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### Mathematical Biostatistics Boot Camp 1

Starts : 2015-07-13
Coursera Free Closed [?] Computer Sciences English Biology & Life Sciences Health & Society Mathematics Statistics and Data Analysis

This class presents the fundamental probability and statistical concepts used in elementary data analysis. It will be taught at an introductory level for students with junior or senior college-level mathematical training including a working knowledge of calculus. A small amount of linear algebra and programming are useful for the class, but not required.

### Coding the Matrix: Linear Algebra through Computer Science Applications

Starts : 2015-02-02
Coursera Free Popular Computer Sciences English Artificial Intelligence Computer Science Computer Science Mathematics Statistics and Data Analysis Theory

Learn the concepts and methods of linear algebra, and how to use them to think about computational problems arising in computer science. Coursework includes building on the concepts to write small programs and run them on real data.

### Algebra: Introduction to algebra

Khan Academy Free Closed [?] Mathematics Algebra College algebra Introduction to algebra

Videos exploring why algebra was developed and how it helps us explain our world. Origins of Algebra. Abstract-ness. The Beauty of Algebra. Descartes and Cartesian Coordinates. Why all the letters in Algebra?. What is a variable?. Why aren't we using the multiplication sign. Example: evaluating an expression. Example: evaluate a formula using substitution. Evaluating exponential expressions 2. Evaluating expressions in one variable. Expressions with two variables. Example: Evaluating expressions with 2 variables. Examples of evaluating variable expressions. Evaluating expressions in 2 variables. Example evaluating expressions in word problems. Evaluating expressions 3. Combining like terms. Adding like rational terms. Combining Like Terms 1. Combining Like Terms 2. Combining Like Terms 3. Combining like terms. Combining like terms and the distributive property. Combining like terms with distribution. Factoring a linear expression with rational terms. Distributive property with rational terms. Manipulating linear expressions with rational coefficients. Equivalent forms of expressions 1. Equivalent forms of expressions 1. Writing Expressions 1. Writing expressions. Writing Expressions 2. Writing expressions 2 exercise example. Writing expressions 2. Interpreting linear expressions example. Interpreting linear expressions example 2. Interpreting linear expressions. Writing expressions 3 exercise example 1. Writing expressions 3 exercise example 2. Writing expressions 3 exercise example 3. Writing expressions 3. Why we do the same thing to both sides: simple equations. Representing a relationship with a simple equation. One-Step Equation Intuition. One step equation intuition exercise intro. One step equation intuition. Adding and subtracting the same thing from both sides. Intuition why we divide both sides. Why we do the same thing to both sides: two-step equations. Why we do the same thing to both sides: multi-step equations. Why we do the same thing to both sides basic systems. Why all the letters in Algebra?. Super Yoga Plans- Basic Variables and Equations. Super Yoga Plans- Solving One-Step Equations. Constructing and solving equations in the real world 1. Super Yoga Plans- Plotting Points. Super Yoga Plans- Solving Systems by Substitution. Super Yoga Plans- Solving Systems by Elimination. Variables Expressions and Equations. Solving equations and inequalities through substitution example 1. Solving equations and inequalities through substitution example 2. Solving equations and inequalities through substitution example 3. Solving equations and inequalities through substitution example 4. Solving equations and inequalities through substitution. Dependent and independent variables exercise example 1. Dependent and independent variables exercise example 2. Dependent and independent variables exercise example 3. Dependent and independent variables. Origins of Algebra. Abstract-ness. The Beauty of Algebra. Descartes and Cartesian Coordinates. Why all the letters in Algebra?. What is a variable?. Why aren't we using the multiplication sign. Example: evaluating an expression. Example: evaluate a formula using substitution. Evaluating exponential expressions 2. Evaluating expressions in one variable. Expressions with two variables. Example: Evaluating expressions with 2 variables. Examples of evaluating variable expressions. Evaluating expressions in 2 variables. Example evaluating expressions in word problems. Evaluating expressions 3. Combining like terms. Adding like rational terms. Combining Like Terms 1. Combining Like Terms 2. Combining Like Terms 3. Combining like terms. Combining like terms and the distributive property. Combining like terms with distribution. Factoring a linear expression with rational terms. Distributive property with rational terms. Manipulating linear expressions with rational coefficients. Equivalent forms of expressions 1. Equivalent forms of expressions 1. Writing Expressions 1. Writing expressions. Writing Expressions 2. Writing expressions 2 exercise example. Writing expressions 2. Interpreting linear expressions example. Interpreting linear expressions example 2. Interpreting linear expressions. Writing expressions 3 exercise example 1. Writing expressions 3 exercise example 2. Writing expressions 3 exercise example 3. Writing expressions 3. Why we do the same thing to both sides: simple equations. Representing a relationship with a simple equation. One-Step Equation Intuition. One step equation intuition exercise intro. One step equation intuition. Adding and subtracting the same thing from both sides. Intuition why we divide both sides. Why we do the same thing to both sides: two-step equations. Why we do the same thing to both sides: multi-step equations. Why we do the same thing to both sides basic systems. Why all the letters in Algebra?. Super Yoga Plans- Basic Variables and Equations. Super Yoga Plans- Solving One-Step Equations. Constructing and solving equations in the real world 1. Super Yoga Plans- Plotting Points. Super Yoga Plans- Solving Systems by Substitution. Super Yoga Plans- Solving Systems by Elimination. Variables Expressions and Equations. Solving equations and inequalities through substitution example 1. Solving equations and inequalities through substitution example 2. Solving equations and inequalities through substitution example 3. Solving equations and inequalities through substitution example 4. Solving equations and inequalities through substitution. Dependent and independent variables exercise example 1. Dependent and independent variables exercise example 2. Dependent and independent variables exercise example 3. Dependent and independent variables.

