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### Algebra: Quadratics functions and equations

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### Algebra: Rational expressions

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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.

### Algebra: Ratios & proportions

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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.

### Algebra: Ratios and proportions

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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.

### Algebra: Systems of equations and inequalities

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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.

### Algebraic Combinatorics

Starts : 2009-02-01
MIT OpenCourseWare (OCW) Free Mathematics Customer Service Certification Program Infor Information control Information Theory Nutrition

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.

### Algebraic Geometry (Fall 2015)

Starts : 2015-09-01
MIT OpenCourseWare (OCW) Free Mathematics Customer Service Certification Program Infor Information environments Information Theory Nutrition

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.

### Algebraic Geometry (Spring 2009)

Starts : 2009-02-01
MIT OpenCourseWare (OCW) Free Mathematics Customer Service Certification Program Infor Information environments Information Theory Nutrition

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.

### Algebraic Techniques and Semidefinite Optimization

Starts : 2006-02-01
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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.

### Algebraic Topology

Starts : 2006-09-01
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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.

### Algebraic Topology II

Starts : 2006-02-01
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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.

### Algorithmic Aspects of Machine Learning

Starts : 2015-02-01
MIT OpenCourseWare (OCW) Free Computer Sciences Customer Service Certification Program Infor Information environments Information Theory Nutrition

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.

### An Introduction to Functional Analysis

Starts : 2014-09-12
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### Analyse numérique pour ingénieurs

Starts : 2015-02-06
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Ce cours contient les 7 premiers chapitres d'un cours donné aux étudiants bachelor de l'EPFL. Il est basé sur le livre "Introduction à l'analyse numérique", J. Rappaz M. Picasso, Ed. PPUR. Des outils de base sont décrits dans les 5 premiers chapitres. Les deux derniers chapitres abordent la question de la résolution numérique d'équations différentielles.

### Analysis I

Starts : 2010-09-01
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Analysis I covers fundamentals of mathematical analysis: metric spaces, convergence of sequences and series, continuity, differentiability, Riemann integral, sequences and series of functions, uniformity, interchange of limit operations.

### Analysis II

Starts : 2005-09-01
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This course continues from Analysis I (18.100B), in the direction of manifolds and global analysis. The first half of the course covers multivariable calculus. The rest of the course covers the theory of differential forms in n-dimensional vector spaces and manifolds.

### Analytic Combinatorics, Part I

Starts : 2013-02-08
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This course teaches a calculus that enables precise quantitative predictions of large combinatorial structures. Part I covers generating functions and real asymptotics and then introduces the symbolic method in the context of applications in the analysis of algorithms and basic structures such as permutations, trees, strings, words, and mappings.

### Analytic Combinatorics, Part II

Starts : 2013-03-29
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This course teaches a calculus that enables precise quantitative predictions of large combinatorial structures.