Exercices - Mathématiques
67 documents à télécharger gratuitement
Exercices de mathématiques partagés par des étudiants et des enseignants. Thèmes couverts : algèbre, analyse, probabilités, statistique, optimisation.
This document contains a series of exercises focused on algebra and analysis for first-year university students. It addresses function definitions, domains, continuity, and limit calculations. Several problems require students to investigate the properties of functions and demonstrate mathematical reasoning.
This document contains a series of revision exercises for a first-year algebra and analysis course at the University of Manouba. It includes defined integral calculations and problems involving functions and their primitives. Students are asked to demonstrate various properties and solutions using integration techniques.
This document contains a series of exercises focused on limited expansion in calculus, specifically targeting algebraic functions and logarithmic functions. Each exercise encourages the derivation of functions and investigations into their behavior at various limits. It's designed for first-year university students studying algebra and analysis.
The document presents a statistical analysis problem focused on estimating the consumption of a specific article for the current year based on last year's data. Monthly consumption figures and percentage variations (Rn) are provided. The task involves using this data to project consumption, specifically rounding values with different precision rules applied to specific parameters. A methodological approach to calculations is implied, though not explicitly detailed.
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.
This document delves into the examination and translation of propositional functions into predicate logic, establishes the validity of specific reasoning examples, and validates representations within model contexts. The methodology involves logical constructs, syntax definitions, and interpretation of predicates and constants within specified universes. Key solutions demonstrate truth values in defined models and introduce formal constructions using quantifiers, predicates, and identity relationships.
This document outlines a series of practice exercises in predicate logic, guiding students in translating natural language statements into formal logic expressions. It includes detailed examples of translations with variations based on ambiguous cases and alternate interpretations. The exercises cover fundamental concepts like quantifiers, opposition squares, and nested logical structures. Correct solutions and multiple translation possibilities are provided in the corresponding solution section to help clarify ambiguities and illustrate proper formalization techniques.
This document contains the solutions to an exam on applied probabilities focusing on various problems including infection probabilities in a cybercafé, accidental medication ingestion and survival rates. It elaborates on probabilistic models and calculations relevant to real-world scenarios.
This document contains exam exercises focusing on probability and statistics concepts. The first exercise involves calculating the minimum value of N for a certain probability condition. The second exercise addresses a candidate's electoral survey with a sample size and needs to establish a minimal effective sample size.
This document covers topics related to resolution methods in mathematical logic. It includes exercises on transforming formulas into clauses and determining satisfiability of certain clause sets. Additionally, it explores logical consequences using predicate symbols.
This document presents a home assignment for the Module of Mathematics for Engineers at the Ecole Nationale des Sciences de l’Informatique. It includes exercises on Fourier transforms, convolution products, and the application of the Shannon theorem regarding band-limited functions. Students are required to calculate specific mathematical integrals and demonstrate key properties of Fourier series.
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 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...