### Algebra: Linear equations

Khan Academy Free Popular Closed [?] Mathematics Algebra College algebra Linear equations

Why we do the same thing to both sides: simple equations. Representing a relationship with a simple equation. One-Step Equation Intuition. One step equation intuition exercise intro. One step equation intuition. Adding and subtracting the same thing from both sides. Intuition why we divide both sides. Why we do the same thing to both sides: two-step equations. Why we do the same thing to both sides: multi-step equations. Why we do the same thing to both sides basic systems. Super Yoga Plans- Basic Variables and Equations. Super Yoga Plans- Solving One-Step Equations. Constructing and solving equations in the real world 1. Super Yoga Plans- Plotting Points. Super Yoga Plans- Solving Systems by Substitution. Super Yoga Plans- Solving Systems by Elimination. Constructing and solving equations in the real world 1 exercise. Simple Equations of the form Ax=B. Example solving x/3 =14. One-step equations with multiplication. Example solving x+5=54. Examples of one-step equations like Ax=B and x+A = B. One step equations. Solving Ax+B = C. Two-Step Equations. Example: Dimensions of a garden. Example: Two-step equation with x/4 term. 2-step equations. Basic linear equation word problem. Linear equation word problems. Linear equation word problem example. Linear equation word problems 2. Variables on both sides. Example 1: Variables on both sides. Example 2: Variables on both sides. Equation Special Cases. Equations with variables on both sides. Number of solutions to linear equations. Number of solutions to linear equations ex 2. Number of solutions to linear equations ex 3. Solutions to linear equations. Another Percent Word Problem. Percent word problems. Percent word problems 1 example 2). Solving Percent Problems 2. Solving Percent Problems 3. Percentage word problems 1. Percentage word problems 2. Rearrange formulas to isolate specific variables. Solving for a Variable. Solving for a Variable 2. Example: Solving for a variable. Solving equations in terms of a variable. Converting Repeating Decimals to Fractions 1. Converting 1-digit repeating decimals to fractions. Converting Repeating Decimals to Fractions 2. Converting multi-digit repeating decimals to fractions. Ex 1 Age word problem. Ex 2 Age word problem. Ex 3 Age word problem. Age word problems. Absolute Value Equations. Absolute Value Equations Example 1. Absolute Value Equation Example 2. Absolute Value Equations. Absolute Value Equations 1. Absolute value equation example. Absolute value equation with no solution. Absolute value equations. Absolute Value Inequalities. Absolute value inequalities Example 1. Absolute Inequalities 2. Absolute value inequalities example 3. Ex 2 Multi-step equation. Solving Equations with the Distributive Property. Solving equations with the distributive property 2. Ex 2: Distributive property to simplify . Ex 1: Distributive property to simplify . Ex 3: Distributive property to simplify . Multistep equations with distribution. Evaluating expressions where individual variable values are unknown. Evaluating expressions with unknown variables 2. Expressions with unknown variables. Expressions with unknown variables 2. Mixture problems 2. Basic Rate Problem. Early Train Word Problem. Patterns in Sequences 1. Patterns in Sequences 2. Equations of Sequence Patterns. Finding the 100th Term in a Sequence. Challenge example: Sum of integers. Integer sums. Integer sums. 2003 AIME II Problem 1. Bunch of examples. Mixture problems 3. Order of Operations examples. Algebra: Linear Equations 1. Algebra: Linear Equations 2. Algebra: Linear Equations 3. Algebra: Linear Equations 4. Averages. Taking percentages. Growing by a percentage. More percent problems. Age word problems 1. Age word problems 2. Age word problems 3. Why we do the same thing to both sides: simple equations. Representing a relationship with a simple equation. One-Step Equation Intuition. One step equation intuition exercise intro. One step equation intuition. Adding and subtracting the same thing from both sides. Intuition why we divide both sides. Why we do the same thing to both sides: two-step equations. Why we do the same thing to both sides: multi-step equations. Why we do the same thing to both sides basic systems. Super Yoga Plans- Basic Variables and Equations. Super Yoga Plans- Solving One-Step Equations. Constructing and solving equations in the real world 1. Super Yoga Plans- Plotting Points. Super Yoga Plans- Solving Systems by Substitution. Super Yoga Plans- Solving Systems by Elimination. Constructing and solving equations in the real world 1 exercise. Simple Equations of the form Ax=B. Example solving x/3 =14. One-step equations with multiplication. Example solving x+5=54. Examples of one-step equations like Ax=B and x+A = B. One step equations. Solving Ax+B = C. Two-Step Equations. Example: Dimensions of a garden. Example: Two-step equation with x/4 term. 2-step equations. Basic linear equation word problem. Linear equation word problems. Linear equation word problem example. Linear equation word problems 2. Variables on both sides. Example 1: Variables on both sides. Example 2: Variables on both sides. Equation Special Cases. Equations with variables on both sides. Number of solutions to linear equations. Number of solutions to linear equations ex 2. Number of solutions to linear equations ex 3. Solutions to linear equations. Another Percent Word Problem. Percent word problems. Percent word problems 1 example 2). Solving Percent Problems 2. Solving Percent Problems 3. Percentage word problems 1. Percentage word problems 2. Rearrange formulas to isolate specific variables. Solving for a Variable. Solving for a Variable 2. Example: Solving for a variable. Solving equations in terms of a variable. Converting Repeating Decimals to Fractions 1. Converting 1-digit repeating decimals to fractions. Converting Repeating Decimals to Fractions 2. Converting multi-digit repeating decimals to fractions. Ex 1 Age word problem. Ex 2 Age word problem. Ex 3 Age word problem. Age word problems. Absolute Value Equations. Absolute Value Equations Example 1. Absolute Value Equation Example 2. Absolute Value Equations. Absolute Value Equations 1. Absolute value equation example. Absolute value equation with no solution. Absolute value equations. Absolute Value Inequalities. Absolute value inequalities Example 1. Absolute Inequalities 2. Absolute value inequalities example 3. Ex 2 Multi-step equation. Solving Equations with the Distributive Property. Solving equations with the distributive property 2. Ex 2: Distributive property to simplify . Ex 1: Distributive property to simplify . Ex 3: Distributive property to simplify . Multistep equations with distribution. Evaluating expressions where individual variable values are unknown. Evaluating expressions with unknown variables 2. Expressions with unknown variables. Expressions with unknown variables 2. Mixture problems 2. Basic Rate Problem. Early Train Word Problem. Patterns in Sequences 1. Patterns in Sequences 2. Equations of Sequence Patterns. Finding the 100th Term in a Sequence. Challenge example: Sum of integers. Integer sums. Integer sums. 2003 AIME II Problem 1. Bunch of examples. Mixture problems 3. Order of Operations examples. Algebra: Linear Equations 1. Algebra: Linear Equations 2. Algebra: Linear Equations 3. Algebra: Linear Equations 4. Averages. Taking percentages. Growing by a percentage. More percent problems. Age word problems 1. Age word problems 2. Age word problems 3.

