Online courses directory (10358)

You have probably been wondering whether our powers of algebraic problem solving break down if we divide by the variable or we have entire expressions in denominator of a fraction. Well, they don't! In this topic, you'll learn how to interpret and manipulate rational expressions (when you have one algebraic expression divided by another)!. Simplifying Rational Expressions Introduction. Simplifying Rational Expressions 1. Dividing polynomials by binomials 1. Simplifying Rational Expressions 2. Dividing polynomials by binomials 2. Simplifying rational expressions 2. Simplifying Rational Expressions 3. Simplifying Rational Expressions Example 2. Dividing polynomials by binomials 3. Simplifying rational expressions 3. Simplifying rational expressions 4. Adding and Subtracting Rational Expressions. Adding and Subtracting Rational Expressions 2. Adding and Subtracting Rational Expressions 3. Subtracting Rational Expressions. Simplifying First for Subtracting Rational Expressions. Adding and subtracting rational expressions 0.5. Adding and subtracting rational expressions 1. Adding and subtracting rational expressions 1.5. Adding and subtracting rational expressions 2. Adding and subtracting rational expressions 3. Multiplying and Simplifying Rational Expressions. Multiplying and Dividing Rational Expressions 1. Multiplying and Dividing Rational Expressions 2. Multiplying and Dividing Rational Expressions 3. Multiplying and dividing rational expressions 1. Multiplying and dividing rational expressions 2. Multiplying and dividing rational expressions 3. Multiplying and dividing rational expressions 4. Multiplying and dividing rational expressions 5. Rationalizing Denominators of Expressions. Asymptotes of Rational Functions. Another Rational Function Graph Example. A Third Example of Graphing a Rational Function. Partial Fraction Expansion 1. Partial Fraction Expansion 2. Partial Fraction Expansion 3. Partial fraction expansion. Ex 1 Multi step equation. Solving rational equations 1. Rational Equations. Solving Rational Equations 1. Solving Rational Equations 2. Solving Rational Equations 3. Applying Rational Equations 1. Applying Rational Equations 2. Applying Rational Equations 3. Solving rational equations 2. Extraneous Solutions to Rational Equations. Extraneous solutions. Rational Inequalities. Rational Inequalities 2. Simplifying Rational Expressions Introduction. Simplifying Rational Expressions 1. Dividing polynomials by binomials 1. Simplifying Rational Expressions 2. Dividing polynomials by binomials 2. Simplifying rational expressions 2. Simplifying Rational Expressions 3. Simplifying Rational Expressions Example 2. Dividing polynomials by binomials 3. Simplifying rational expressions 3. Simplifying rational expressions 4. Adding and Subtracting Rational Expressions. Adding and Subtracting Rational Expressions 2. Adding and Subtracting Rational Expressions 3. Subtracting Rational Expressions. Simplifying First for Subtracting Rational Expressions. Adding and subtracting rational expressions 0.5. Adding and subtracting rational expressions 1. Adding and subtracting rational expressions 1.5. Adding and subtracting rational expressions 2. Adding and subtracting rational expressions 3. Multiplying and Simplifying Rational Expressions. Multiplying and Dividing Rational Expressions 1. Multiplying and Dividing Rational Expressions 2. Multiplying and Dividing Rational Expressions 3. Multiplying and dividing rational expressions 1. Multiplying and dividing rational expressions 2. Multiplying and dividing rational expressions 3. Multiplying and dividing rational expressions 4. Multiplying and dividing rational expressions 5. Rationalizing Denominators of Expressions. Asymptotes of Rational Functions. Another Rational Function Graph Example. A Third Example of Graphing a Rational Function. Partial Fraction Expansion 1. Partial Fraction Expansion 2. Partial Fraction Expansion 3. Partial fraction expansion. Ex 1 Multi step equation. Solving rational equations 1. Rational Equations. Solving Rational Equations 1. Solving Rational Equations 2. Solving Rational Equations 3. Applying Rational Equations 1. Applying Rational Equations 2. Applying Rational Equations 3. Solving rational equations 2. Extraneous Solutions to Rational Equations. Extraneous solutions. Rational Inequalities. Rational Inequalities 2.

