodic Assessment or Final Exam
Periodic Assessment:
2 Tests (90%), with a theoretical and practical component. Minimum final average of 9.5, distributed as follows: (45%) Test 1 with a minimum score of 7.5 and (45%) Test 2 with a minimum score of 7.5
(10%) Application and demonstration of knowledge tasks
Final Exam:
 (100%) Final Exam with a theoretical and practical component
Students have access to the Exam assessment in Season 1 if they choose it at the beginning of the semester or if they fail the Periodic Assessment.
Season 2: Final Exam
 (100%) Final Exam with a theoretical and practical component
Special Season: Final Exam
 (100%) Final Exam with a theoretical and practical component
Title: Para as licenciaturas Python: Python  Algoritmia e Programação Web, FCA,
Para as licenciaturas Java: Estruturas de Dados e Algoritmos em Java, FCA
Introduction to Algorithms, 3rd edition, MIT Press,
Algorithms, 4th edition, AddisonWesley, 2012
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Multivariable Calculus
LG1 Apprehend the generalization of limit, continuity and differentiability in multivariable functions
LG2 Calculate partial and second derivatives of any nonnull 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 (120 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 (120 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
Title: Stewart, J. (2013). Cálculo. Vol II, 7ª Edição [tradução EZ2 Translate, São Paulo]. Cengage Learning [recurso eletrónico: https://profmcruz.files.wordpress.com/2019/03/calculojamesstewart7edic3a7c3a3ovolume2.pdf].
Lipsman, R.L., Rosenberg, J.M. (2018). Multivariable Calculus with MATLAB. Springer.
Strang, G. (2007). Computational Science and Engineering, WellesleyCambridge Press .
Kong Q., Siauw T., M. Bayen A.M. (2021). Python Programming and Numerical Methods: A Guide for Engineers and Scientists. Elsevier Inc..
Rossun G. (2018). Python Tutorial Release 3.7.0. Python Software Foundation.
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Title: Quarteroni A., Saleri F. (2007). Cálculo Científico com o MATLAB e o Octave. Springer.
Lima E.L. (2000). Curso de Análise, Vol 2, (Projeto Euclides). IMPA.
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Project Planning and Management
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.
Title: Lester A. (2017), Project Management Planning and Control, 7th edition, Elsevier Science & Technology.
Tugrul U. Daim, Melinda Pizarro, e outros. (2014), Planning and Roadmapping Technological Innovations: Cases and Tools (Innovation, Technology, and Knowledge Management), Spinger.
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Public Speaking with Drama Techniques
Learning Outcomes:
LO1. Develop oral communication skills
LO2. Improve body expression
LO3. Master the art of using the vocal apparatus
LO4. Learn performance techniques
Compatibility with the Teaching Method:
The course combines theory and practice, providing students with an immersive experience in the world of public performances with theatrical techniques. The teaching method is interactive and participatory, encouraging students to put into practice the concepts learned through individual and group exercises.
The knowledge acquired involves both theatrical theory and specific oral communication techniques. Participants will learn about the fundamentals of vocal expression, character interpretation and improvisation, adapting these skills to the context of public presentations
S1  Preparation for presentation (3 hours)
S2  Non verbal communication (3 hours)
S3  Introduction to using the vocal apparatus (3 hours)
S4  Introduction to the term Performance (3 hours)
Modality of continuous assessment:
Practical Presentations (50%): Participants will be assessed based on their public presentations during the course. Criteria such as clarity of communication, vocal and body expression, use of theatrical techniques and performance will be considered. Presentations may be individual or group presentations, depending on the activities proposed.
Exercises and Written Assignments (50%): In addition to the practical presentations, participants may be asked to complete exercises and written assignments related to the content covered in each module. These may include reflections on learned techniques, analysis of case studies, answers to theoretical questions or even the creation of presentation scripts. These activities will help to assess participants' conceptual understanding.
To conclude the curricular unit in the modality of continuous assessment the student must be present in 75% of the classes.
Although not recommended, students may opt for final assessment by written and oral examination (100%).
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Introduction to Design Thinking
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)
Modality of continuous assessment:
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, 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, quality of the solutions and collaboration among group members.
To conclude the curricular unit in the modality of continuous assessment the student must be present in 75% of the classes.
Although not recommended, students may opt for final assessment by written and oral examination (100%).
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Academic Work with Artificial Intelligence
"LO1. Knowledge about the structure, language, ethical and normative procedures for the elaboration of academic texts.
LO2. Skills to use generative algorithms to assist the elaboration of academic work.
LO3. Skills in analysing and scrutinising the independence, relevance and reliability of AI generated data.
LO4. Overall abilities to recognise the ethical and civic implications underlying the access, sharing and use of AI tools in an academic context."
"S1. Introduction to Academic Writing and generative algorithms (3h)
S2. Procedures for planning and constructing argumentative texts with the aid of AI (3h)
S3. Critical analysis of texts produced: identification and referencing of data sources and analysis of their relevance in the ligth of the objectives of the academic work (3h)
S4. Opportunities and risks of AI use: good practice guide for accessing, sharing and using AI tools in an academic context (3h)"
"Modality of continuous assessment:
Class participation: Class participation: assesses students' attendance, involvement and individual contributions to class discussions and activities (20%).
