Algèbre Linéaire (Partie 1) from edX

Vous voulez apprendre l'algèbre linéaire, un précieux outil complémentaire à vos connaissances acquises durant vos études en économie, ingénierie, physique, ou statistique? Ou simplement pour la beauté de la matière? Alors ce cours est fait pour vous! Outre remplir le rôle d'outil dans les différentes branches mentionnées ci-dessus (permettant la résolution de problèmes concrets), l'algèbre linéaire, qui capture l'essence des mathématiques -à savoir, l'algèbre et la géométrie- vous introduira au monde plus abstrait des mathématiques.

Proposé comme complément de cours aux ingénieurs de première année à l'Ecole Polytechnique Fédérale de Lausanne, ce MOOC (composé de trois parties) n'en est pas moins un cours à part entière et peut être considéré comme une base solide d'algèbre linéaire pour tout étudiant intéressé par l'apprentissage de cette matière.

Bien que les vidéos constituent le coeur du cours, des exercices de type QCM (Questions à choix multiples) ainsi que des séries au format PDF seront disponibles chaque semaine, ainsi que des corrigés appropriés. Plus précisément, les séries d'exercices seront accompagnées d'un corrigé au format PDF et certains problèmes bénéficieront d'une correction détaillée en vidéo, dans laquelle l'un des enseignants présentera la solution, étape par étape. Finalement, chaque vidéo de cours sera suivie d'un quiz, dont le but est de tester le degré d’assimilation des connaissances acquises.

Le cours est organisé en dix chapitres dans lesquels une approche très détaillée des concepts théoriques est proposée, ainsi que de multiples exemples illustratifs :

1) Systèmes d'équations linéaires.

2) Algèbre matricielle.

3) Espaces vectoriels.

4) Bases et dimensions.

5) Applications linéaires.

6) Matrices et applications linéaires.

7) Déterminants.

8) Vecteurs propres, valeurs propres, diagonalisation.

9) Produits scalaires et espaces euclidiens.

10) Matrices orthogonales et matrices symétriques.

Cette première partie du cours sera dévouée à l'étude des quatre premiers chapitres cités plus haut. Aucune connaissance particulière n’est requise pour comprendre les concepts abordés dans ce MOOC, mais il est conseillé de travailler régulièrement et de manière assidue, de façon à ne pas prendre de retard lors de l'apprentissage de la matière.

What's inside

Learning objectives

De définir les concepts théoriques introduits en cours et d'en donner des exemples illustratifs ;
D'appliquer la théorie matricielle à la résolution de systèmes linéaires et d’interpréter les résultats obtenus ;
De déterminer si un ensemble muni d'une addition et d'une multiplication par scalaires est un espace vectoriel (ou si un sous-ensemble d'un espace vectoriel est un sous-espace vectoriel) ;

De maîtriser les diverses notions relatives à la théorie des espaces vectoriels (e.g. bases, dimensions, sous-espaces).
A la fin du cours, l'étudiant sera capable

De définir les concepts théoriques introduits en cours et d'en donner des exemples illustratifs ;
D'appliquer la théorie matricielle à la résolution de systèmes linéaires et d’interpréter les résultats obtenus ;
De déterminer si un ensemble muni d'une addition et d'une multiplication par scalaires est un espace vectoriel (ou si un sous-ensemble d'un espace vectoriel est un sous-espace vectoriel) ;
De maîtriser les diverses notions relatives à la théorie des espaces vectoriels (e.g. bases, dimensions, sous-espaces).
A la fin du cours, l'étudiant sera capable

Good to know

Know what's good

, what to watch for

, and possible dealbreakers

Examine les fondements de l'algèbre linéaire, essentielle en économie, ingénierie, physique et statistique

Explore les applications pratiques de l'algèbre linéaire pour résoudre des problèmes concrets

Développe une solide compréhension des concepts théoriques et des exemples illustratifs

Applique la théorie matricielle à la résolution de systèmes linéaires et interprète les résultats obtenus

Détermine si un ensemble est un espace vectoriel ou un sous-espace vectoriel

Maîtrise les notions de bases, de dimensions et de sous-espaces dans les espaces vectoriels