Solving and writing algebraic ratios and proportions. Solving rational equations. Introduction to Ratios (new HD version). Understanding Proportions. Ratios as Fractions in Simplest Form. Simplifying Rates and Ratios. Find an Unknown in a Proportion. Ratio and Proportion. Find an Unknown in a Proportion 2. Another Take on the Rate Problem. Finding Unit Rates. Finding Unit Prices. Writing Proportions. Ratio problem with basic algebra (new HD). More advanced ratio problem--with Algebra (HD version). Alternate Solution to Ratio Problem (HD Version). Advanced ratio problems. Unit conversion. Conversion between metric units. Converting within the metric system. Converting pounds to ounces. Converting Gallons to quarts pints and cups. Converting Farenheit to Celsius. Comparing Celsius and Farenheit temperature scales. Applying the Metric System. U.S. Customary and Metric units. Converting Yards into Inches. Unit Conversion with Fractions. Performing arithmetic calculations on units of volume. Application problems involving units of weight. Solving application problems involving units of volume. Unit Conversion Example: Drug Dosage. Perimeter and Unit Conversion. Rational Equations. Solving Rational Equations 1. Solving Rational Equations 2. Solving Rational Equations 3. Applying Rational Equations 1. Applying Rational Equations 2. Applying Rational Equations 3. Extraneous Solutions to Rational Equations. Rational Inequalities 2.

What ratios and proportions are. Using them to solve problems in the real world. Ratio problem with basic algebra (new HD). Writing proportions. Writing proportions. Find an Unknown in a Proportion. Find an Unknown in a Proportion 2. Proportions 1. Proportions 2 exercise examples. Proportions 2. Constructing proportions to solve application problems. Constructing proportions to solve application problems. The Golden Ratio. Advanced ratio problems. More advanced ratio problem--with Algebra (HD version). Another Take on the Rate Problem. Alternate Solution to Ratio Problem (HD Version). Mountain height word problem. Ratio problem with basic algebra (new HD). Writing proportions. Writing proportions. Find an Unknown in a Proportion. Find an Unknown in a Proportion 2. Proportions 1. Proportions 2 exercise examples. Proportions 2. Constructing proportions to solve application problems. Constructing proportions to solve application problems. The Golden Ratio. Advanced ratio problems. More advanced ratio problem--with Algebra (HD version). Another Take on the Rate Problem. Alternate Solution to Ratio Problem (HD Version). Mountain height word problem.