Group work will require students to form groups to revise and edit academic texts between themselves, using generative algorithms. Assessment will be based on the quality of the revisions, edits and feedback provided (40%).
Individual report: with an indepth reflection on the civic and ethical questions posed by the use of AI tools as an aid to academic writing (40%).
There is a required minimum of 7 values in each component that is graded.
To conclude the curricular unit in the modality of continuous assessment the student must be present in, at least, 75% of the classes.
Although not recommended, students may opt for final assessment by written and oral examination (100%).
In addition to the practical presentations, students will be asked to carry out exercises and written tasks related to the content covered. These may include: reflecting on techniques learnt, analysing case studies, answering theoretical questions or even creating presentation scripts. These activities will help to assess conceptual understanding of the content taught.
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Numerical Analysis
The learning goals (LGs) of this CU are:
LG1. Understand the relevance and challenges that exist in the field of analytical and numerical solutions for nonlinear models;
LG2. Identify the main methodologies for solving static nonlinear models;
LG3. Identify the main methodologies for solving dynamic linear and nonlinear models;
LG4. Gain ability to use numerical approximations methods for solving nonlinear models, when analytical methods fail;
LG5. Understand why it is necessary to employ numerical methods to obtain an approximate solution and the consequences of an inexact approximation;
LG6. Recognize the importance of numerical approximation methods and the variety of applications in real life problems.
LG7. Communicate the results of numerical computation, with appropriate and clear explanations supported by graphical material.
This CU has the following programmatic contents (PCs):
PC1. Introduction to Numerical Methods with Python
PC2. Convergence and stability of methods. Error and loss of meaning of numerical approximation.
PC3. Numerical derivative; solution of first order ordinary differential equations (RungeKutta method); existence and uniqueness of solutions
PC4. Numerical integration: NewtonCotes formulas and GaussLegendre quadrature for different number of points; range change; graphic interpretation of quadrature; integration error
PC5. Zeros of a function and search for function extremums (with and without differentiability, with and without continuity); bisection and Newton methods, secant method. Introduction to solving systems of nonlinear equations (Newton's method for systems)
PC6. Difference equations and iterative methods
PC7. Solution of higher order ordinary differential equations (Euler finite difference approximations)
Approval with classification not less than 10 points (scale 120) in one of the following modalities:
 Periodic assessment: 1 midterm test (25%) + weekly autonomous work (AW) activities (10%) + 1 Project with Python in group work (25%) + final test (40%); a minimum score of 7 values (scale 120) is required in each of the midterm and final tests
 Assessment by Exam (100%), in any of the exam periods, with individual written test.
Title: Gupta R.K., (2019). Numerical Methods: Fundamentals and Applications. Cambridge University Press.
Kong Q, Siauw T., Bayen A.M. (2021). Python Programming and Numerical Methods: A Guide for Engineers and Scientists. Elsevier Inc..
Cohen H., Numerical Approximation Methods. Springer New York., 2011, null,
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Title: Allen, M.B., Isaacson, E.L. (2019). Numerical analysis for applied science. John Wiley & Sons, Inc..
Rossun G. (2018). Python Tutorial Release 3.7.0. Python Software Foundation.
Christian C. (2017). Differential Equations: A Primer for Scientists and Engineers, Second Edition. Springer International Publishing.
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Entrepreneurship and Innovation I
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 technologybased 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%.
BibliographyTitle: Osterwalder, A., & Pigneur, Y. (2014). Value Proposition Design: How to Create Products and Services Customers Want. John Wiley & Sons.
Osterwalder, A., & Pigneur, Y. (2010). Business Model Generation: A Handbook for Visionaries, Game Changers, and Challengers. John Wiley & Sons;
Burns, P. (2016). Entrepreneurship and Small Business. Palgrave Macmillan;
Mariotti, S., Glackin, C. (2015). Entrepreneurship: Starting and Operating A Small Business, Global Edition. Pearson; Dorf. R., Byers, T. Nelson, A. (2014). Technology Ventures: From Idea to Enterprise. McGrawHill Education;
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Graphs and Complex Networks
LG1. Understand the language of graph theory, and the corresponding in network science, as well as the emergence of these scientific areas.
LG2. Distinguish graphs from networks and the application scenarios of each of the scientific areas.
LG3. Represent problems in graph or network structure.
LG4. Critically evaluate the adoption of a network model, including from empirical data.
LG5. Understand the measures to extract from a model and the characteristics of nodes/vertices and arcs/edges.
LG6. Perform graphs and networks research.
LG7. Take the first steps in detection, inference and controllability.
LG8. Know how to use software for network representation and visualization.
LG9. Relate the learning in graphs and networks with themes and problems discussed in other CUs.