### Algebra: Graphing and analyzing linear functions

Khan Academy Free Popular Closed [?] Mathematics Algebra College algebra Graphing and analyzing linear functions

Use the power of algebra to understand and interpret points and lines (something we typically do in geometry). This will include slope and the equation of a line. Descartes and Cartesian Coordinates. The Coordinate Plane. Plot ordered pairs. Graphing points exercise. Graphing points. Quadrants of Coordinate Plane. Graphing points and naming quadrants exercise. Graphing points and naming quadrants. Points on the coordinate plane. Points on the coordinate plane. Coordinate plane word problems exercise. Coordinate plane word problems. Reflecting points exercise. Reflecting points. Ordered pair solutions of equations. Ordered Pair Solutions of Equations 2. Determining a linear equation by trying out values from a table. Equations from tables. Plotting (x,y) relationships. Graphs of Linear Equations. Application problem with graph. Ordered pair solutions to linear equations. Interpreting Linear Graphs. Exploring linear relationships. Recognizing Linear Functions. Interpreting linear relationships. Graphing lines 1. Recognizing Linear Functions. Linear and nonlinear functions (example 1). Linear and nonlinear functions (example 2). Linear and nonlinear functions (example 3). Linear and nonlinear functions. Graphing using X and Y intercepts. Graphing Using Intercepts. X and Y intercepts. X and Y intercepts 2. Solving for the x-intercept. Finding x intercept of a line. Finding intercepts for a linear function from a table. Linear function intercepts. Interpreting intercepts of linear functions. Interpreting and finding intercepts of linear functions. Analyzing and identifying proportional relationships ex1. Analyzing and identifying proportional relationships ex2. Analyzing and identifying proportional relationships ex3. Analyzing and identifying proportional relationships. Comparing proportional relationships. Constructing an equation for a proportional relationship. Constructing and comparing proportional relationships. Graphing proportional relationships example. Graphing proportional relationships example 2. Graphing proportional relationships example 3. Graphing proportional relationships. Comparing rates. Representing and comparing rates. Rates and proportional relationships. Rate problem with fractions 1. Unit cost with fractions 1. Rate problems 1. Slope of a line. Slope of a Line 2. Slope and Rate of Change. Graphical Slope of a Line. Slope of a Line 3. Slope Example. Hairier Slope of Line. Identifying slope of a line. Slope and Y-intercept Intuition. Line graph intuition. Algebra: Slope. Algebra: Slope 2. Algebra: Slope 3. Graphing a line in slope intercept form. Converting to slope-intercept form. Graphing linear equations. Fitting a Line to Data. Comparing linear functions 1. Comparing linear functions 2. Comparing linear functions 3. Comparing linear functions. Interpreting features of linear functions example. Interpreting features of linear functions example 2. Interpreting features of linear functions. Comparing linear functions applications 1. Comparing linear functions applications 2. Comparing linear functions applications 3. Comparing linear functions applications. Constructing a linear function word problem. Constructing and interpreting a linear function. Constructing linear graphs. Constructing and interpreting linear functions. Multiple examples of constructing linear equations in slope-intercept form. Constructing equations in slope-intercept form from graphs. Constructing linear equations to solve word problems. Linear equation from slope and a point. Finding a linear equation given a point and slope. Equation of a line from fractional slope and point. Constructing the equation of a line given two points. Finding y intercept given slope and point. Solving for the y-intercept. Slope intercept form from table. Slope intercept form. Idea behind point slope form. Linear Equations in Point Slope Form. Point slope form. Linear Equations in Standard Form. Point-slope and standard form. Converting between slope-intercept and standard form. Converting from point slope to slope intercept form. Converting between point-slope and slope-intercept. Finding the equation of a line. Midpoint formula. Midpoint formula. The Pythagorean theorem intro. Pythagorean theorem. Distance Formula. Distance formula. Perpendicular Line Slope. Equations of Parallel and Perpendicular Lines. Parallel Line Equation. Parallel Lines. Parallel Lines 2. Parallel lines 3. Perpendicular Lines. Perpendicular lines 2. Equations of parallel and perpendicular lines. Distance between a point and a line. Distance between point and line. Algebra: Slope and Y-intercept intuition. Algebra: Equation of a line. CA Algebra I: Slope and Y-intercept. Graphing Inequalities. Solving and graphing linear inequalities in two variables 1. Graphing Linear Inequalities in Two Variables Example 2. Graphing Inequalities 2. Graphing linear inequalities in two variables 3. Graphs of inequalities. Graphing linear inequalities. Graphing Inequalities 1. Graphing and solving linear inequalities. CA Algebra I: Graphing Inequalities. Similar triangles to prove that the slope is constant for a line. Slope and triangle similarity 1. Slope and triangle similarity 2. Slope and triangle similarity 3. Slope and triangle similarity 4. Slope and triangle similarity. Average Rate of Change