Mathématiques
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Cours, examens, TD, TP et exercices de mathématiques. Thèmes couverts : algèbre, analyse, probabilités, statistique, optimisation.
This document contains a series of solutions to linear optimization exercises from a numerical methods course at Université Paris Ouest Nanterre. It specifically covers the simplex method and duality in linear programming. The solutions include step-by-step transformations leading to optimal solutions.
The document presents a series of exercises focused on solving linear programming problems using the simplex method. It includes detailed steps for standardizing the problems, constructing simplex tables, and performing base changes for optimal solutions. The final results of optimal solutions for each exercise are also summarized.
This document discusses two exercises on linear programming, specifically focusing on graphical resolution and the simplex method. The first exercise involves maximizing an objective function with given constraints, while the second exercise entails minimizing another function under different constraints. The document provides detailed steps and illustrations of the simplex algorithm for both exercises.
This document is a homework assignment focused on applying the simplex method to solve linear programming problems. It includes detailed steps for solving two separate problems using primal and dual simplex methods, along with phase one and phase two simplex methods. Each problem is approached methodically, detailing the transformations and calculations needed to arrive at the optimal solutions.
This document presents two exercises in linear programming, focusing on graphical resolution and the identification of feasible solutions. It discusses optimal solutions derived from graphical representation and provides constraints analysis for optimization problems.
This document contains exercises focused on linear programming and the simplex method. It details the resolution of specific linear equations through a structured process of finding optimal solutions. Various mathematical notations and graphical representations are provided to clarify the problem-solving approach.
This document presents an operational research course led by Nadia Brauner at Grenoble, detailing the contributions of various authors and associated activities. It outlines the foundational aspects of operational research, its applications, and the theoretical problems addressed within the course framework. The course is designed for both initial and continuing education in operational research and its applications in industry.
Ce document traite de la recherche opérationnelle avec un accent sur les modèles mathématiques et les techniques de programmation linéaire. Il présente également des applications pratiques des méthodes d'optimisation, y compris la programmation en nombres entiers et les méthodes heuristiques. Finalement, le document se conclut par une discussion sur l'efficacité des algorithmes et des études de cas spécifiques.
Ce chapitre présente des problèmes NP-complets, notamment le 3-SAT et le NAESAT. Il fournit des définitions et des démonstrations pour prouver leur NP-complétude. L'objectif est d'expliquer la relation entre ces problèmes et la classe NP.
This textbook is the product of a decade of pedagogical experience at the University of Geneva, aimed at undergraduate students in fields requiring foundational knowledge in probability and statistical inference. It offers a collection of 212 solved problems spread across eight chapters, each building progressively from basic probability calculations to multivariate random variables and inference techniques. The book covers both combinatorial analyses and theoretical limits, integrating historical insights and theoretical underpinnings like Bayes’ theorem and Kolmogorov's axioms. It serves...
This document is a comprehensive pedagogical resource based on ten years of university teaching experience at the University of Geneva. It contains 212 solved exercises organized into eight chapters that progressively guide the reader through topics such as elementary probabilities, random variables, statistical inference, and Bayesian methods. The exercises include varying difficulties and cover both foundational theories and real-world applications. The book also serves as supplementary material for undergraduate-level courses in economics, psychology, and other sciences and is designed f...
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This document serves as a comprehensive reference for over 500 concepts, formulas, and hypothesis tests related to probability and statistics. It is structured to support students from early university levels and professionals with minimal mathematics background, featuring accessible definitions, intuitive explanations, and discussions of key probability laws. A particular focus is on statistical tests and fundamental mathematical techniques, with emphasis on clarity and usability. The work also offers redundancy and alternative terminologies to bridge gaps in domain-specific language.
This second edition of the reference book provides comprehensive coverage of statistical and probability tools for engineers. It includes the foundational definitions, laws, and formulas of statistics and probability. It is structured into four parts: basic definitions and data summarization techniques; concepts, discrete and continuous probability laws; decision-making topics such as sampling, estimation, hypothesis testing, and regression; and an overview of data analysis, with an added chapter on multiple regression in this new edition.