Course: Advanced Data Analysis and Mathematical Models 2

Objectives

Introduction to the fundamental models involved in the classical optimization problems of operational research, from linear programming (simplex) to integer programming (branch-and-bound). The framework of the modern theory of decision under risk, from Von Neumann and Morgenstern's Expected Utility Theory to Kahneman and Tversky's Cumulative Prospect Theory. Finally, introduction to the theory of ordinary linear differential equations.

Contents

The syllabus of the module is structured into three parts, after a preliminary review of the fundamental notions and techniques of linear algebra and linear systems: (I) linear programming (simplex) and integer programming (branch-and-bound); (II) models of decision under risk, the framework of anticipated utility theory; (III) first and second order ordinary linear differential equations.

Requirements

The fundamental knowledge obtained in the basic mathematics and statistics undergraduate courses.

Teaching Methods

Traditional lectures and exercise classes on the blackboard.

Verification of learning

A final written exam, involving both theory and exercises, in which the student is assessed on his knowledge and understanding of the topics covered in the course. Exceptionally, the lecturer may request a supplementary oral exam.

References

Notes taken in class are the essential course material.

The following material might be of interest for further reading (iNotes taken in class are the essential course material. The following material might be of interest for further reading (in alphabetical order):

• Gleb Beliakov, Ana Pradera, Tomasa Calvo, "Aggregation Functions: a guide for practitioners", Springer 2009, ISBN 9783642092893. Richard Bronson, Govindasami Naadimuthu, "Schaum's Outline of Operations Research" (2nd ed.), McGraw Hill, 1997, ISBN 9780070080201. Tomasa Calvo, A. Kolesarova, M. Komornikova, Radko Mesiar, Aggregation operators: properties, classes and construction methods, pp. 3-104, in: Tomasa Calvo, Gaspar Mayor, Radko Mesiar (Eds.), "Aggregation Operators: new trends and applications", Physica-Verlag, 2002, ISBN 9783790814682. Itzhak Gilboa, "Rational Choice", MIT Press, 2010, ISBN 9780262014007.
• Daniel M. Hausman, "Preference, Value, Choice, and Welfare", Cambridge University Press, 2011, ISBN 9781107695122. Frederick S. Hillier, Gerald J. Lieberman, "Introduction to Operations Research" (8th ed.), McGraw Hill, 2004, ISBN 9780073017792, and 2005, ISBN 9780073211141 (with CD-ROM).
• Frederick S. Hillier, Gerald J. Lieberman, "Introduction to Operations Research" (9th ed.), McGraw Hill, 2009, ISBN 9780077298340 (with student access card). David M. Kreps, "Notes on the Theory of Choice", Westview Press, 1988, ISBN 9780813375533.
• David M. Kreps, "Microeconomic Foundations I: choice and competitive markets", Princeton University Press, 2012, ISBN 9780691155838.
• Seymour Lipschutz, Marc Lipson, "Shaum's Outline of Linear Algebra", (4th edition), McGraw Hill, 2008, ISBN 9780071543521.
• John Quiggin (Ed.), "Generalized Expected Utility Theory: the rank-dependent model", Kluwer Academic, 1993, ISBN 9780792393023. Martin Peterson, "An Introduction to Decision Theory", Cambridge University Press, 2009, ISBN 9780521888370.
• Gilbert Strang, "Linear Algebra and Its Applications" (4th edition) and "Student Solutions Manual for Strang's Linear Algebra and Its Applications" (4th edition), Cengage Learning, 2005, ISBN 9780030105678 and 9780495013259.
• John von Neumann, Oskar Morgenstern, "Theory of Games and Economic Behavior", Princeton University Press, 2007, ISBN 9780691130613.
• Peter P. Wakker, "Additive Representations of Preferences: a new foundation of decision analysis", Kluwer Academic, 1989, ISBN 9780792300502.
• Peter P. Wakker, "Prospect Theory for Risk and Ambiguity", Cambridge University Press, 2010, ISBN 9780521765015.