Example 1). Average Rate of Change Example 2). Average Rate of Change Example 3). Average rate of change when function defined by equation. Average rate of change. Descartes and Cartesian Coordinates. The Coordinate Plane. Plot ordered pairs. Graphing points exercise. Graphing points. Quadrants of Coordinate Plane. Graphing points and naming quadrants exercise. Graphing points and naming quadrants. Points on the coordinate plane. Points on the coordinate plane. Coordinate plane word problems exercise. Coordinate plane word problems. Reflecting points exercise. Reflecting points. Ordered pair solutions of equations. Ordered Pair Solutions of Equations 2. Determining a linear equation by trying out values from a table. Equations from tables. Plotting (x,y) relationships. Graphs of Linear Equations. Application problem with graph. Ordered pair solutions to linear equations. Interpreting Linear Graphs. Exploring linear relationships. Recognizing Linear Functions. Interpreting linear relationships. Graphing lines 1. Recognizing Linear Functions. Linear and nonlinear functions (example 1). Linear and nonlinear functions (example 2). Linear and nonlinear functions (example 3). Linear and nonlinear functions. Graphing using X and Y intercepts. Graphing Using Intercepts. X and Y intercepts. X and Y intercepts 2. Solving for the x-intercept. Finding x intercept of a line. Finding intercepts for a linear function from a table. Linear function intercepts. Interpreting intercepts of linear functions. Interpreting and finding intercepts of linear functions. Analyzing and identifying proportional relationships ex1. Analyzing and identifying proportional relationships ex2. Analyzing and identifying proportional relationships ex3. Analyzing and identifying proportional relationships. Comparing proportional relationships. Constructing an equation for a proportional relationship. Constructing and comparing proportional relationships. Graphing proportional relationships example. Graphing proportional relationships example 2. Graphing proportional relationships example 3. Graphing proportional relationships. Comparing rates. Representing and comparing rates. Rates and proportional relationships. Rate problem with fractions 1. Unit cost with fractions 1. Rate problems 1. Slope of a line. Slope of a Line 2. Slope and Rate of Change. Graphical Slope of a Line. Slope of a Line 3. Slope Example. Hairier Slope of Line. Identifying slope of a line. Slope and Y-intercept Intuition. Line graph intuition. Algebra: Slope. Algebra: Slope 2. Algebra: Slope 3. Graphing a line in slope intercept form. Converting to slope-intercept form. Graphing linear equations. Fitting a Line to Data. Comparing linear functions 1. Comparing linear functions 2. Comparing linear functions 3. Comparing linear functions. Interpreting features of linear functions example. Interpreting features of linear functions example 2. Interpreting features of linear functions. Comparing linear functions applications 1. Comparing linear functions applications 2. Comparing linear functions applications 3. Comparing linear functions applications. Constructing a linear function word problem. Constructing and interpreting a linear function. Constructing linear graphs. Constructing and interpreting linear functions. Multiple examples of constructing linear equations in slope-intercept form. Constructing equations in slope-intercept form from graphs. Constructing linear equations to solve word problems. Linear equation from slope and a point. Finding a linear equation given a point and slope. Equation of a line from fractional slope and point. Constructing the equation of a line given two points. Finding y intercept given slope and point. Solving for the y-intercept. Slope intercept form from table. Slope intercept form. Idea behind point slope form. Linear Equations in Point Slope Form. Point slope form. Linear Equations in Standard Form. Point-slope and standard form. Converting between slope-intercept and standard form. Converting from point slope to slope intercept form. Converting between point-slope and slope-intercept. Finding the equation of a line. Midpoint formula. Midpoint formula. The Pythagorean theorem intro. Pythagorean theorem. Distance Formula. Distance formula. Perpendicular Line Slope. Equations of Parallel and Perpendicular Lines. Parallel Line Equation. Parallel Lines. Parallel Lines 2. Parallel lines 3. Perpendicular Lines. Perpendicular lines 2. Equations of parallel and perpendicular lines. Distance between a point and a line. Distance between point and line. Algebra: Slope and Y-intercept intuition. Algebra: Equation of a line. CA Algebra I: Slope and Y-intercept. Graphing Inequalities. Solving and graphing linear inequalities in two variables 1. Graphing Linear Inequalities in Two Variables Example 2. Graphing Inequalities 2. Graphing linear inequalities in two variables 3. Graphs of inequalities. Graphing linear inequalities. Graphing Inequalities 1. Graphing and solving linear inequalities. CA Algebra I: Graphing Inequalities. Similar triangles to prove that the slope is constant for a line. Slope and triangle similarity 1. Slope and triangle similarity 2. Slope and triangle similarity 3. Slope and triangle similarity 4. Slope and triangle similarity. Average Rate of Change Example 1). Average Rate of Change Example 2). Average Rate of Change Example 3). Average rate of change when function defined by equation. Average rate of change.

