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This book provides an introduction to elementary probability and to Bayesian statistics using de Finetti's subjectivist approach. The subjective evaluation of expectation and of conditional expectation is based on an economic choice of an acceptable bet or penalty.

Finite volume methods are used in numerous applications and by a broad multidisciplinary scientific community. The book communicates this important tool to students, researchers in training and academics involved in the training of students in different science and technology fields.

This textbook presents problems and exercises at various levels of difficulty in the following areas: Classical Methods in PDEs (diffusion, waves, transport, potential equations); Variational Formulation of Elliptic Problems; and Weak Formulation for Parabolic Problems and for the Wave Equation.

This is an introductory textbook on general and algebraic topology, aimed at anyone with a basic knowledge of calculus and linear algebra. complete metric spaces and function spaces; It is suitable for anyone needing a basic, comprehensive introduction to general and algebraic topology and its applications.

The second edition has been revised to correct minor errata, and features a number of carefully selected new exercises, together with more detailed explanations of some of the topics. A complete Solutions Manual, containing solutions to all the exercises published in the book, is available.

Accordingly, this textbook is not meant to cover the whole range of this high-performance technical programming environment, but to motivate first- and second-year undergraduate students in mathematics and computer science to learn Matlab by studying representative problems, developing algorithms and programming them in Matlab.

Questo testo e espressamente concepito per i corsi brevi del nuovo ordinamento delle Facolta di Ingegneria e di Scienze. Esso affronta tutti gli argomenti tipici della Matematica Numerica, spaziando dal problema di approssimare una funzione, al calcolo dei suoi zeri, delle sue derivate e del suo integrale definito fino alla risoluzione approssimata di equazioni differenziali ordinarie e di problemi ai limiti. Due capitoli sono inoltre dedicati alla risoluzione di sistemi lineari ed al calcolo degli autovalori di una matrice, mentre un capitolo iniziale conduce lo studente ad un rapido ripasso degli argomenti dell'Analisi Matematica di uso frequente nel volume e ad una introduzione al linguaggio Matlab. I vari argomenti sono volutamente affrontati a livello elementare ed i paragrafi che richiedono maggior impegno sono stati opportunamente contrassegnati. In questa quarta edizione il linguaggio Octave (di distribuzione gratuita) si affianca a MATLAB.

This book provides an introduction to the analysis of discrete dynamical systems. The content is presented by an unitary approach that blends the perspective of mathematical modeling together with the ones of several discipline as Mathematical Analysis, Linear Algebra, Numerical Analysis, Systems Theory and Probability.

Stats for social sciences is frequently the subject of textbooks, while maths for social sciences is often neglected: monographs on specific themes (like, for instance, social choice systems or game theory applications) are available, but they do not adequately cover the topic in general.

This book provides an introduction to various aspects of Algebraic Statistics with the principal aim of supporting Master's and PhD students who wish to explore the algebraic point of view regarding recent developments in Statistics.

As a limit theory of quantum mechanics, classical dynamics comprises a large variety of phenomena, from computable (integrable) to chaotic (mixing) behavior.

This textbook will present, in a rigorous way, the basic theory of the discrete-time and the continuous-time Markov chains, along with many examples and solved problems. This textbook is intended for a basic course on stochastic processes at an advanced undergraduate level and the background needed will be a first course in probability theory.

The purpose of the volume is to provide a support textbook for a second lecture course on Mathematical Analysis. This new edition features additional material with the aim of matching the widest range of educational choices for a second course of Mathematical Analysis.

This primer covers a remarkably wide range of topics in discrete calculus, from combinatorics to recurrence relations. With examples and exercises throughout, the text's clarity and rigor are informed by extensive teaching experience and academic discussion.

The book collects over 120 exercises on different subjects of Mathematical Finance, including Option Pricing, Risk Theory, and Interest Rate Models.

This book provides a basic introduction to reduced basis (RB) methods for problems involving the repeated solution of partial differential equations (PDEs) arising from engineering and applied sciences, such as PDEs depending on several parameters and PDE-constrained optimization.

This book provides a basic, initial resource, introducing science and engineering students to the field of optimization. It covers three main areas: mathematical programming, calculus of variations and optimal control, highlighting the ideas and concepts and offering insights into the importance of optimality conditions in each area.

In this book we describe the magic world of mathematical models: starting from real-life problems, we formulate them in terms of equations, transform equations into algorithms and algorithms into programs to be executed on computers.A broad variety of examples and exercises illustrate that properly designed models can, e.g.: predict the way the number of dolphins in the Aeolian Sea will change as food availability and fishing activity vary; describe the blood flow in a capillary network; calculate the PageRank of websites.This book also includes a chapter with an elementary introduction to Octave, an open-source programming language widely used in the scientific community. Octave functions and scripts for dealing with the problems presented in the text can be downloaded from https://paola-gervasio.unibs.it/quarteroni-gervasioThis book is addressed to any student interested in learning how to construct and apply mathematical models.

Then, after a self-contained presentation of degree theory for continuous self-maps of the circumference, we study the global theory of plane curves, introducing winding and rotation numbers, and proving the Jordan curve theorem for curves of class C2, and Hopf theorem on the rotation number of closed simple curves.

This textbook is the result of many years of teaching quantum and statistical mechanics, drawing on exercises and exam papers used on courses taught by the authors.

The book represents a basic support for a master course in electromagnetism oriented to numerical simulation.

In turn, the second part focuses on applications, covering a large variety of significant results ranging from ordinary differential equations in Banach spaces, to partial differential equations, operator theory, functional analysis, measure theory, and game theory.

L'analisi statistica dei dati sperimentali, la loro elaborazione ed una corretta stima degli errori sono conoscenze necessarie agli studenti di fisica, biologia, chimica, ingegneria e dei corsi di specializzazione tecnico-scientifici in cui è richiesta pratica di laboratorio. Chi si occupa di problemi tecnici e di misure, per studio o per lavoro, deve possedere gli strumenti matematici di calcolo e di analisi necessari ad una corretta interpretazione dei dati sperimentali.Il testo fornisce in modo sintetico, chiaro ed esaustivo, tutte le nozioni e le conoscenze utili allo scopo. Gli argomenti sono esposti in modo rigoroso ma fluido e vengono introdotti con gradualità. Sono riportati i teoremi e le formule essenziali per una completa comprensione evitando, tuttavia, eccessivi appesantimenti matematici.Il libro è stato pensato per consentire ai docenti di scegliere autonomamente gli esperimenti per l'applicazione delle nozioni studiate.

This short book, geared towards undergraduate students of computer science and mathematics, is specifically designed for a first course in mathematical logic.