Quantitative Methods
A.Y. 2024/2025
Learning objectives
The purpose is that students learn the main mathematical and computational tools needed for formal methods in advanced courses for Environmental Science, and other life sciences. The course serves mostly to refresh students' knowledge in certain topics, and to ensure that all students taking the advanced courses have a common mathematical level.
Expected learning outcomes
Students should develop an understanding of the dynamical systems with application in the environmental science and the knowledge of optimization methods.
Lesson period: First semester
Assessment methods: Esame
Assessment result: voto verbalizzato in trentesimi
Single course
This course can be attended as a single course.
Course syllabus and organization
Single session
Responsible
Lesson period
First semester
Course syllabus
Linear Algebra and applications. Real vector spaces. Linear combination, dependence and linear independence. Basis and dimension in R^n. Algebra of vectors, inner product and Norm. Matrix algebra (inverse, rank, derivatives, eigenvalues, diagonalization and factorization).
Introduction to Graph theory and applications.
Basic Calculus for Real functions on Rn.
Optimization. First and Second order conditions for unconstrained problems. Constrained optimization: equality constraints and Lagrange Multipliers. Inequality constraints. Linear programming. Discrete and continuous dynamical systems with applications.
[Brief introduction to R or Matlab Laboratory ]
Introduction to Graph theory and applications.
Basic Calculus for Real functions on Rn.
Optimization. First and Second order conditions for unconstrained problems. Constrained optimization: equality constraints and Lagrange Multipliers. Inequality constraints. Linear programming. Discrete and continuous dynamical systems with applications.
[Brief introduction to R or Matlab Laboratory ]
Prerequisites for admission
Prerequisites for this course include a good knowledge of the mathematical tools presented in a basic Calculus course and a Basic Linear Algebra course.
Teaching methods
Frontal Lessons and practicals
[Brief introduction to R or Matlab Laboratory ]
[Brief introduction to R or Matlab Laboratory ]
Teaching Resources
As a complement to the notes of the teachers, we suggest the following books:
David C. Lay, Steven R. Lay and Judi J. McDonald, Linear Algebra and Its Applications, Pearson, 2016
K. Sydsaeter, P. Hammond, A. Strom, A. Carvajal, Essential Mathematics for Economic Analysis, Pearson, 2016
E. Salinelli, F. Tomarelli, Discrete-Dynamical Models, Springer, 2014, ISBN: 978-3-319-02290-1
MyAriel web site
David C. Lay, Steven R. Lay and Judi J. McDonald, Linear Algebra and Its Applications, Pearson, 2016
K. Sydsaeter, P. Hammond, A. Strom, A. Carvajal, Essential Mathematics for Economic Analysis, Pearson, 2016
E. Salinelli, F. Tomarelli, Discrete-Dynamical Models, Springer, 2014, ISBN: 978-3-319-02290-1
MyAriel web site
Assessment methods and Criteria
Assignments (not mandatory):
Assignments using exam.net: maximum 2 points.
P% = percentage of points compared to total points (considering all homework)
It is necessary to have done at least half of the homework
P% >= 75% 2 points
P% >= 45% and < 75% 1 points
P% >0 and < 45% 0.5 points
-----
Written test
6 multiple choice answers = 2 points for each correct answer;
2 multiple choice answers = 4 points for each correct answer;
2 open answers = 6 points for each correct answer.
Minimum (threshold) =18 points
maximum = 32 points
........................................................................................
Project (not mandatory)
3 points if basic requirements are met
Assignments using exam.net: maximum 2 points.
P% = percentage of points compared to total points (considering all homework)
It is necessary to have done at least half of the homework
P% >= 75% 2 points
P% >= 45% and < 75% 1 points
P% >0 and < 45% 0.5 points
-----
Written test
6 multiple choice answers = 2 points for each correct answer;
2 multiple choice answers = 4 points for each correct answer;
2 open answers = 6 points for each correct answer.
Minimum (threshold) =18 points
maximum = 32 points
........................................................................................
Project (not mandatory)
3 points if basic requirements are met
MAT/06 - PROBABILITY AND STATISTICS - University credits: 2
MAT/08 - NUMERICAL ANALYSIS - University credits: 4
MAT/08 - NUMERICAL ANALYSIS - University credits: 4
Practicals: 32 hours
Lessons: 32 hours
Lessons: 32 hours
Professor:
Naldi Giovanni
Professor(s)