# Unit MATHEMATICAL METHODS FOR GEOSCIENCES

Course
Geosciences for risk and environment management
Study-unit Code
A002122
Location
PERUGIA
Curriculum
In all curricula
Teacher
Maurizio Petrelli
Teachers
• Maurizio Petrelli
Hours
• 42 ore - Maurizio Petrelli
CFU
6
Course Regulation
Coorte 2023
Offered
2023/24
Learning activities
Caratterizzante
Area
Discipline mineralogiche, petrografiche e geochimiche
GEO/07
Type of study-unit
Obbligatorio (Required)
Type of learning activities
Attività formativa monodisciplinare
Language of instruction
English
Contents
Initial review and alignment activity about partial derivatives, integrals, the study of functions, vectors, and matrices.

* Basic notions of descriptive statistics, inference, geostatistics, and applications;
* Data processing, reliability, and applications;
* Time series, spatial series, and applications;
* Interpolation and regression methods;
* Elements of numerical calculation and applications.

For all contents there are exercises, based on geological case studies in the different disciplines of Earth Sciences, to be carried out in the classroom with the students and independently using Python.
Reference texts
Measurements and their Uncertainties - Huges and Hase - Oxdord University Press

Introductory Statistics - S.M. Ross - Academic Press

An Introduction to Error Analysis - J.R. Taylor - University Science Books

Programming for Computations - Python - S.Linge and H.P. Langtangen - Springer
Educational objectives
The primary objective of the teaching is to provide the essential mathematical tools for analyzing and interpreting data for geological applications.

The main knowledge acquired will be:

- knowledge of the statistical principles to analyze and interpret geological data;

- knowledge of the concepts of measurement, error, precision, and accuracy

- Basic knowledge of spatial and temporal series;

- knowledge of the theoretical and practical concepts and methods of interpolation and regression;

- knowledge of the theoretical and practical methods of numerical calculation applied to geological problems;

- Introduction to Python to solve geological problems.
Prerequisites
It could be useful a basic knowledge of mathematic concepts.
Teaching methods
Theoretical lessons and practical training
Other information
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Learning verification modality
The evaluation is determined by passing one or more written tests, aimed at verifying the acquisition of knowledge and skills as reported by the European descriptors system (Descriptors of Dublin).

In detail, students must be able to demonstrate that they can develop and apply original ideas, solve problems in new or unfamiliar environments, manage complex problems, analyze incomplete data, communicate conclusions and knowledge to specialists and non-specialists interlocutors.
Extended program
Initial review and alignment activity about partial derivatives, integrals, the study of functions, vectors, and matrices.

Basic notions of descriptive statistics, inference, geostatistics, and applications
* Concept of population and sampling, average, mode, median, variance, and standard deviation;
* frequency distributions (frequency histogram of a dataset, normal distribution, log-normal distribution, exponential distribution, the meaning of descriptive parameters in frequency distributions);
* concept of probability, frequency distributions;

Data processing, reliability, and applications
* Elements of error theory, sampling, and sample representativity;
* graphical representation techniques of data.

Time series, spatial series, and applications
* Introduction to different approaches for the study of time series (classic, stochastic);
* basic concepts (stationary and non-stationary, persistent and antipersistent series, etc.);
* correlation and autocorrelation;

Interpolation and regression methods
* Regression analysis (covariance and correlation, correlation coefficient, linear and non-linear regression).

Elements of numerical calculation and applications
* resolution of linear systems;
* an outline of least squares approximation (least squares in data approximation problems);
* introduction to the numerical solution of differential equations.

Examples of applications include: stratigraphic logs, sedimentary sequences, topographic profiles, compositional series, hydrological series, climatic series, series of events (ie earthquakes, volcanic eruptions, instabilities), interpolation of geochemical data and topographic attributes, satellite image analysis, of outcrops, thin sections and segmentation of objects, numerical modeling of aquifers and landslides, etc ...

For all contents there are exercises, based on geological case studies in the different disciplines of Earth Sciences, to be carried out in the classroom with the students and independently using the Python language.
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