This CU has the following programmatic contents (PCs):
PC1 Introduction: Networks everywhere
PC2 Fundamentals and graph representations
PC3 Paths and search on networks: Dijkstra and A*
PC4 Centrality and structure measures
PC5 Distributions and algorithms
PC6 Random networks
PC7 Representing and visualizing networks using Python and NetworkX
PC8 Small Worlds model
PC9 Scalefree networks
PC10 Adapting empirical data to network models
PC11 Introduction to complex network applications and advanced topics
Approval with classification not less than 10 points (scale 120) in one of the following modalities:
 Periodic assessment: 1 project in Python realized in group work (50%) + 1 test (40%) + autonomous work (AW)
activities (10%); all the elements of assessment have a minimum score of 7 points.
 Assessment by Exam (100%), in any of the exam periods.
Title: Maarten van Steen, Graph Theory and Complex Networks, 2010, 9081540610,
Mark Newman, Networks, 2018, 9780198805090,
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Title: Menczer F., Fortunato S., Davis C.A., A first course in network science (Cambridge University Press), 2020, 9781108471138,
Sayama H., Introduction to the Modeling and Analysis of Complex Systems. Open SUNY Textbooks. Milne Library., 2015, null,
Erwin Kreyszig, Advanced Engineering Mathematics, 2011, 9780470458365,
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Artificial Intelligence
Upon completion of the course, 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 AIbased 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 genetic algorithms, being able to implement and adapt them 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 searchbased approach.
S2: Search algorithms: depth first and breadth first, A*, greedy BFS, Dijkstra.
S3: Fundamental notions relating to knowledge, representation and the architecture of knowledgebased systems.
S4: Firstorder predicate logic: representation and deduction.
S5: Declarative knowledge represented in Logic Programming.
S6: Genetic algorithms.
The periodic assessment throughout the semester consists of 3 assessment blocks (BA), and each BA consists of one or more assessment moments. It is distributed as follows:
 BA1: 4 miniassignments [7.5% each miniassignment * 4 = 30%]
 BA2: 2 minitests [20% each minitest * 2 = 40%]
 BA3: 1 project on Artificial Intelligence [30%]
Assessment by exam:
 1st Epoch [100%]
 2nd Epoch [100%]
All periodic assessment blocks (BA1, BA2 and BA3) have a minimum grade of 8.5. In any BA, an individual oral discussion may be required.
Assessment by exam consists of a written exam that covers all the knowledge provided in the syllabus of the course, and has a weighting of 100%.
Attendance at classes is not mandatory.
Title: Bishara, M. H. A., & Bishara, M. H. A. (2019). Search algorithms types: Breadth and depth first search algorithm
Brachman, R., & Levesque, H. (2004). Knowledge representation and reasoning. Morgan Kaufmann
Clocksin, W. F., & Mellish, C. S. (2003). Programming in Prolog. Springer Berlin Heidelberg.
Russell, S. & Norvig, P. (2010). Artificial Intelligence: A Modern Approach (3rd ed.). Prentice Hall.
S., V. C. S., & S., A. H. (2014). Artificial intelligence and machine learning (1.a ed.). PHI Learning.
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Introduction to Statistics and Probabilities
LG1 Understand the meaning of probability and probabilistic event, including the notions of event, outcome and sample space
LG2 To be familiar with the mathematical formalism of probability and, in particular, the axiomatic approach
LG3 To be able to calculate simple probability results using combinatorics and understand the concept of conditional probability.
LG4 Understand the concept of random variable and how it can be characterised, including through probability distributions.
LG5 Identify different types of distributions and get started in modelling real world phenomena.
LG6 Know how to describe a sample, highlighting the main features and properties.
LG7 Understand the fundamental principles of statistical reasoning, at descriptive and inferential levels.
LG8 To be critical about the degree of certainty of an inference
LG9 To be able to use R or Phyton as a computational tool in the CU
CP1 Algebra of sets. Probability concepts. Space of probability, sample space, space of events. Measure. Kolmogorov's Axioms
CP2 Sampling and distribution. Counting rules. Probability calculus
CP3 Discrete and continuous conditional probability. Independence. Density. Bayes' Theorem
CP4 Deterministic versus stochastic experiment. Discrete and continuous random variables. Distribution and density functions. Law of large numbers and Chebyshev lemma. Central limit theorem
CP5 Distributions: normal, binomial, uniform, Poisson, Bernoulli, tstudent, exponential, chisquare. Expected value. Moment generating function
CP6 Descriptive vs inductive statistics. Random sampling. Sample measures: central and relative location, dispersion and asymmetry
CP7 Inference: parameter estimation (point and interval), confidence intervals and hypothesis testing. Maximum likelihood. Pearson, KS and contingency adjustment tests.
Approval with an overall grade of at least 10 points (out of 20) in one of the following modes:
 Periodic assessment: Test 1 (35%) + Test 2 (35%) + 1 practical work in Python (or R) (25%) + 2 quizzes (5%), or
 Assessment by Exam (75%), in any of the exam periods, where the practical work (mentioned above) maintains the weight of 25%.
All the elements of evaluation have a minimum score of 8 points (out of 20).
