Algèbre Linéaire (Partie 3) 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 :

Systèmes d'équations linéaires.
Algèbre matricielle.
Espaces vectoriels.
Bases et dimensions.
Applications linéaires.
Matrices et applications linéaires.
Déterminants.
Vecteurs propres, valeurs propres, diagonalisation.
Produits scalaires et espaces euclidiens.
Matrices orthogonales et matrices symétriques.

Cette troisième (et dernière) partie du cours sera dévouée à l'étude des chapitres 9 et 10 cités plus haut. Une bonne connaissance de la matière enseignée dans les MOOCs _Algèbre Linéaire (Partie 1) _et _Algébre Linéaire (Partie 2) _est requise. Aussi, 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.

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Learning objectives

De définir les concepts théoriques introduits en cours et d'en donner des exemples illustratifs ;
De reconnaître un produit scalaire et maîtriser les propriétés associées à un tel objet (e.g. inégalité de cauchy-schwarz, inégalité du triangle) ;
De et maîtriser les notions de bases liées à l'orthogonalité (e.g. familles/bases orthogonales, familles/bases orthonormales, orthogonal d'un sous-espace, théorème de pythagore) ;
De construire une base orthonormée d'un sous-espace vectoriel d'un espace euclidien à l'aide du procédé de gram-schmidt ;
De calculer la meilleure approximation quadratique d'un vecteur ;
De calculer la solution au sens des moindres carrés d'un système linéaire ;

De calculer la factorisation qr d'une matrice donnée, lorsque cela est possible ;
De diagonaliser orthogonalement une matrice symétrique donnée ;
De déterminer les axes principaux d'une forme quadratique donnée ;
De calculer la décomposition en valeurs singulières d'une matrice donnée.
A la fin du cours, l'étudiant sera capable

De définir les concepts théoriques introduits en cours et d'en donner des exemples illustratifs ;
De reconnaître un produit scalaire et maîtriser les propriétés associées à un tel objet (e.g. inégalité de cauchy-schwarz, inégalité du triangle) ;
De et maîtriser les notions de bases liées à l'orthogonalité (e.g. familles/bases orthogonales, familles/bases orthonormales, orthogonal d'un sous-espace, théorème de pythagore) ;
De construire une base orthonormée d'un sous-espace vectoriel d'un espace euclidien à l'aide du procédé de gram-schmidt ;
De calculer la meilleure approximation quadratique d'un vecteur ;
De calculer la solution au sens des moindres carrés d'un système linéaire ;
De calculer la factorisation qr d'une matrice donnée, lorsque cela est possible ;
De diagonaliser orthogonalement une matrice symétrique donnée ;
De déterminer les axes principaux d'une forme quadratique donnée ;
De calculer la décomposition en valeurs singulières d'une matrice donnée.
A la fin du cours, l'étudiant sera capable

Good to know

Know what's good

, what to watch for

, and possible dealbreakers

Ce cours s'adresse aux étudiants en économie, ingénierie, physique ou statistique, ainsi qu'aux passionnés de mathématiques pures

Il offre une approche détaillée des concepts théoriques, étayée par de nombreux exemples illustratifs

Le cours est dispensé par des instructeurs reconnus pour leur expertise dans le domaine de l'algèbre linéaire

Il s'inscrit dans un cursus académique solide, notamment les cours d'algèbre linéaire dispensés à l'Ecole Polytechnique Fédérale de Lausanne

Il combine efficacement vidéos, exercices interactifs et corrigés détaillés, offrant une expérience d'apprentissage équilibrée

Reviews summary

Cours d'algèbre linéaire complet et engageant

Ce cours d'algèbre linéaire est fortement recommandé pour les étudiants cherchant une base solide dans le sujet. Il aborde les concepts théoriques de manière détaillée, avec de nombreux exemples illustratifs et des exercices pratiques, ce qui en fait un cours complet et engageant. Les vidéos sont claires et concises, et les exercices et QCM aident à consolider l'apprentissage. Le seul inconvénient est que le cours nécessite une bonne connaissance des deux premières parties de la série, mais à part cela, c'est un excellent choix pour les étudiants souhaitant approfondir leurs connaissances en algèbre linéaire.