### Algebra: Systems of equations and inequalities

Khan Academy Free Closed [?] Mathematics Algebra College algebra Systems of equations and inequalities

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.

### Algebra: Polynomials

Khan Academy Free Closed [?] Mathematics Algebra College algebra Polynomials

Using polynomial expressions and factoring polynomials. Terms coefficients and exponents in a polynomial. Interesting Polynomial Coefficient Problem. Polynomials1. Polynomials 2. Evaluating a polynomial at a given value. Simplify a polynomial. Adding Polynomials. Example: Adding polynomials with multiple variables. Addition and Subtraction of Polynomials. Adding and Subtracting Polynomials 1. Adding and Subtracting Polynomials 2. Adding and Subtracting Polynomials 3. Subtracting Polynomials. Subtracting polynomials with multiple variables. Adding and subtracting polynomials. Multiplying Monomials. Dividing Monomials. Multiplying and Dividing Monomials 1. Multiplying and Dividing Monomials 2. Multiplying and Dividing Monomials 3. Monomial Greatest Common Factor. Factoring and the Distributive Property. Factoring and the Distributive Property 2. Factoring and the Distributive Property 3. Multiplying Binomials with Radicals. Multiplication of Polynomials. Multiplying Binomials. Multiplying Polynomials1. Multiplying Polynomials 2. Square a Binomial. Special Products of Binomials. Special Polynomials Products 1. Factor polynomials using the GCF. Special Products of Polynomials 1. Special Products of Polynomials 2. Multiplying expressions 0.5. Factoring linear binomials. Multiplying expressions 1. Multiplying Monomials by Polynomials. Multiplying Polynomials. Multiplying Polynomials 3. More multiplying polynomials. Multiplying polynomials. Level 1 multiplying expressions. Polynomial Division. Polynomial divided by monomial. Dividing multivariable polynomial with monomial. Dividing polynomials 1. Dividing polynomials with remainders. Synthetic Division. Synthetic Division Example 2. Why Synthetic Division Works. Factoring Sum of Cubes. Difference of Cubes Factoring. Algebraic Long Division. Algebra II: Simplifying Polynomials. Terms coefficients and exponents in a polynomial. Interesting Polynomial Coefficient Problem. Polynomials1. Polynomials 2. Evaluating a polynomial at a given value. Simplify a polynomial. Adding Polynomials. Example: Adding polynomials with multiple variables. Addition and Subtraction of Polynomials. Adding and Subtracting Polynomials 1. Adding and Subtracting Polynomials 2. Adding and Subtracting Polynomials 3. Subtracting Polynomials. Subtracting polynomials with multiple variables. Adding and subtracting polynomials. Multiplying Monomials. Dividing Monomials. Multiplying and Dividing Monomials 1. Multiplying and Dividing Monomials 2. Multiplying and Dividing Monomials 3. Monomial Greatest Common Factor. Factoring and the Distributive Property. Factoring and the Distributive Property 2. Factoring and the Distributive Property 3. Multiplying Binomials with Radicals. Multiplication of Polynomials. Multiplying Binomials. Multiplying Polynomials1. Multiplying Polynomials 2. Square a Binomial. Special Products of Binomials. Special Polynomials Products 1. Factor polynomials using the GCF. Special Products of Polynomials 1. Special Products of Polynomials 2. Multiplying expressions 0.5. Factoring linear binomials. Multiplying expressions 1. Multiplying Monomials by Polynomials. Multiplying Polynomials. Multiplying Polynomials 3. More multiplying polynomials. Multiplying polynomials. Level 1 multiplying expressions. Polynomial Division. Polynomial divided by monomial. Dividing multivariable polynomial with monomial. Dividing polynomials 1. Dividing polynomials with remainders. Synthetic Division. Synthetic Division Example 2. Why Synthetic Division Works. Factoring Sum of Cubes. Difference of Cubes Factoring. Algebraic Long Division. Algebra II: Simplifying Polynomials.