Title: Blitzstein, J. K., Hwang J. (2015). Introduction to probability. Chapman and Hall/CRC.
Baclawski, K. (2008). Introduction to Probability with R, Chapman & Hall/CRC
André, J. (2018). Probabilidades e Estatística Para Engenharia, 2ª Edição. Lidel.
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Title: Reis, E., P. Melo, R. Andrade, Calapez, T. (2014). Exercícios de Estatística Aplicada, Vol. 2, 2ªed, Lisboa, Sílabo.
Reis, E., P. Melo, R. Andrade e Calapez, T. (2012). Exercícios de Estatística Aplicada, Vol. 1, 2ªed, Lisboa, Sílabo.
Reis, E., P. Melo, R. Andrade, Calapez, T. (2016). Estatística Aplicada, Vol. 2, 5ªEdição. Sílabo.
Reis, E., P. Melo, R. Andrade, Calapez, T. (2015). Estatística Aplicada, Vol. 1, 6ª Edição. Sílabo.
Wackerly, D., Mendenhall, W., Scheaffer, R. L. (2008). Mathematical statistics with applications. Cengage Learning.
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Supervised Machine Learning
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 problemsolving and decisionmaking.
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, NaiveBayes and kNN.
LO7. Understand ensemble algorithms: bagging and boosting
LO8. Know and understand the workings of Artificial Neural Networks (ANN)
LO9. 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, NaiveBayes and kNN.
S5. Bagging and Boosting in supervised algorithms
S6. Artificial Neural Networks
S7. Hyperparameter optimization
As this course is of a very practical and applied nature, it follows the 100% projectbased assessment model, which is why there is no final exam. Assessment takes place throughout the semester and consists of 3 assessment blocks (AB), each AB consisting of one or more assessment moments. It is distributed as follows:
 AB1: 1st tutorial + 1st minitest [20% for the 1st tutorial + 10% for the 1st minitest = 30%]
 AB2: 2nd tutorial + 2nd minitest [20% for the 2nd tutorial + 10% for the 2nd minitest = 30%]
 AB3: 1 final project [40%]
The tutorials consist of individual oral discussions to assess the students' performance in the projects proposed for the tutorial.
The minitests make it possible to assess the theoretical knowledge applied to each of the projects also assessed during the tutorial.
The final project consists of developing a practical piece of work that brings together the knowledge and skills acquired throughout the semester, in which external organizations/companies may participate in the proposed challenge.
The 1st Season and 2nd Season can be used for assessment.
Attendance at classes is not mandatory.
Title: Witten, I. H., Frank, E., Hall, M. A., & Pal, C. J. (2016). Data Mining: Practical machine learning tools and techniques. Morgan Kaufmann.
Sharda, R., Delen, D., Turban, E., Aronson, J., & Liang, T. P. (2014). Businesss Intelligence and Analytics: Systems for Decision Support. Prentice Hall.
VanderPlas, J. (2016). Python Data Science Handbook. O’Reilly Media.
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Title: Foster Provost, Tom Fawcett (2013) Data Science for Business. What you need to know about data mining and dataanalytic thinking, 1st edition. O'Reilly.
Ller, A. & Guido, S. (2017). Introduction To Machine Learning with Python: A Guide for Data Scientists. Sebastopol, CA: O'Reilly Media, Inc.
Avila, J. (2017). ScikitLearn Cookbook  Second Edition. Birmingham: Packt Publishing.
Mueller, J. P. (2019). Python for Data Science for Dummies, 2nd Edition (2.a ed.). John Wiley & Sons.
McKinney, W. (2022). Python for Data Analysis: Data Wrangling with Pandas, NumPy, and Jupyter (3.a ed.). O’Reilly Media.
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Database and Information Management
LO1 Know the basic principles of Information Systems and their role in organizations
LO2 Know the fundamental concepts of Information Systems Analysis and develop semantic (conceptual) models for systems described in text, through practical application of the UML language, and understand the conversion of such conceptual models into relational database models (RDBs)
LO3 Know how to model and design a Relational DB (RDB), with the Relational Model
LO4 Know the normal forms and relational algebra and understand the normalization of an existing RDB based on performance metrics
LO5 Know how to create and modify the physical structure of a RDB using SQL
LO6 Know how to use, at an elementary level, the administration tools associated with a Database Management System (DBMS)
LO7 Develop selflearning, peer review, teamwork, oral and written expression
S1 Introduction to Information Systems and its role in organizations
S2 Introduction to Information Systems Analysis with UML language: requirements analysis, data models, schemas and UML diagrams
S3 Database Design. Relational Model: relationships, attributes, primary keys, foreign keys, integrity rules, optimizations and indexes
S4 Normalization. Redundancy and inconsistency of data. Normal forms
S5 SQL Language  Table variables, set operators, simple queries, subqueries, operators (SELECT, Insert, delete, update), views, indexes, triggers, stored procedures and transactions
S6 Introduction to Database Management Systems administration, DBMS
Periodical Assessment:
 1 test to be done in the middle of the semester (30%)
 1 test to be taken in the 1st season of exams (30%)
 1 modelling and implementation project (40%)
Both tests have a minimum grade of 8 values and the project is mandatory for approval.