Les vidéos sont claires et faciles à suivre.

"Les vidéos constituent le coeur du cours..."

Fournit de nombreux exemples illustratifs.

"...ainsi que de multiples exemples illustratifs :"

Couvre les concepts théoriques en détail.

"Une approche très détaillée des concepts théoriques est proposée..."

Inclut des exercices et des QCM pour la pratique.

"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."

Nécessite une bonne connaissance des parties précédentes.

"Une bonne connaissance de la matière enseignée dans les MOOCs _Algèbre Linéaire (Partie 1) _et _Algébre Linéaire (Partie 2) _est requise."

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 3) with these activities:

Review the key concepts of linear algebra

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Help build a stronger foundation and clear prerequisites for success in this course by reviewing essential concepts in linear algebra.

Browse courses on Eigenvalues and Eigenvectors

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Go over your notes from previous linear algebra courses or textbooks.
Review online resources such as Khan Academy or MIT OpenCourseWare.
Solve practice problems from textbooks or online sources.

Mentor a junior student or classmate in linear algebra

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Solidify your understanding by helping others learn linear algebra through mentoring and knowledge sharing.

Browse courses on Knowledge Sharing

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Identify a junior student or classmate who could benefit from your guidance in linear algebra.
Provide support and guidance through regular study sessions or discussions.

Create a video tutorial explaining a challenging linear algebra concept

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Deepen your understanding by attempting to teach a challenging linear algebra concept through a video tutorial.

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Choose a specific concept that you find particularly challenging.
Research the concept thoroughly and prepare a clear and concise explanation.
Create a video tutorial using screen recording software or a video editing tool.

Show all three activities

Career center

Learners who complete Algèbre Linéaire (Partie 3) will develop knowledge and skills that may be useful to these careers:

Quantitative Analyst

Quantitative Analysts use mathematical and statistical models to analyze financial data and make investment decisions. They work with a variety of financial instruments, including stocks, bonds, and derivatives. Linear Algebra is used in quantitative finance for a variety of tasks, including portfolio optimization, risk management, and pricing financial instruments. Taking this course can help you develop the skills you need to be successful as a Quantitative Analyst.

See salaries and explore the career path for Quantitative Analyst

Statistician

Statisticians use mathematical and statistical techniques to collect, analyze, and interpret data. They work in a variety of fields, including research, government, and business. Linear Algebra is used in statistics for a variety of tasks, including data analysis, modeling, and forecasting. Taking this course can help you develop the skills you need to be successful as a Statistician.

See salaries and explore the career path for Statistician

Data Scientist

Data Scientists use mathematical and statistical techniques to extract insights from data. They work with data in a variety of formats, including structured and unstructured data. Linear Algebra is a fundamental mathematical tool used in data science, as it provides methods for working with data in high-dimensional spaces. Taking this course can help you build a strong foundation in Linear Algebra, which will make you more effective in your role as a Data Scientist.

See salaries and explore the career path for Data Scientist

Data Analyst

Data Analysts use mathematical and statistical techniques to analyze data and extract insights. They work with a variety of data sources, including structured and unstructured data. Linear Algebra is a fundamental mathematical tool used in data analysis, as it provides methods for working with data in high-dimensional spaces. Taking this course can help you develop the skills you need to be successful as a Data Analyst.

See salaries and explore the career path for Data Analyst

Actuary

Actuaries use mathematical and statistical techniques to assess risk and uncertainty. They work in a variety of industries, including insurance, finance, and healthcare. Linear Algebra is used in actuarial science for a variety of tasks, including pricing insurance policies, managing risk, and developing financial models. Taking this course can help you develop the skills you need to be successful as an Actuary.

