MATHEMATICAL MODELS FOR DECISION MAKING

The course will cover some theory, mathematical tools and applications of decision models, stressing practical use of the software R (downloadable at http://cran.r-project.org/ or https://www.rstudio.com/ ) to solve exercises and study cases. Many topics are related to linear algebra, which allows formal definitions of problems and models used in international markets and economies.

a) Knowledge and understanding:
- know terms and concepts of linear algebra to define decision problems; know the main results used to solve linear systems;
- know terms and ideas to formulate optmization problems and their applications;
- know terms and functioning of methods to rank a set of discrete alternatives;

b) Applying knowledge and understanding:
- ability to use linear algebra and solve linear systems with R;
- ability to formally define a free or constrained optmization problem and find a numerical solution;
- ability to devise a decision problem using AHP ann obtain its computational solutions.

c) Making judgements:
- understand and critically assess numerical results obtained solving some decision problems and evaluate potential issues of the tools that were used;
- make sense of the solutions and assess the consitency of the decision maker suggesting, if appropriate, revision and further invetigations (e.g., in AHP cases).

Students must already know calculus and the basics of matrices and vectors (the course will begin with a reinterpretation of matrix-vector product and definition of linear dependence/independence). There are no prerequisites related to R or programming and no previous experience in decision theory is assumed.

Famous theorems for the solutions of linear systems;
Inverses and pseudo-inverses;
Introduction to the State Preference Model, arbitrage and financial examples;
Optimization (basic topics);
Advanced optimization and eigenvalues/eigenvectors;
Analytic Hierarchical Process (AHP).

There is no formal textbook (but any good treatment of linear algebra would do the job), learning material will be provided online.

There is a test of 10 questions at the end of each unit. Questions are made public in advance and the test can be attempted only once (after the material has been studied). A certificate will be issued to anyone with an average score of 70% or more (on the 6 tests).
Formal credits will be awarded after an oral exam.
[Update of May 2020: due to the state of prolonged covid-19 emergency the exam will be held on GMeet or similar platforms. See the moodle page of the course for additional info and details]

The course has 6 learning units (to be covered approximately in 6 weeks) and will be delivered entirely online on http://moodle.unive.it/ , similarly to what is done in a Massive Open Online Course (MOOC). The course is open to anyone and students enrolled at Ca’ Foscari will work on the material to gain credits for their academic program (with additional studying activities). We expect the forum to be lively and participated by all the students taking the course.

On Moodle the course is named "Take LineaR Decisions".

English

Information and videos are available at http://moodle.unive.it/ (enroll in "Take LineaR Decisions").

Accessibility, Disability and Inclusion
Accommodation and support services for students with disabilities and students with specific learning impairments

Ca' Foscari abides by Italian Law (Law 17/1999; Law 170/2010) regarding support services and accommodation available to students with disabilities. This includes students with mobility, visual, hearing and other disabilities (Law 17/1999), and specific learning impairments (Law 170/2010). If you have a disability or impairment that requires accommodations (i.e., alternate testing, readers, note takers or interpreters) please contact the Disability and Accessibility Offices in Student Services: disabilita@unive.it.

oral

This subject deals with topics related to the macro-area "Human capital, health, education" and contributes to the achievement of one or more goals of U. N. Agenda for Sustainable Development