Mathématiques
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Cours, examens, TD, TP et exercices de mathématiques. Thèmes couverts : algèbre, analyse, probabilités, statistique, optimisation.
This document provides course notes designed for professional undergraduate students (L3) specializing in optical instrumentation and visualization. It covers fundamental Matlab concepts, such as its interface, basic data structures, matrices and vectors, and statistical operations. Graphical data representation in 2D and 3D, as well as numerical simulation based on differential equations, are also explained. Additionally, it touches on signal processing, including Fourier series and discrete Fourier transforms, with a focus on practical data analysis and simulations.
This document discusses the simulation of uniform distribution on (0,1) and explains the necessity of simulations in eliminating biases in physical experiments. It also covers methods for approximating integrals and the generation of random numbers from given distributions using techniques such as rejection methods and the Box-Muller method.
This document introduces the mathematical theories of image processing, focusing particularly on variational methods. It explains the nature of digital images as pixel-based representations with different grayscale or color scales and discusses mathematical techniques like sampling, quantification, and histogram equalization. The key applications of image processing in fields such as robotics, medical imaging, and remote sensing are highlighted, with fundamental methods like filtering, segmentation, and restoration being extensively discussed. Additionally, it elaborates on mathematical too...
This document is a hands-on guide focused on understanding and applying Fourier transformations in image processing using MATLAB. It introduces foundational concepts of 1D and 2D Fourier Transforms, alongside practical exercises exploring image manipulation and frequency dimensions, including spectrum periodicity and FFT visualization. The guide later transitions into compression techniques, explaining JPEG compression via Discrete Cosine Transform (DCT), with step-by-step implementations for block-level compression and reconstruction. The methodology emphasizes frequency domain manipulatio...
This module focuses on statistical hypothesis testing methodologies, covering practical cases such as evaluating the efficiency of marketing campaigns, comparing medication effectiveness, analyzing machine performance in industrial settings, and testing variances of data distributions. Through normal approximation, t-tests, and z-tests, alongside critical value-based decisions and p-value calculations, the document instructs on hypothesis formulation and interpretation within varied real-world contexts.
The document discusses statistical methodologies applied to practical problems such as pollution analysis, election result interpretations, and grading systems. Confidence intervals are employed to estimate population means and probabilities with varying sample sizes and confidence levels. Methodologically, it emphasizes hypothesis testing using normality assumptions, Student's t-distribution for small samples, and Central Limit Theorem approximations for larger samples. It highlights practical decision-making based on statistical inferences, interpreting confidence intervals in real-world...
This chapter discusses the fundamental principles of probability, including axioms, mutually exclusive events, non-mutually exclusive events, and independence. It also covers Bayes' theorem and its application in decision making, providing examples for better understanding. The chapter emphasizes the importance of revising beliefs based on new information and offers practical examples related to market analysis.
This chapter explores decision-making under risk and uncertainty, emphasizing the modeling of decision problems. It discusses the preferences of decision-makers, the nature of uncertainty, and the application of probabilities in decision-making contexts.
This document covers decision trees, a key concept in probability theory. It provides an overview of elementary axioms of probability, independent events, and Bayes' theorem. The content is geared towards understanding how to revise beliefs based on new information.
This document contains the examination for Algebra II held on May 16, 2017. The exam is structured into two main exercises, which assess students' understanding of linear systems, matrix properties, and diagonalization. Students are required to perform calculations and provide theoretical discussions based on the given mathematical problems.
Ce document présente un examen de statistiques et de probabilités pour les étudiants de première année. Il comprend plusieurs questions sur l'analyse des distributions, l'application de théories de probabilités et des tests d'indépendance. L'examen met l'accent sur les justifications et les calculs précis requis pour démontrer la compréhension des concepts abordés.
This document provides an in-depth overview of statistical concepts including central tendency, dispersion, probability distributions, and statistical inference. It highlights the importance of statistics in forecasting and process improvement, emphasizing stability, variability, and data-driven decision-making. Core methodologies include the calculation of statistical measures, analysis of distributions, and exercises on real-life machine operations using statistical tools. It concludes with practical insights into minimizing variability and achieving target objectives while balancing qual...
This document outlines an examination in descriptive statistics for first-year LFIG students. It presents a scenario involving defective computer parts and tasks students with analyzing data related to the repair of these computers. The exam consists of two parts focused on statistical distributions and calculations.
Ce document présente un devoir surveillé sur la statistique descriptive effectué à l'École Supérieure d'Économie Numérique. Il couvre divers exercices sur le calcul des moyennes, médianes et distributions. Les étudiants sont également évalués sur l'interpolation linéaire et les calculs de coûts.
Le cours d’enquête et sondage aborde les aspects théoriques et pratiques de l'analyse de données en traitant de la présence conjointe de variables. Il est scindé en deux parties : la première concerne le sondage et la deuxième le choix du questionnaire. Les étudiants apprendront à créer des questionnaires, coder des variables, et utiliser des logiciels d'analyse de données tels que SPSS.
Ce document présente un cours sur la statistique descriptive et la probabilité. Il aborde les distributions statistiques, les caractéristiques des données, ainsi que l'introduction aux phénomènes aléatoires et aux variables aléatoires discrètes et continues. Le cours vise à donner aux étudiants des outils pour interpréter et résumer des données quantitatives.
Ce document présente un plan de cours sur la statistique descriptive et les probabilités, comprenant des chapitres sur les distributions statistiques et le calcul de probabilité. Il aborde des concepts clés tels que la population, l'échantillon et les types de caractères. Les étudiants apprendront à collecter, organiser et interpréter des données statistiques.
This document presents a series of exercises focused on the diagonalization of matrices, characteristics polynomials, and eigenvalues. It includes various problems that challenge the understanding of matrix properties and diagonalizability. The exercises are intended for first-year students in a mathematics program.
Ce document traite de la diagonalisation des matrices carrées, en introduisant les concepts de vecteurs propres et de valeurs propres, ainsi que les polynômes caractéristiques associés. Il fournit des définitions, des théorèmes, et des exemples pratiques pour illustrer ces notions essentielles en algèbre linéaire.
Ce document présente un mémoire de fin d'études soutenu à l'Université de la Manouba, qui traite de la recherche et de la mise en œuvre d'un logiciel pour réaliser des statistiques de fréquentation à l'aide de caméras. Le travail a été réalisé au sein de l'entreprise ACOBA, spécialisée dans les services de Cloud liés aux caméras de surveillance. L'objectif du projet est d'analyser les données collectées pour fournir des informations précieuses sur le comportement des clients dans les magasins.
This document covers the topic of linear systems within the context of Algebra II. It spans over a period of 4 weeks and is instructed by Tawfik Ben Amor. The references used in the course include a significant textbook on mathematics in economic and management sciences.
Ce chapitre traite des systèmes linéaires dans le cadre d'un cours d'Algèbre II. Il est enseigné par Ben Amor Tawfik sur une période de quatre semaines. Le matériel de référence utilisé provient de l'ouvrage de F. Maghrebi et H. Mallek sur les mathématiques en sciences économiques et de gestion.
This document discusses exercises related to binary symmetric channels, Huffman coding, and the Fano-Shannon coding method. It covers the concepts of probabilities, entropy, and efficiency in coding systems. The exercises require calculations and comparisons of different coding techniques using given random variables.
This document contains solutions to exercises related to information theory and coding, focusing on concepts such as joint probabilities, conditional probabilities, entropy, and mutual information. It explains the calculations for different probabilities and entropies based on given parameters and provides examples of how these concepts apply to communication systems.