Assessment by exam:
1 Written exam weighted at 100%
The minimum grade for approval in this course is 10 values.
Title: Ramos, P, Desenhar Bases de Dados com UML, Conceitos e Exercícios Resolvidos, Editora Sílabo, 2ª Edição, 2007
Elmasri Ramez, Navathe Shamkant, "Fundamentals Of Database Systems", 7th Edition, Pearson, 2016
Damas, L., SQL  Structured Query Language, FCA Editora de Informática, 3ª Edição,2017
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Title: Nunes, O´Neill, Fundamentos de UML, FCA Editora de Informática, 3ª Edição, 2004
C. J. Date, "SQL and Relational Theory: How to Write Accurate SQL Code", 3rd Edition, O'Reilly Media, 2011
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Entrepreneurship and Innovation II
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.
Title: Osterwalder, A., & Pigneur, Y. (2014). Value Proposition Design: How to Create Products and Services Customers Want. John Wiley & Sons.
Osterwalder, A., & Pigneur, Y. (2010). Business Model Generation: A Handbook for Visionaries, Game Changers, and Challengers. John Wiley & Sons;
Burns, P. (2016). Entrepreneurship and Small Business. Palgrave Macmillan;
Dorf. R., Byers, T. Nelson, A. (2014). Technology Ventures: From Idea to Enterprise. McGrawHill Education;
Mariotti, S., Glackin, C. (2015). Entrepreneurship: Starting and Operating A Small Business, Global Edition. Pearson;
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Financial Modelling
LG1. Analysing, comparing and synthesising concepts in solving financial problems.
LG2. Extracting information by analysing models and making deductions from financial data.
LG3. Understand concepts and methods used in financial calculus and financial mathematics.
LG4. Calculate simple and compound interest, rates, instalments and different types of discounts
LG5. Understand and argue about equivalence of capital, financing options and amortisation systems.
LG6. Acquire the basic analytical knowledge to apply the concept of interest in the solution of loan and capital investment problems
LG7. Model financial relationships using differential calculus.
LG8. Understand the importance of financial modelling to improve business performance.
LG9. Apply mathematics in the financial processes of a company (or of the business market) and in financial plans, whether strategic (long term) or operational (short term).
PC1 Concepts and terms in finance. Analysis and forecasting of financial extracts. Income forecasting. Equivalence of capital
PC2 Time value of money. Cash budgeting. Cost of capital. Profit and break even.
PC3 Capital budgeting: risk analysis with scenarios and Monte Carlo simulations
PC4 Evaluating common stocks and bonds. Time diversification and long term investment risk.
PC5 Portfolio models. Estimating systematic risk and testing asset pricing models
PC6 VBA for creating efficient meanvariance portfolios. Portfolio optimization and style analysis. BlackLitterman approach.
PC7 Simulation of stock prices and portfolio returns. Simulating retirement asset growth.
PC8 Pricing options and structured products with the BlackScholes model
PC9 Binomial option pricing model. Monte Carlo method for pricing exotic options
PC10 Estimation and control of interest rate sensitivity by immunization strategies.
Approval with classification not less than 10 points (out of 20) in one of the following modalities:
 Periodic assessment: Practical work (30%) + 1 Test (70%), or
 Assessment by Exam (100%).
All the elements of the assessment have a minimum score of 8 points (out of 20).
Title: Chambers D.R., Qin L. (2021). Introduction to financial mathematics: with computer applications. Chapman & Hall/CRC Press. ISBN 9780367410391
Wilders R.J. (2020). Financial Mathematics for Actuarial Science: The Theory of Interest. Taylor & Francis Group/CRC Press. ISBN: 9780367253080
Ohsaki S., RuppertFelsot J., Yoshikawa D. (2018). R Programming and Its Applications in Financial Mathematics. Taylor & Francis Group/CRC Press. ISBN: 9781498766098
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Title: Beninga, S. (2014). Financial Modeling, 4th Edition. MIT Press. ISBN: 9780262027281
Samanez C.P. (2010). Matemática Financeira, 5ª Edição. Pearson Prentice Hall.
Hazzan, S., Ponpeu, J.N. (2007). Matemática Financeira, 6ª Edição. Saraiva.
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Mathematical Optimization
LG1. Formulate problems in linear and nonlinear programming, integer programming and goal programming.
LG2. Distinguish between linear and nonlinear 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 linesearch.
LG10. Distinguish the advantages and limitations of the applied methods (convergence, robustness).
LG11. Carrying out technical analysis (single objective) and making tradeoff 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 bigM
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. Multiobjective linear programming. Goaloriented programming. Sequential and penaltyweight methods.
PC11. Polynomial approximations and line search methods. Convergence criteria.
PC12. Lagrangean duality. KarushKuhnTucker conditions.
Approval with classification not less than 10 points (120 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 (120 scale) is required in the Final Test
 Assessment by Exam (100%), in any of the exam periods, with individual written test.