Convient aux étudiants de première année en ingénierie à l'Ecole Polytechnique Fédérale de Lausanne

Requiert un travail régulier et assidu pour suivre le rythme d'apprentissage

Reviews summary

Algèbre linéaire, complément des mathématiques

Ce cours d'algèbre linéaire offre une base solide pour les étudiants en complément de leurs études en économie, ingénierie, physique ou statistique. Il se compose de 10 chapitres couvrant les systèmes d'équations linéaires, l'algèbre matricielle, les espaces vectoriels, les bases et les dimensions, les applications linéaires, les déterminants, les vecteurs propres, les valeurs propres et la diagonalisation, les produits scalaires et les espaces euclidiens, les matrices orthogonales et les matrices symétriques. Les vidéos constituent le cœur du cours, complétées par des exercices QCM, des séries au format PDF et des corrigés. L'approche très détaillée des concepts théoriques et les exemples illustratifs rendent ce cours accessible aux débutants, mais il est recommandé de travailler régulièrement pour suivre le rythme.

Base solide d'algèbre linéaire

"n'en est pas moins un cours à part entière"

Outil complémentaire des maths

"Vous voulez apprendre l'algèbre linéaire, un précieux outil complémentaire à vos connaissances acquises durant vos études en économie, ingénierie, physique, ou statistique"

Travail régulier et assidu

"il est conseillé de travailler régulièrement et de manière assidue"

Activities

Be better prepared before your course. Deepen your understanding during and after it. Supplement your coursework and achieve mastery of the topics covered in Algèbre Linéaire (Partie 1) with these activities:

Review the basics of linear algebra

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This course assumes you have a basic understanding of linear algebra. If you need to brush up on the basics, there are many online tutorials that can help.

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Find an online tutorial on linear algebra
Watch the tutorial videos
Complete the practice exercises

Compile your course materials

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Combine all of your notes, assignments, practice questions, and handouts into a single digital or physical folder for easy reference.

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Gather all the materials you need
Decide on a storage system
Organize and label your materials

Create a visual representation of matrices

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By creating a visual representation of matrices, you will improve your understanding of their structure and properties.

Browse courses on Matrices

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Choose a visualization method (e.g. graphs, tables)
Select the matrices you want to represent
Create your visual representation

Show all three activities

Career center

Learners who complete Algèbre Linéaire (Partie 1) will develop knowledge and skills that may be useful to these careers:

Mathematician

Mathematicians develop new mathematical theories and solve mathematical problems. This course will provide you with a strong foundation in linear algebra, a fundamental area of mathematics with broad applications across various fields. By understanding the concepts of matrices, vectors, and linear transformations, you'll be well-equipped to pursue advanced studies in mathematics and contribute to the field.

See salaries and explore the career path for Mathematician

Computer Scientist

Computer Scientists design, develop, and analyze computer systems. This course will provide you with a foundation in linear algebra, which is increasingly used in computer science for tasks such as computer graphics, image processing, and machine learning. By understanding the concepts of matrices, vectors, and linear transformations, you'll be able to develop efficient algorithms, optimize software performance, and solve complex technical problems.

See salaries and explore the career path for Computer Scientist

Software Engineer

Software Engineers design, develop, and maintain software systems. This course will provide you with a foundation in linear algebra, which is increasingly used in software development for tasks such as computer graphics, image processing, and machine learning. By understanding the concepts of matrices, vectors, and linear transformations, you'll be able to develop efficient algorithms, optimize software performance, and solve complex technical problems.

See salaries and explore the career path for Software Engineer

Operations Research Analyst

Operations Research Analysts use mathematical and analytical techniques to solve complex business problems. This course will provide you with a foundation in linear algebra, which is used in operations research to model and optimize decision-making processes. By understanding the concepts of matrices, vectors, and linear transformations, you'll be able to develop mathematical models, analyze data, and make recommendations to improve operational efficiency.