Solving a system of equations or inequalities in two variables by elimination, substitution, and graphing. Trolls, Tolls, and Systems of Equations. Solving the Troll Riddle Visually. Solving Systems Graphically. Graphing systems of equations. King's Cupcakes: Solving Systems by Elimination. How many bags of potato chips do people eat?. Simple Elimination Practice. Systems of equations with simple elimination. Systems with Elimination Practice. Systems of equations with elimination. Talking bird solves systems with substitution. Practice using substitution for systems. Systems of equations with substitution. Systems of equations. Systems of equations word problems. Solving linear systems by graphing. Graphing systems of equations. Solving linear systems by substitution. Systems of equations with substitution. Solving systems of equations by elimination. Systems of equations with simple elimination. Solving systems of equations by multiplication. Systems of equations with elimination. Systems of equations. Special types of linear systems. Solutions to systems of equations. Old video on systems of equations. Solving linear systems by graphing. Testing a solution for a system of equations. Graphing Systems of Equations. Graphical Systems Application Problem. Example 2: Graphically Solving Systems. Example 3: Graphically Solving Systems. Solving Systems Graphically. Graphing systems of equations. Inconsistent systems of equations. Infinite solutions to systems. Consistent and Inconsistent Systems. Independent and Dependent Systems. Practice thinking about number of solutions to systems. Graphical solutions to systems. Solutions to systems of equations. Constructing solutions to systems of equations. Constructing consistent and inconsistent systems. Example 1: Solving systems by substitution. Example 2: Solving systems by substitution. Example 3: Solving systems by substitution. The Substitution Method. Substitution Method 2. Substitution Method 3. Practice using substitution for systems. Systems of equations with substitution. Example 1: Solving systems by elimination. Example 2: Solving systems by elimination. Addition Elimination Method 1. Addition Elimination Method 2. Addition Elimination Method 3. Addition Elimination Method 4. Example 3: Solving systems by elimination. Simple Elimination Practice. Systems of equations with simple elimination. Systems with Elimination Practice. Systems of equations with elimination. Using a system of equations to find the price of apples and oranges. Linear systems word problem with substitution. Systems of equations word problems. Systems of equation to realize you are getting ripped off. Thinking about multiple solutions to a system of equations. Understanding systems of equations word problems. Systems and rate problems. Systems and rate problems 2. Systems and rate problems 3. Officer on Horseback. Two Passing Bicycles Word Problem. Passed Bike Word Problem. System of equations for passing trains problem. Overtaking Word Problem. Multple examples of multiple constraint problems. Testing Solutions for a System of Inequalities. Visualizing the solution set for a system of inequalities. Graphing systems of inequalities. Graphing systems of inequalities 2. Graphing systems of inequalities. Graphing and solving systems of inequalities. System of Inequalities Application. CA Algebra I: Systems of Inequalities. Systems of Three Variables. Systems of Three Variables 2. Solutions to Three Variable System. Solutions to Three Variable System 2. Three Equation Application Problem. Non-Linear Systems of Equations 3. Non-Linear Systems of Equations 1. Non-Linear Systems of Equations 2. Non-Linear Systems of Equations 3. Systems of nonlinear equations 1. Systems of nonlinear equations 2. Systems of nonlinear equations 3. Systems of nonlinear equations. Trolls, Tolls, and Systems of Equations. Solving the Troll Riddle Visually. Solving Systems Graphically. Graphing systems of equations. King's Cupcakes: Solving Systems by Elimination. How many bags of potato chips do people eat?. Simple Elimination Practice. Systems of equations with simple elimination. Systems with Elimination Practice. Systems of equations with elimination. Talking bird solves systems with substitution. Practice using substitution for systems. Systems of equations with substitution. Systems of equations. Systems of equations word problems. Solving linear systems by graphing. Graphing systems of equations. Solving linear systems by substitution. Systems of equations with substitution. Solving systems of equations by elimination. Systems of equations with simple elimination. Solving systems of equations by multiplication. Systems of equations with elimination. Systems of equations. Special types of linear systems. Solutions to systems of equations. Old video on systems of equations. Solving linear systems by graphing. Testing a solution for a system of equations. Graphing Systems of Equations. Graphical Systems Application Problem. Example 2: Graphically Solving Systems. Example 3: Graphically Solving Systems. Solving Systems Graphically. Graphing systems of equations. Inconsistent systems of equations. Infinite solutions to systems. Consistent and Inconsistent Systems. Independent and Dependent Systems. Practice thinking about number of solutions to systems. Graphical solutions to systems. Solutions to systems of equations. Constructing solutions to systems of equations. Constructing consistent and inconsistent systems. Example 1: Solving systems by substitution. Example 2: Solving systems by substitution. Example 3: Solving systems by substitution. The Substitution Method. Substitution Method 2. Substitution Method 3. Practice using substitution for systems. Systems of equations with substitution. Example 1: Solving systems by elimination. Example 2: Solving systems by elimination. Addition Elimination Method 1. Addition Elimination Method 2. Addition Elimination Method 3. Addition Elimination Method 4. Example 3: Solving systems by elimination. Simple Elimination Practice. Systems of equations with simple elimination. Systems with Elimination Practice. Systems of equations with elimination. Using a system of equations to find the price of apples and oranges. Linear systems word problem with substitution. Systems of equations word problems. Systems of equation to realize you are getting ripped off. Thinking about multiple solutions to a system of equations. Understanding systems of equations word problems. Systems and rate problems. Systems and rate problems 2. Systems and rate problems 3. Officer on Horseback. Two Passing Bicycles Word Problem. Passed Bike Word Problem. System of equations for passing trains problem. Overtaking Word Problem. Multple examples of multiple constraint problems. Testing Solutions for a System of Inequalities. Visualizing the solution set for a system of inequalities. Graphing systems of inequalities. Graphing systems of inequalities 2. Graphing systems of inequalities. Graphing and solving systems of inequalities. System of Inequalities Application. CA Algebra I: Systems of Inequalities. Systems of Three Variables. Systems of Three Variables 2. Solutions to Three Variable System. Solutions to Three Variable System 2. Three Equation Application Problem. Non-Linear Systems of Equations 3. Non-Linear Systems of Equations 1. Non-Linear Systems of Equations 2. Non-Linear Systems of Equations 3. Systems of nonlinear equations 1. Systems of nonlinear equations 2. Systems of nonlinear equations 3. Systems of nonlinear equations.