Title: Taha, H.A. (2017). Operations Research: an introduction, 10th Ed.. Pearson.
Ragsdale, C.T. (2017). Spreadsheet Modeling and Decision Analysis: A Practical Introduction to Business Analytics. 8th Ed. Cemgage Learning.
Hillier, F.S. Lieberman, G.J. (2014). Introduction to Operations Research, 10th Ed.. McGrawHill.
Nash, S.G, Sofer A. (1996). Linear and Nonlinear Programming. McGrawHill.
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Title: Winston, W.L. (2004). Operations Research: Applications and Algorithms, 4th Ed.. Duxbury Press.
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Computational Mathematics
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 MATLAB 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. Semilinear DE. Wave Equation.
PC6. Fourier Transform. Convolution. Partial BlackScholes 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 classification not less than 10 points (120 scale) in one of the following modalities:
 Periodic assessment: Three practical work in Python (20%+30%+40%=90%) done in groups of 23 students + online minitests (10%), or
 Assessment by Examination (100%), in any of the examination periods.
Title: [5] Materiais científicopedagógicos (slides, notas de desenvolvimento, código e pseudo código, fichas de exercícios, problemas) disponibilizados pela equipa docente. / Scientificpedagogical materials (slides, lectures, code and pseudo code, exercise sheets, problems) provided by the teaching team.
[4] Pedro Girão (2014) Introdução à Análise Complexa, Séries de Fourier e Equações diferenciais, IST press
[3] Ronald L. Lipsman and Jonathan M. Rosenberg (2018) Multivariable Calculus with MATLAB, Springer
[2] A. V. Oppenheim, A. S. Willlsky (2013) Signals and Systems, 2nd Ed., Pearson
[1] Djairo G. Figueiredo (1987) Análise de Fourier e Equações Diferenciais Parciais. IMPA, 2ª Ed
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Project in Applied Mathematics I
At the end of the course, the student should be able to:
LO1: Apply cocreation 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 cocreation dynamics and make written and oral presentations, in the context of group work.
S1 Cocreation 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 projectbased teachinglearning 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%.
Title: Outra bibliografia dependente dos temas específicos do projeto e das orgaizações onde os alunos o irão desenvolver.
Brown, T (2009), Change by Design: How Design Thinking Transforms Organizations and Inspires Innovation, HarperCollins, 2009, ISBN13: 9780062856623
Osterwalder, A., Pigneur, Y., Papadakos, P., Bernarda, G., Papadakos, T., & Smith, A. (2014). Value proposition design. John Wiley & Sons.
Knapp, J., Zeratsky, J., & Kowitz, B. (2016). Sprint: How to Solve Big Problems and Test New Ideas in Just Five Days. Bantam Press.
Lewrick, M, Link, P., Leifer, L. (2020). The Design Thinking Toolbox, Wiley, ISBN 9781119629191
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Technology, Economy and Society
The student who successfully completes this UC will be able to:
OA1. Identify the main contemporary issues and debates;
OA2. Analyze current issues and debates in a reasoned manner;
OA3. Identify the implications of technological change and digitalization in economic, social, cultural and environmental terms;
OA4. Understand the role and the importance of technology in the challenges of contemporary societies;
OA5. Explore the boundaries between technological knowledge and social science knowledge;
OA6. Develop forms of interdisciplinary learning and critical thinking.
S1. Debates XXI: technological change and contemporary societal challenges.
S2. Digital transition: meaning and implications.
S3. Technology, social change and inequalities.
S4. Environment and transition towards to sustainability.
S5. Globalization, financialisation and development.
S6. Capitalism and democracy.
S7. Migrations and multiculturality.
The periodic assessment process comprises the following elements:
1. Preparation and presentation (class) of a group work on technological change and society (40%).
2. Test (60%).
The final assessment corresponds to 1st and 2nd phase exams (100% of the grade).
