
Course unit
MATHEMATICS FOR ECONOMICS
EPP6077338, A.A. 2018/19
Information concerning the students who enrolled in A.Y. 2018/19
ECTS: details
Type 
ScientificDisciplinary Sector 
Credits allocated 
Core courses 
SECSS/06 
Mathematics for Economics, Actuarial Studies and Finance 
9.0 
Course unit organization
Period 
First semester 
Year 
1st Year 
Teaching method 
frontal 
Type of hours 
Credits 
Teaching hours 
Hours of Individual study 
Shifts 
Lecture 
9.0 
63 
162.0 
No turn 
Examination board
Board 
From 
To 
Members of the board 
2 Commissione A.A. 2018/19 
01/10/2018 
30/09/2019 
BURATTO
ALESSANDRA
(Presidente)
GROSSET
LUCA
(Membro Effettivo)
VISCOLANI
BRUNO
(Membro Effettivo)

Prerequisites:

Basic calculus, Differential calculus, Integrals, Basic Linear Algebra 
Target skills and knowledge:

The objective of this course is to equip students with the basic mathematical techniques required for a rigorous study of Economics. Students are expected to acquire knowledge and understanding of advanced mathematical tools in order to use them with autonomy in Economics and Finance issues. 
Examination methods:

Exercises and problems related to the arguments just presented in class will be assigned through Moodle each week. Homework contribution to the final evaluation up to 3 points.
A final written test with exercises (max evaluation 28/30). 
Assessment criteria:

The evaluation will be based on the knowledge of the topics covered during the lessons. In addition to a good learning ability, it is expected the ability to apply the acquired knowledge in an autonomous and competent way. 
Course unit contents:

 Calculus of a Single Variable: differentiation and optimization of realvalued functions of a single variable, (a brief review)
 Vector Algebra: matrices and linear systems (review), eigenvalues and eigenvectors
 Multivariable Calculus: Differentiation of RealValued Functions of several variables, Concave and Quasiconcave functions. Implicit function theorem.
 Optimization (unconstrained and constrained): Equality constraints: Lagrange Method (review), Inequality constraints: KuhnTucker conditions, Envelope theorem, Comparative statics
 Fixed Point Theorems and Applications: Brouwer’s and Kakutani’s theorems, Implicit function theorem
 Differential Equations: ODE systems, dynamic systems
 Optimal control: Pontryagin's Maximum Principle
 Dynamic Programming: Hamilton Jacobi Bellman equation 
Planned learning activities and teaching methods:

All the slides presented during the classes will be uploaded in Moodle together with the related audio records.
All "Mathematica" files created for the course will be uploaded in Moodle.
The homework assigned in Moodle will be evaluated and commented in class focussing on tricky concepts. 
Additional notes about suggested reading:

The lecture notes in pdf, the audio recording of the lessons (mp3 files) and other teaching material, together with specific communications from the lecturer can be found, inside the Moodle platform. 
Textbooks (and optional supplementary readings) 

Simon, Carl P. and Lawrence Blume, Mathematics for Economists  International student edition. New York  London: Norton, 2010.

Morton I. Kamien and Nancy L. Schwartz, Dynamic Optimization. Mineola New York: Dover Publications, Inc, 2012. 2nd. Ed

Innovative teaching methods: Teaching and learning strategies
 Interactive lecturing
 Working in group
 Problem solving
 Flipped classroom
 Loading of files and pages (web pages, Moodle, ...)
 Students peer review
 recordered audios of lessons
Innovative teaching methods: Software or applications used
 Moodle (files, quizzes, workshops, ...)
 One Note (digital ink)
 Latex
 Mathematica
Sustainable Development Goals (SDGs)