### Algebra: Functions

Khan Academy Free Closed [?] Mathematics Algebra College algebra Functions

Identifying, solving, and graphing various types of functions. What is a function. Difference between Equations and Functions. Function example problems. Ex: Constructing a function. Understanding Function Notation Example 1). Understanding Function Notation Example 2). Understanding Function Notation Example 3). Understanding function notation. Testing if a relationship is a function. Graphical Relations and Functions. Functions as Graphs. Recognizing functions (example 1). Recognizing functions (example 2). Recognizing functions. Relations and Functions. Functional Relationships 1. Recognizing functions (example 3). Recognizing functions (example 4). Recognizing functions (example 5). Recognizing functions 2. Domain of a function. Domain and Range of a Relation. Domain and Range of a Function Given a Formula. Domain and Range 1. Domain of a Radical Function. Domain of a function. Domain and Range 2. Domain and Range of a Function. Range of a function. Domain and range from graphs. Domain and range from graph. Direct and Inverse Variation. Recognizing Direct and Inverse Variation. Proportionality Constant for Direct Variation. Direct and inverse variation. Direct Variation Models. Direct Variation 1. Inverse Variation Application. Direct Inverse and Joint Variation. Direct Variation Application. Ex 1: Evaluating a function. Ex 2: Graphing a basic function. Graphing a parabola with a table of values. Ex 4: Graphing radical functions. Ex: Graphing exponential functions. Views of a function. Interpreting a graph exercise example. Interpreting graphs of linear and nonlinear functions. Quotient of Functions. Sum of Functions. Product of Functions. Difference of Functions. Evaluating a function expression. Evaluating expressions with function notation. Evaluating composite functions example. Evaluating composite functions. Introduction to Function Inverses. Function Inverse Example 1. Function Inverses Example 2. Function Inverses Example 3. Inverses of functions. New operator definitions. New operator definitions 1. New operator definitions 2. New operator definitions 2. Introduction to functions. Functions Part 2. Functions (Part III). Functions (part 4). What is a function. Difference between Equations and Functions. Function example problems. Ex: Constructing a function. Understanding Function Notation Example 1). Understanding Function Notation Example 2). Understanding Function Notation Example 3). Understanding function notation. Testing if a relationship is a function. Graphical Relations and Functions. Functions as Graphs. Recognizing functions (example 1). Recognizing functions (example 2). Recognizing functions. Relations and Functions. Functional Relationships 1. Recognizing functions (example 3). Recognizing functions (example 4). Recognizing functions (example 5). Recognizing functions 2. Domain of a function. Domain and Range of a Relation. Domain and Range of a Function Given a Formula. Domain and Range 1. Domain of a Radical Function. Domain of a function. Domain and Range 2. Domain and Range of a Function. Range of a function. Domain and range from graphs. Domain and range from graph. Direct and Inverse Variation. Recognizing Direct and Inverse Variation. Proportionality Constant for Direct Variation. Direct and inverse variation. Direct Variation Models. Direct Variation 1. Inverse Variation Application. Direct Inverse and Joint Variation. Direct Variation Application. Ex 1: Evaluating a function. Ex 2: Graphing a basic function. Graphing a parabola with a table of values. Ex 4: Graphing radical functions. Ex: Graphing exponential functions. Views of a function. Interpreting a graph exercise example. Interpreting graphs of linear and nonlinear functions. Quotient of Functions. Sum of Functions. Product of Functions. Difference of Functions. Evaluating a function expression. Evaluating expressions with function notation. Evaluating composite functions example. Evaluating composite functions. Introduction to Function Inverses. Function Inverse Example 1. Function Inverses Example 2. Function Inverses Example 3. Inverses of functions. New operator definitions. New operator definitions 1. New operator definitions 2. New operator definitions 2. Introduction to functions. Functions Part 2. Functions (Part III). Functions (part 4).

### Algebra: ck12.org Algebra 1 Examples

Khan Academy Free Closed [?] Mathematics Algebra Ck12.org Algebra 1 Examples College algebra