Title: Pires, R. P.; Pereira, C.; Azevedo, J.; Vidigal, I., & Veiga, C. M. (2020). A emigração portuguesa no século XXI.?Sociologia, Problemas e Práticas, (94), 938
Marques, P., & Salavisa, I. (2017). Young people and dualization in Europe: a fuzzy set analysis.?SocioEconomic Review,?15(1), 135160
Figay, N.; Silva, C.; Ghodous, P; JardimGonçalves, R. (2015). Resolving interoperability in concurrent engineering, in Concurrent Engineering in the 21st Century: Foundations, Developments and Challenges, Springer International Publishing
Bento, N., Wilson, C., Anadon, L.D. (2018), ?Time to get ready: Conceptualizing the temporal and spatial dynamics of formative phases for energy technologies,? Energy Policy 119: 282293
Barradas, R., & Lagoa, S. (2017). Financialization and Portuguese real investment: A supportive or disruptive relationship?.?Journal of Post Keynesian Economics,?40(3), 413439
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Title: Yearley, S. (2014).?Science, Technology, and Social Change (Routledge Revivals). Routledge
Wilson, C., Grubler, A., Bento, N., Healey, S., De Stercke, S., & Zimm, C. (2020). Granular technologies to accelerate decarbonization.?Science,?368(6486), 3639
Silva, P. A., & Cadeiras, P. (2019). From Paris to Lisbon: The EverChanging European Social Policy Landscape. In?The Future of Pension Plans in the EU Internal Market?(pp. 255281). Springer, Cham
Silva, J., Ferreira, J. C., & Gonçalves, F. (2019, September). The ??aftermath??of Industry 4.0 in Small and Medium Enterprises. In?IFIP Conference on HumanComputer Interaction?(pp. 2633). Springer, Cham
Rodrigues, M. D. L., & Silva, P. A. (2016). A constituição e as políticas públicas em Portugal.?Sociologia, Problemas e Práticas, (ESP1), 1322
Rego, R., Alves, P. M., Naumann, R., & Silva, J. (2014). A typology of trade union websites with evidence from Portugal and Britain.?European Journal of Industrial Relations,?20(2), 185195
Ratto, M. (2011). Critical making: Conceptual and material studies in technology and social life.?The information society,?27(4), 252260
Pires, R. P., Machado, F. L., Peixoto, J., & Vaz, M. J. (2010). Portugal: Atlas das migrações internacionais.?Lisboa: Tinta da China
Pedro, M. D. L. R. E., & Silva, A. E. (2012).?Políticas públicas em Portugal. Leya
Nascimento, S., Pólvora, A., Paio, A., Oliveira, S., Rato, V., Oliveira, M. J., ... & Sousa, J. P. (2016). Sustainable technologies and transdisciplinary futures: from collaborative design to digital fabrication.?Science as Culture,?25(4), 520537
Monteiro, V., Afonso, J. A., Ferreira, J. C., & Afonso, J. L. (2019). Vehicle electrification: New challenges and opportunities for smart grids.?Energies,?12(1), 118.
Matthewman, S. (2011).?Technology and social theory. Macmillan International Higher Education
Matos, F. (2020).?Knowledge, People, and Digital Transformation: Approaches for a Sustainable Future. Springer Nature
Luís, S., Pinho, L., Lima, M. L., RosetaPalma, C., Martins, F. C., & Betâmio de Almeida, A. (2016). Is it all about awareness? The normalization of coastal risk.?Journal of Risk Research,?19(6), 810826
Leach, M., Scoones, I., & Stirling, A. (2010).?Dynamic sustainabilities: technology, environment, social justice. Routledge
Lagoa, S., Leao, E., Mamede, R. P., & Barradas, R. (2014).?Financialisation and the financial and economic crises: The case of Portugal?(No. fstudy24). Financialisation, Economy, Society & Sustainable Development (FESSUD) Project
Grubler, A., Wilson, C., Bento, N., BozaKiss, B., Krey, V., McCollum, D. L., ... & Valin, H. (2018). A low energy demand scenario for meeting the 1.5 C target and sustainable development goals without negative emission technologies.?Nature energy,?3(6), 515527
Jörgens, H., & Solorio, I. (2019). Contested Energy Transition? Europeanization and Authority Turns in EU Renewable Energy Policy
Jörgens, H. (2018). Políticas para um desenvolvimento sustentável: sucessos passados e desafios para o futuro
Jörgens, H., Goritz, A., & Kolleck, N. (2018). Vantagens e desafios da análise de dados do Twitter: O caso das negociações multilaterais sobre as mudanças climáticas
Horta, P., Lagoa, S., & Martins, L. (2016). Unveiling investorinduced channels of financial contagion in the 2008 financial crisis using copulas.?Quantitative Finance,?16(4), 625637
Frois, C. (2013).?Peripheral vision: Politics, technology, and surveillance?(Vol. 22). Berghahn Books
Facer, K. (2011).?Learning futures: Education, technology and social change. Taylor & Francis
Berbel, J., BorregoMarin, M., Exposito, A., Giannoccaro, G., MontillaLopez, N. M., & RosetaPalma, C. (2019). Analysis of irrigation water tariffs and taxes in Europe.?Water Policy,?21(4), 806825
Bento, N. (2010). Dynamic competition between plugin hybrid and hydrogen fuel cell vehicles for personal transportation.?International journal of hydrogen energy,?35(20), 1127111283
Bento, N., & Fontes, M. (2015). Spatial diffusion and the formation of a technological innovation system in the receiving country: The case of wind energy in Portugal.?Environmental Innovation and Societal Transitions,?15, 158179
Bento, N. (2016). Calling for change? Innovation, diffusion, and the energy impacts of global mobile telephony.?Energy Research & Social Science,?21, 84100.
Bento, N., & Fontes, M. (2019). Emergence of floating offshore wind energy: Technology and industry.?Renewable and Sustainable Energy Reviews,?99, 6682
Bento, N., Gianfrate, G., & Thoni, M. H. (2019). Crowdfunding for sustainability ventures.?Journal of Cleaner Production,?237, 117751
Barak, M. (2017). Science teacher education in the twentyfirst century: A pedagogical framework for technologyintegrated social constructivism.?Research in Science Education,?47(2), 283303.