See salaries and explore the career path for Actuary

Investment Analyst

Investment Analysts use mathematical and statistical techniques to analyze investment opportunities. They work with a variety of financial instruments, including stocks, bonds, and derivatives. Linear Algebra is used in investment analysis for a variety of tasks, including portfolio optimization, risk management, and pricing financial instruments. Taking this course can help you develop the skills you need to be successful as an Investment Analyst.

See salaries and explore the career path for Investment Analyst

Financial Analyst

Financial Analysts use mathematical and statistical techniques to analyze financial data and make investment recommendations. They work with a variety of financial instruments, including stocks, bonds, and derivatives. Linear Algebra is used in financial analysis for a variety of tasks, including portfolio optimization, risk management, and pricing financial instruments. Taking this course can help you develop the skills you need to be successful as a Financial Analyst.

See salaries and explore the career path for Financial Analyst

Economist

Economists use mathematical and statistical techniques to analyze economic data and make predictions about the economy. They work with a variety of data sources, including government data, business data, and consumer data. Linear Algebra is used in economics for a variety of tasks, including econometric modeling, forecasting, and policy analysis. Taking this course can help you develop the skills you need to be successful as an Economist.

See salaries and explore the career path for Economist

Operations Research Analyst

Operations Research Analysts use mathematical and statistical techniques to improve the efficiency of organizations. They work in a variety of industries, including manufacturing, transportation, and logistics. Linear Algebra is used in operations research for a variety of tasks, including scheduling, routing, and inventory management. Taking this course can help you develop the skills you need to be successful as an Operations Research Analyst.

See salaries and explore the career path for Operations Research Analyst

Risk Manager

Risk Managers use mathematical and statistical techniques to assess and manage risk. They work in a variety of industries, including insurance, finance, and healthcare. Linear Algebra is used in risk management for a variety of tasks, including risk modeling, risk assessment, and risk mitigation. Taking this course can help you develop the skills you need to be successful as a Risk Manager.

See salaries and explore the career path for Risk Manager

Market Researcher

Market Researchers use mathematical and statistical techniques to collect and analyze data about markets and consumers. They work with a variety of data sources, including surveys, interviews, and focus groups. Linear Algebra is used in market research for a variety of tasks, including data analysis, segmentation, and forecasting. Taking this course can help you develop the skills you need to be successful as a Market Researcher.

See salaries and explore the career path for Market Researcher

Software Engineer

Software Engineers design, develop, and maintain software systems. They work with a variety of programming languages and technologies, and must have a strong understanding of mathematical concepts. Linear Algebra is used in software engineering for a variety of tasks, including computer graphics, image processing, and machine learning. Taking this course can help you develop the skills you need to be successful as a Software Engineer.

See salaries and explore the career path for Software Engineer

Business Analyst

Business Analysts use mathematical and statistical techniques to analyze business data and make recommendations for improvement. They work with a variety of data sources, including financial data, sales data, and customer data. Linear Algebra is used in business analysis for a variety of tasks, including data analysis, forecasting, and optimization. Taking this course can help you develop the skills you need to be successful as a Business Analyst.

See salaries and explore the career path for Business Analyst

Math Teacher

A Math Teacher helps students understand and apply mathematical skills, from basic arithmetic to advanced topics like matrix algebra. To be successful in this role, you'll need to have strong knowledge of mathematical concepts, and be able to explain them in a clear and engaging way. This course can help you develop a deeper understanding of Linear Algebra, which will enhance your skills in teaching this subject to students.

See salaries and explore the career path for Math Teacher

Financial Planner

Financial Planners use mathematical and statistical techniques to help clients plan for their financial future. They work with a variety of financial products, including investments, insurance, and retirement plans. Linear Algebra is used in financial planning for a variety of tasks, including portfolio optimization, risk management, and retirement planning. Taking this course can help you develop the skills you need to be successful as a Financial Planner.

See salaries and explore the career path for Financial Planner