See salaries and explore the career path for Operations Research Analyst

Engineer

Engineers design, build, and maintain structures, machines, and systems. This course will provide you with a foundation in linear algebra, a mathematical tool that is widely used in engineering for tasks such as structural analysis, mechanical design, and control systems. By understanding the concepts of matrices, vectors, and linear transformations, you'll be able to model engineering systems, analyze data, and make informed design decisions.

See salaries and explore the career path for Engineer

Data Analyst

Data Analysts collect, process, and analyze data to extract meaningful insights. This course will provide you with a foundation in linear algebra, which is essential for wrangling and analyzing large datasets. By understanding the concepts of matrices, vectors, and linear transformations, you'll be able to clean and prepare data, build statistical models, and communicate data-driven insights.

See salaries and explore the career path for Data Analyst

Quantitative Analyst

Quantitative Analysts (Quants) use mathematical and statistical modeling to analyze financial data and make investment recommendations. This course will provide you with a strong foundation in linear algebra, which is widely used in financial modeling. By understanding the concepts of matrices, vectors, and linear transformations, you'll be able to develop complex financial models, analyze risk, and make data-driven investment decisions.

See salaries and explore the career path for Quantitative Analyst

Statistician

Statisticians collect, analyze, and interpret data to draw conclusions and make predictions. This course will provide you with a strong foundation in linear algebra, which is essential for statistical modeling and data analysis. By understanding the concepts of matrices, vectors, and linear transformations, you'll be able to develop statistical models, analyze data, and make informed decisions based on data.

See salaries and explore the career path for Statistician

Financial Analyst

Financial Analysts use financial data and models to make investment recommendations and advise clients on financial planning. This course will provide you with a strong foundation in linear algebra, which is widely used in financial analysis for tasks such as portfolio optimization, risk management, and financial forecasting. By understanding the concepts of matrices, vectors, and linear transformations, you'll be able to develop financial models, analyze data, and make informed investment decisions.

See salaries and explore the career path for Financial Analyst

Physicist

Physicists study the fundamental laws of nature and the physical world. This course will provide you with a foundation in linear algebra, a mathematical tool that is essential for understanding and describing physical phenomena. By understanding the concepts of matrices, vectors, and linear transformations, you'll be able to model physical systems, analyze data, and make predictions based on physical principles.

See salaries and explore the career path for Physicist

Economist

Economists use economic theories and data to analyze economic trends and make policy recommendations. This course will provide you with a foundation in linear algebra, which is widely used in economics for tasks such as modeling economic growth, forecasting inflation, and analyzing market behavior. By understanding the concepts of matrices, vectors, and linear transformations, you'll be able to develop economic models, analyze data, and make informed policy decisions.

See salaries and explore the career path for Economist

Actuary

Actuaries use mathematical and statistical techniques to assess risk and uncertainty in insurance, finance, and other fields. This course will provide you with a foundation in linear algebra, which is used in actuarial science to model insurance risks, calculate premiums, and design insurance products. By understanding the concepts of matrices, vectors, and linear transformations, you'll be able to develop actuarial models and make informed decisions.

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Business Analyst

Business Analysts use data and analytical techniques to solve business problems and improve decision-making. This course will provide you with a foundation in linear algebra, which is used in business analysis for tasks such as financial modeling, forecasting, and risk assessment. By understanding the concepts of matrices, vectors, and linear transformations, you'll be able to develop mathematical models, analyze data, and make informed business decisions.

See salaries and explore the career path for Business Analyst

Market Researcher

Market Researchers conduct research to understand consumer behavior and market trends. This course will provide you with a foundation in linear algebra, which is used in market research for tasks such as data analysis, survey design, and forecasting. By understanding the concepts of matrices, vectors, and linear transformations, you'll be able to analyze market data, develop research models, and make data-driven recommendations.

See salaries and explore the career path for Market Researcher

Data Scientist

Data Scientists are responsible for collecting and analyzing data to help businesses make informed decisions. This course will provide you with the foundational knowledge in linear algebra, a mathematical tool that is essential for processing and analyzing complex datasets. By understanding the concepts of matrices, vectors, and linear transformations, you'll be well-equipped to build statistical models, develop machine learning algorithms, and extract meaningful insights from data.

See salaries and explore the career path for Data Scientist