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Stochastic Processes and Simulation
LG1. Study the basic concepts of the theory of stochastic processes
LG2. Understand the most important types of stochastic processes and study the properties and characteristics of processes
LG3. Understand the methods of description and analysis of complex stochastic models
LG4. 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
LG5. Understand the nature of diffusion processes in a network like Twitter, where information diffusion is ubiquitous
LG6. Understand the two 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
LG7. Understand the mathematical study and numerical simulation of branching processes that reveal the dissemination of information in a network, especially an online social network, such as Twitter
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. Examples of modelling with random matrices with MATLAB;
PC8. Study of difussion models in a graph. Applications to complex networks. Discussion of a reallife case: study of diffusion of information on Twitter;
PC9. Numerical simulation of a branching process that reveals the dissemination of information in a network, such as Twitter.
Approval with an overall grade of at least 10 points (scale 120) in one of the following modes:
 Periodic assessment: Test 1 (35%) + Test 2 (45%) + 2 practical work in Python (or MATLAB) (20%), or
 Assessment by Exam (80%), in any of the exam periods, where the practical work (mentioned above) maintain the weight of 20%.
All the elements of the assessment have a minimum score of 8 points (scale 120).
Title: Levin D.A., Peres Y. (2017). Markov Chains and Mixing Times, 2nd Revised edition.American Mathematical Society.
Brzezniak Z., Zastawniak T. (1998). Basic Stochastic Processes: A Course Through Exercises. Springer Undergraduate Mathematics Series.
Dobrow R.P. (2006). Introduction to Stochastic Processes with R, 1st Edition. Wyley.
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Title: A. Edelman, "Random matrix theory and its innovative applications" (MATLAB codes) https://math.mit.edu/~edelman/publications/random_matrix_theory_innovative.pdf
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Project in Applied Mathematics II
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 (lofi, hifi, 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  lofi, high fidelity  hifi, 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 projectbased 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: Lofi and Hifi 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 Audiovisual presentation of the solution and its demonstration in a Workshop: 20%.
Title: Outra bibliografia dependente dos temas específicos do projeto e das organizações onde os alunos o irão desenvolver.
Brown, T (2009), Change by Design: How Design Thinking Transforms Organizations and Inspires Innovation, HarperCollins, 2009, ISBN13: 9780062856623
Lewrick, M, Link, P., Leifer, L. (2020). The Design Thinking Toolbox, Wiley, ISBN 9781119629191
Knapp, J., Zeratsky, J., & Kowitz, B. (2016). Sprint: How to Solve Big Problems and Test New Ideas in Just Five Days. Bantam Press.
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DataDriven Decision Making
PC1. Regression models: correlation and causality, simple linear regression, multiple regression. Multicollinearity
PC2. Estimation and inference, ordinary least squares (OLS) and maximum likelihood (ML)
PC3. Residuals assumptions: hypothesis and diagnostic tests
PC4. Polynomial regression and regression with categorical variables. Dummy variable
PC5. Prediction (insample and outofsample). Training set and test set. Metrics for evaluating prediction performance (RMSERoot Mean Squared Error, MAPEMean Absolute Percentage Error, MAEMean Absolute Error). Predictive analytics
PC6. Logistic regression. Classification problems. Confidence matrix and ROC (Receiver Operating Characteristic) curve
PC7. Fuzzy sets. QCA (Qualitative Comparative Analysis): csQCA, fsQCA, mvQCA and tQCA
PC8. Other multivariate statistical models: cluster analysis, discriminant analysis, principal components and fuzzy clustering.
The programmatic contents are structured with a theoretical and practical basis, which allows reaching and ensuring knowledge that enables decision making based on regression models (for prediction and classification problems). This demonstration of coherence derives from the interconnection of the programmatic contents (PCs) with the learning goals (LGs), as explained below:
LG1: PC1
LG2: PC2
LG3: PC3
LG4: PC4
LG5: PC5
LG6: PC6, PC7, PC8
LG7: from PC1 to PC8
LG8: from PC1 to PC8
Approval with classification not less than 10 points (scale 120) in one of the following modalities:
 Periodic assessment: 2 practical works in Python (50%) + Individual discussion of the two practical works (20%) + 3 quizzes (30%)
 Assessment by Exam (65%), in any of the exam periods, where one of the practical Python practical work (mentioned above) maintains the weight of 35% (with discussion).
All the elements of evaluation have a minimum score of 8 points (scale 120).
Title: RogelSalazar J. (2018). Data Science and Analytics with Python. Taylor & Francis Group.
Hastie T., Tibshirani R., Friedman J. (2017). The elements of statistical learning: data mining, inference, and prediction. Springer. [electronic resource: https://web.stanford.edu/~hastie/Papers/ESLII.pdf ]
Agresti A., Franklin C., Klingenberg B. (2018). Statistics: The Art and Science of Learning from Data, 4th Edition. Pearson.
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Title: Albright S.C., and Winston W.L. (2019). Business Analytics: Data Analysis & Decision Making, 7th Edition. Cengage Learning.
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Accreditations