This is an introductory course in algebraic combinatorics. No prior knowledge of combinatorics is expected, but assumes a familiarity with linear algebra and finite groups. Topics were chosen to show the beauty and power of techniques in algebraic combinatorics. Rigorous mathematical proofs are expected.

This is the first semester of a two-semester sequence on Algebraic Geometry. The goal of the course is to introduce the basic notions and techniques of modern algebraic geometry. It covers fundamental notions and results about algebraic varieties over an algebraically closed field; relations between complex algebraic varieties and complex analytic varieties; and examples with emphasis on algebraic curves and surfaces. This course is an introduction to the language of schemes and properties of morphisms.

This course provides an introduction to the language of schemes, properties of morphisms, and sheaf cohomology. Together with 18.725 Algebraic Geometry, students gain an understanding of the basic notions and techniques of modern algebraic geometry.

This research-oriented course will focus on algebraic and computational techniques for optimization problems involving polynomial equations and inequalities with particular emphasis on the connections with semidefinite optimization. The course will develop in a parallel fashion several algebraic and numerical approaches to polynomial systems, with a view towards methods that simultaneously incorporate both elements. We will study both the complex and real cases, developing techniques of general applicability, and stressing convexity-based ideas, complexity results, and efficient implementations. Although we will use examples from several engineering areas, particular emphasis will be given to those arising from systems and control applications.

This course is a first course in algebraic topology. The emphasis is on homology and cohomology theory, including cup products, Kunneth formulas, intersection pairings, and the Lefschetz fixed point theorem.

In this second term of Algebraic Topology, the topics covered include fibrations, homotopy groups, the Hurewicz theorem, vector bundles, characteristic classes, cobordism, and possible further topics at the discretion of the instructor.

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.

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 deuxième partie du cours sera dévouée à l'étude des chapitres 5 à 8 cités plus haut. Une bonne connaissance de la matière enseignée dans le MOOC Algèbre Linéaire (Partie 1) 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. 

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 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. 

How do you optimally encode a text file? How do you find shortest paths in a map? How do you design a communication network? How do you route data in a network? What are the limits of efficient computation?

This course, part of the Computer Science Essentials for Software Development Professional Certificate program, is an introduction to design and analysis of algorithms, and answers along the way these and many other interesting computational questions.

You will learn about algorithms that operate on common data structures, for instance sorting and searching; advanced design and analysis techniques such as dynamic programming and greedy algorithms; advanced graph algorithms such as minimum spanning trees and shortest paths; NP-completeness theory; and approximation algorithms.

After completing this course you will be able to design efficient and correct algorithms using sophisticated data structures for complex computational tasks.

This course is organized around algorithmic issues that arise in machine learning. Modern machine learning systems are often built on top of algorithms that do not have provable guarantees, and it is the subject of debate when and why they work. In this class, we focus on designing algorithms whose performance we can rigorously analyze for fundamental machine learning problems.

6.890 Algorithmic Lower Bounds: Fun with Hardness Proofs is a class taking a practical approach to proving problems can't be solved efficiently (in polynomial time and assuming standard complexity-theoretic assumptions like P ≠ NP). The class focuses on reductions and techniques for proving problems are computationally hard for a variety of complexity classes. Along the way, the class will create many interesting gadgets, learn many hardness proof styles, explore the connection between games and computation, survey several important problems and complexity classes, and crush hopes and dreams (for fast optimal solutions).

Experienced Computer Scientists analyze and solve computational problems at a level of abstraction that is beyond that of any particular programming language. This class is designed to train students in the mathematical concepts and process of "Algorithmic Thinking", allowing them to build simpler, more efficient solutions to computational problems.

Experienced Computer Scientists analyze and solve computational problems at a level of abstraction that is beyond that of any particular programming language. This two-part class is designed to train students in the mathematical concepts and process of "Algorithmic Thinking", allowing them to build simpler, more efficient solutions to computational problems.

Experienced Computer Scientists analyze and solve computational problems at a level of abstraction that is beyond that of any particular programming language. This two-part class is designed to train students in the mathematical concepts and process of "Algorithmic Thinking", allowing them to build simpler, more efficient solutions to computational problems.