### Linear Algebra

Khan Academy Free Closed [?] Mathematics Linear Algebra

Matrices, vectors, vector spaces, transformations. Covers all topics in a first year college linear algebra course. This is an advanced course normally taken by science or engineering majors after taking at least two semesters of calculus (although calculus really isn't a prereq) so don't confuse this with regular high school algebra. Introduction to matrices. Matrix multiplication (part 1). Matrix multiplication (part 2). Idea Behind Inverting a 2x2 Matrix. Inverting matrices (part 2). Inverting Matrices (part 3). Matrices to solve a system of equations. Matrices to solve a vector combination problem. Singular Matrices. 3-variable linear equations (part 1). Solving 3 Equations with 3 Unknowns. Introduction to Vectors. Vector Examples. Parametric Representations of Lines. Linear Combinations and Span. Introduction to Linear Independence. More on linear independence. Span and Linear Independence Example. Linear Subspaces. Basis of a Subspace. Vector Dot Product and Vector Length. Proving Vector Dot Product Properties. Proof of the Cauchy-Schwarz Inequality. Vector Triangle Inequality. Defining the angle between vectors. Defining a plane in R3 with a point and normal vector. Cross Product Introduction. Proof: Relationship between cross product and sin of angle. Dot and Cross Product Comparison/Intuition. Matrices: Reduced Row Echelon Form 1. Matrices: Reduced Row Echelon Form 2. Matrices: Reduced Row Echelon Form 3. Matrix Vector Products. Introduction to the Null Space of a Matrix. Null Space 2: Calculating the null space of a matrix. Null Space 3: Relation to Linear Independence. Column Space of a Matrix. Null Space and Column Space Basis. Visualizing a Column Space as a Plane in R3. Proof: Any subspace basis has same number of elements. Dimension of the Null Space or Nullity. Dimension of the Column Space or Rank. Showing relation between basis cols and pivot cols. Showing that the candidate basis does span C(A). A more formal understanding of functions. Vector Transformations. Linear Transformations. Matrix Vector Products as Linear Transformations. Linear Transformations as Matrix Vector Products. Image of a subset under a transformation. im(T): Image of a Transformation. Preimage of a set. Preimage and Kernel Example. Sums and Scalar Multiples of Linear Transformations. More on Matrix Addition and Scalar Multiplication. Linear Transformation Examples: Scaling and Reflections. Linear Transformation Examples: Rotations in R2. Rotation in R3 around the X-axis. Unit Vectors. Introduction to Projections. Expressing a Projection on to a line as a Matrix Vector prod. Compositions of Linear Transformations 1. Compositions of Linear Transformations 2. Matrix Product Examples. Matrix Product Associativity. Distributive Property of Matrix Products. Introduction to the inverse of a function. Proof: Invertibility implies a unique solution to f(x)=y. Surjective (onto) and Injective (one-to-one) functions. Relating invertibility to being onto and one-to-one. Determining whether a transformation is onto. Exploring the solution set of Ax=b. Matrix condition for one-to-one trans. Simplifying conditions for invertibility. Showing that Inverses are Linear. Deriving a method for determining inverses. Example of Finding Matrix Inverse. Formula for 2x2 inverse. 3x3 Determinant. nxn Determinant. Determinants along other rows/cols. Rule of Sarrus of Determinants. Determinant when row multiplied by scalar. (correction) scalar multiplication of row. Determinant when row is added. Duplicate Row Determinant. Determinant after row operations. Upper Triangular Determinant. Simpler 4x4 determinant. Determinant and area of a parallelogram. Determinant as Scaling Factor. Transpose of a Matrix. Determinant of Transpose. Transpose of a Matrix Product. Transposes of sums and inverses. Transpose of a Vector. Rowspace and Left Nullspace. Visualizations of Left Nullspace and Rowspace. Orthogonal Complements. Rank(A) = Rank(transpose of A). dim(V) + dim(orthogonal complement of V)=n. Representing vectors in Rn using subspace members. Orthogonal Complement of the Orthogonal Complement. Orthogonal Complement of the Nullspace. Unique rowspace solution to Ax=b. Rowspace Solution to Ax=b example. Showing that A-transpose x A is invertible. Projections onto Subspaces. Visualizing a projection onto a plane. A Projection onto a Subspace is a Linear Transforma. Subspace Projection Matrix Example. Another Example of a Projection Matrix. Projection is closest vector in subspace. Least Squares Approximation. Least Squares Examples. Another Least Squares Example. Coordinates with Respect to a Basis. Change of Basis Matrix. Invertible Change of Basis Matrix. Transformation Matrix with Respect to a Basis. Alternate Basis Transformation Matrix Example. Alternate Basis Transformation Matrix Example Part 2. Changing coordinate systems to help find a transformation matrix. Introduction to Orthonormal Bases. Coordinates with respect to orthonormal bases. Projections onto subspaces with orthonormal bases. Finding projection onto subspace with orthonormal basis example. Example using orthogonal change-of-basis matrix to find transformation matrix. Orthogonal matrices preserve angles and lengths. The Gram-Schmidt Process. Gram-Schmidt Process Example. Gram-Schmidt example with 3 basis vectors. Introduction to Eigenvalues and Eigenvectors. Proof of formula for determining Eigenvalues. Example solving for the eigenvalues of a 2x2 matrix. Finding Eigenvectors and Eigenspaces example. Eigenvalues of a 3x3 matrix. Eigenvectors and Eigenspaces for a 3x3 matrix. Showing that an eigenbasis makes for good coordinate systems. Vector Triple Product Expansion (very optional). Normal vector from plane equation. Point distance to plane. Distance Between Planes.

### Numerical Methods Applied to Chemical Engineering (Fall 2006)

Starts : 2006-09-01
MIT OpenCourseWare (OCW) Free Engineering Chemical Engineering Graduate MIT OpenCourseWare

Numerical methods for solving problems arising in heat and mass transfer, fluid mechanics, chemical reaction engineering, and molecular simulation. Topics: numerical linear algebra, solution of nonlinear algebraic equations and ordinary differential equations, solution of partial differential equations (e.g. Navier-Stokes), numerical methods in molecular simulation (dynamics, geometry optimization). All methods are presented within the context of chemical engineering problems. Familiarity with structured programming is assumed. The examples will use MATLAB®.

## Acknowledgements

The instructor would like to thank Robert Ashcraft, Sandeep Sharma, David Weingeist, and Nikolay Zaborenko for their work in preparing materials for this course site.

### Linear Algebra - Foundations to Frontiers (LAFF)

Starts : 2015-06-03
edX Free Closed [?] English Computer Science EdX Math UTAustinX

Foundations to Frontiers (LAFF) is packed full of challenging, rewarding material that is essential for mathematicians, engineers, scientists, and anyone working with large datasets. Students appreciate our unique approach to teaching linear algebra because:

• It’s visual.
• It connects hand calculations, mathematical abstractions, and computer programming.
• It illustrates the development of mathematical theory.
• It’s applicable.

In this course, you will learn all the standard topics that are taught in typical undergraduate linear algebra courses all over the world, but using our unique method, you'll also get more! LAFF was developed following the syllabus of an introductory linear algebra course at The University of Texas at Austin taught by Professor Robert van de Geijn, an expert on high performance linear algebra libraries. Through short videos, exercises, visualizations, and programming assignments, you will study Vector and Matrix Operations, Linear Transformations, Solving Systems of Equations, Vector Spaces, Linear Least-Squares, and Eigenvalues and Eigenvectors. In addition, you will get a glimpse of cutting edge research on the development of linear algebra libraries, which are used throughout computational science.

MATLAB licenses will be made available to the participants free of charge for the duration of the course.

This summer version of the course will be released at an accelerated pace. Each of the three releases will consist of four ”Weeks” plus an exam . There will be suggested due dates, but only the end of the course is a true deadline.

We invite you to LAFF with us!

FAQs

What is the estimated effort for the course?

How much does it cost to take the course?

You can choose! Auditing the course is free.  If you want to challenge yourself by earning a Verified Certificate of Achievement, the contributions start at \$50.

Will the text for the videos be available?

