Instructional goals
1) To learn basic quantitative methods needed to attack simple, yet nontrivial, problems in management which concern Optimization and Data Analysis in various forms.
The main tools to be learned are in the families of basic Linear Algebra and basic Optimization. In particular there will be a specific focus on Linear Programming and its management applications.
These are essential tools to understand and develop basic mathematical models in management.
2)To understand how basic mathematical modeling can help to solve simple, yet nontrivial, problems in management. To develop and solve such models in simple cases. To bring such models to the real world.
Prerequisites
All basic mathematics courses of Laurea Triennale in Management.
In particular:
- Calculus for one variable functions (basic topology, functions and their properties, limits derivatives and their connection with monotonicity and convexity, integrals, graph of functions);
- Searching extremals and zeros for one-variable functions using the appropriate theorems;
- Basic linear algebra concepts (vector spaces and their bases, linear dependence and independence of vectors, matrices, rank, determinant, linear systems, Rouché-Capelli Theorem)
- Basic calculus for several variables: topology in R^n, limits, continuity, differentiability, gradient and its properties (the last two parts will be briefly reviewed during the course when needed).
Intended learning outcomes
1) Knowledge and understanding:
The course will offer the basic theoretical tools of Linear Algebra and Optimization. These are key tools to understand and develop mathematical models in management.
2) Applying knowledge and understanding:
The students will be taught how to use the above basic tools to develop simple mathematical models of real phenomena such as:
- Robust ranking methods;
- Data Approximation;
- Production/logistic management
3) Making judgements:
We expect students to be able to - understand the main mathematical features of basic management models;
- judge the reliability of information on quantitative modeling that they read in papers;
- build simple mathematical models of real problems.
4) Communications Skills:
This course will give the students the possibility to acquire and understand major terms and concepts in order to communicate their ideas, proposals, analysis and critical reasoning in the field of mathematical modeling in the most effective and appropriate way.
5) Learning skills:
This course will contribute to empower learners giving them the tools to evaluate the statements on quantitative mathematical modeling (that they can read in the press or in specialized journals) in an independent way.
Course Contents
- Some motivating problems;
- Review of calculus of one variable;
- Basic linear algebra concepts (vector spaces and their bases, linear dependence and independence of vectors, matrices, rank, determinant, linear systems, Rouché-Capelli Theorem, Eigenvalues)
- Basic ideas of Optimizazion
- Linear Programming
- Integer Programming
- Basic calculus for several variables: topology in R^n, limits, continuity, differentiability, gradient and its properties;
- Least square method and use of it in regression.
- Gradient Descent Method and use of it
- Use of the above techniques to build mathematical models of real phenomena.
Reference Books
1)
A Guide to Business Mathematics
By Gerard O'Regan
2)
Mathematical Applications for the Management, Life, and Social Sciences Copertina rigida – 1 gennaio 2018
Edizione Inglese di Ronald J. Harshbarger (Autore), James J. Reynolds (Autore)
3)
MATEMATICS FOR ECONOMISTS
Carl Simon e Lawrence Blume
W.W. NORTON & COMPANY.
4)
Notes given by the teacher.
Teaching Methods
Lessons and Exercises sessions.
“Teaching is not transferring knowledge, but creating the conditions for its production or construction”
Assessment Method
33% project assigned during the course:
67% final exam: written and oral
Thesis assignment criteria
Interviewv
Week 1
- Introduction to the course and motivating problems: data aggregation, optimization, ranking.
- What you need to know about calculus of one variable functions: mainly finding maxima, minima and zeros, but in a clever way.
Week 2
- On vectors and their use: basic operations and examples (production processes, data strings, financial positions, etc);
Week 3
Vector spaces, bases, dimension, linear dependence, rank and their practical interpretation (e.g. in production processes, data analysis, financial portfolios)
Week 4
On matrices and their practical use in the above examples.
- rank and determinant of matrices and their use
Week 5
Linear Systems and the way to use them in the above examples
Week 6
Matrices as linear operators: basic eigenvalue theory and its use in data interpretation (Principal Component Analysis).
Week 7
More on eigenvalue theory and its use.
Week 8
Introduction to Optimization.
Linear programming as the simplest optimization theory, basic ideas and examples on transport and inventory problems
Week 9
Linear Programming and Simplex Algorithm and its use in the above problems
Week 10
When granularity arise: integer programming.
Basic ideas and examples in storage problems.
Week 11
Basic Calculus in several variables: the tool for more complex optimization problems
Week 12
Least Squares method and its use in regression theory and practice.
Gradient descent and its use in basic convex optimization.
Ideas on what to do in nonconvex problems.