Yes. All of our videos will have transcripts synced to the videos.

Do I need to watch the videos live?

No. You watch the videos at your leisure.

Can I contact the Instructor or Teaching Assistants?

Yes, but not directly. The discussion forums are the appropriate venue for questions about the course. The instructors will monitor the discussion forums and try to respond to the most important questions; in many cases response from other students and peers will be adequate and faster.

Is this course related to a campus course of The University of Texas at Austin?

Yes. This course corresponds to the Division of Statistics and Scientific Computing titled “SDS329C: Practical Linear Algebra”, one option for satisfying the linear algebra requirement for the undergraduate degree in computer science.

Is there a certificate available for completion of this course?

Online learners who successfully complete LAFF can obtain an edX certificate. This certificate indicates that you have successfully completed the course, but does not include a grade.

Must I work every problem correctly to receive the certificate?

No, you are neither required nor expected to complete every problem.

What textbook do I need for the course?

What are the principles by which assignment due dates are established?

There is a window of 19 days between the material release and the due date for the homework of that week. While we encourage you to complete a week’s work before the launch of the next week, we realize that life sometimes gets in the way so we have established a flexible cushion. Please don’t procrastinate. The course closes 25 May 2015. This is to give you nineteen days from the release of the final to complete the course.

Are there any special system requirements?

You may need at least 768MB of RAM memory and 2-4GB of free hard drive space. You should be able to successfully access the course using Chrome and Firefox.

### Mathematical Methods for Quantitative Finance

Starts : 2015-06-01
Coursera Free Mathematics English Business & Management Economics & Finance

Mathematical Methods for Quantitative Finance covers topics from calculus and linear algebra that are fundamental for the study of mathematical finance. Students successfully completing this course will be mathematically well prepared to study quantitative finance at the graduate level.

### Differential Equations (Fall 2011)

MIT OpenCourseWare (OCW) Free Mathematics MIT OpenCourseWare Undergraduate

The laws of nature are expressed as differential equations. Scientists and engineers must know how to model the world in terms of differential equations, and how to solve those equations and interpret the solutions. This course focuses on the equations and techniques most useful in science and engineering.

#### Course Format

This course has been designed for independent study. It provides everything you will need to understand the concepts covered in the course. The materials include:

• Lecture Videos by Professor Arthur Mattuck.
• Course Notes on every topic.
• Practice Problems with Solutions.
• Problem Solving Videos taught by experienced MIT Recitation Instructors.
• Problem Sets to do on your own with Solutions to check your answers against when you're done.
• A selection of Interactive Java® Demonstrations called Mathlets to illustrate key concepts.
• A full set of Exams with Solutions, including practice exams to help you prepare.

Haynes Miller
Jeremy Orloff
Dr. John Lewis
Arthur Mattuck

## Other OCW Versions

OCW has published multiple versions of this subject.

## Related Content

### Linear Algebra (Fall 2011)

MIT OpenCourseWare (OCW) Free Mathematics MIT OpenCourseWare Undergraduate

This course covers matrix theory and linear algebra, emphasizing topics useful in other disciplines such as physics, economics and social sciences, natural sciences, and engineering. It parallels the combination of theory and applications in Professor Strang’s textbook linearalgebra/">Introduction to Linear Algebra.

#### Course Format

linear-algebra-fall-2011/Syllabus"> This course has been designed for independent study. It provides everything you will need to understand the concepts covered in the course. The materials include:

• A complete set of Lecture Videos by Professor Gilbert Strang.
• Summary Notes for all videos along with suggested readings in Prof. Strang's textbook linearalgebra/">Linear Algebra.
• Problem Solving Videos on every topic taught by an experienced MIT Recitation Instructor.
• Problem Sets to do on your own with Solutions to check your answers against when you're done.
• A selection of Java® Demonstrations to illustrate key concepts.
• A full set of Exams with Solutions, including review material to help you prepare.

## Other OCW Versions

OCW has published multiple versions of this subject.

## Related Content

### Linear Algebra - Communications Intensive

Starts : 2004-02-01
MIT OpenCourseWare (OCW) Free Mathematics MIT OpenCourseWare Undergraduate

This is a communication intensive supplement to Linear Algebra (linear-algebra-spring-2005/index.htm">18.06). The main emphasis is on the methods of creating rigorous and elegant proofs and presenting them clearly in writing. The course starts with the standard linear algebra syllabus and eventually develops the techniques to approach a more advanced topic: abstract root systems in a Euclidean space.

### Linear Partial Differential Equations: Analysis and Numerics

Starts : 2014-09-01
MIT OpenCourseWare (OCW) Free Mathematics MIT OpenCourseWare Undergraduate

This course provides students with the basic analytical and computational tools of linear partial differential equations (PDEs) for practical applications in science engineering, including heat / diffusion, wave, and Poisson equations. Analytics emphasize the viewpoint of linear algebra and the analogy with finite matrix problems. Numerics focus on finite-difference and finite-element techniques to reduce PDEs to matrix problems. The Julia Language (a free, open-source environment) is introduced and used in homework for simple examples.

### Introduction to Numerical Analysis (Spring 2012)

Starts : 2012-02-01
MIT OpenCourseWare (OCW) Free Mathematics MIT OpenCourseWare Undergraduate

This course analyzed the basic techniques for the efficient numerical solution of problems in science and engineering. Topics spanned root finding, interpolation, approximation of functions, integration, differential equations, direct and iterative methods in linear algebra.

### Introduction to Representation Theory

Starts : 2010-09-01