# Online courses directory (90)

<p>This course is ideal for people who want to gain a thorough understanding and knowledge of advanced topics in algebra. </p><br /> <p>The advanced algebra topics include linear equations, inequalities, graphs, matrices, polynomials, radical expressions, quadratic equations, functions, exponential, logarithmic expressions, sequences, series, probability and trigonometry. </p> <br /> <p>The course is divided into 13 modules and each module is divided into lessons with theory, examples and video explanations, making for an enhanced study experience. </p>

Select problems from ck12.org's Algebra 1 FlexBook (Open Source Textbook). This is a good playlist to review if you want to make sure you have a good understanding of all of the major topics in Algebra I. Variable Expressions. Order of Operations Example. Patterns and Equations. Equations and Inequalities. Domain and Range of a Function. Functions as Graphs. Word Problem Solving Plan 1. Word Problem Solving Strategies. Integers and Rational Numbers. Addition of Rational Numbers. Subtraction of Rational Numbers. Multiplication of Rational Numbers. Distributive Property Example 1. Division of Rational Numbers. Square Roots and Real Numbers. Problem Solving Word Problems 2. One Step Equations. Two-Step Equations. Ex 1: Distributive property to simplify . Ex 3: Distributive property to simplify . Ratio and Proportion. Scale and Indirect Measurement. Percent Problems. Another percent example. The Coordinate Plane. Graphing Using Intercepts. Graphs of Linear Equations. Slope and Rate of Change. Graphs Using Slope-Intercept Form. Direct Variation Models. Function example problems. Word Problem Solving 4. Linear Equations in Slope Intercept Form. Linear Equations in Point Slope Form. Linear Equations in Standard Form. Equations of Parallel and Perpendicular Lines. Fitting a Line to Data. Predicting with Linear Models. Using a Linear Model. Inequalities Using Addition and Subtraction. Inequalities Using Multiplication and Division. Compound Inequalities. Absolute Value Equations. Absolute Value Inequalities. Graphing Inequalities. Solving Linear Systems by Graphing. Solving Linear Systems by Substitution. Solving Systems of Equations by Elimination. Solving Systems of Equations by Multiplication. Special Types of Linear Systems. Systems of Linear Inequalities. Exponent Properties Involving Products. Exponent Properties Involving Quotients. Zero, Negative, and Fractional Exponents. Scientific Notation. Exponential Growth Functions. Exponential Decay Functions. Geometric Sequences (Introduction). Word Problem Solving- Exponential Growth and Decay. Addition and Subtraction of Polynomials. Multiplication of Polynomials. Special Products of Binomials. Polynomial Equations in Factored Form. Factoring quadratic expressions. Factoring Special Products. Factor by Grouping and Factoring Completely. Graphs of Quadratic Functions. Solving Quadratic Equations by Graphing. Solving Quadratic Equations by Square Roots. Solving Quadratic Equations by Completing the Square. How to Use the Quadratic Formula. Proof of Quadratic Formula. Discriminant of Quadratic Equations. Linear, Quadratic, and Exponential Models. Identifying Quadratic Models. Identifying Exponential Models. Quadratic Regression. Shifting functions. Radical Expressions with Higher Roots. More Simplifying Radical Expressions. How to Rationalize a Denominator. Extraneous Solutions to Radical Equations. Radical Equation Examples. More Involved Radical Equation Example. Pythagorean Theorem. Distance Formula. Midpoint Formula. Visual Pythagorean Theorem Proof. Average or Central Tendency: Arithmetic Mean, Median, and Mode. Range, Variance and Standard Deviation as Measures of Dispersion. Stem and Leaf Plots. Histograms. Box-and-whisker Plot. Proportionality. Asymptotes of Rational Functions. Another Rational Function Graph Example. A Third Example of Graphing a Rational Function. Polynomial Division. Simplifying Rational Expressions Introduction. Multiplying and Dividing Rational Expressions. Adding Rational Expressions Example 1. Adding Rational Expressions Example 2. Adding Rational Expressions Example 3. Solving Rational Equations. Two more examples of solving rational equations. Surveys and Samples.

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).

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.

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.

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.

Exploring a world where both sides aren't equal anymore!. Inequalities Using Multiplication and Division. One-step inequality with multiplication and division example. Constructing and solving one-step inequality. One step inequalities. One-Step inequality involving addition. Inequalities Using Addition and Subtraction. Two-step inequality example. Multi-Step Inequalities. Multi-Step Inequalities 2. Multi-Step Inequalities 3. Multi-step linear inequalities. Interpreting Inequalities. Writing and using inequalities 2. Writing and using inequalities 3. Interpreting and solving linear inequalities. Inequality examples. Compound Inequalities. Compound Inequalities. Compound Inequalities 2. Compound Inequalities 3. Compound Inequalities 4. Compound inequalities. Absolute Value Inequalities. Absolute value inequalities Example 1. Absolute Value Inequalities Example 2. Absolute value inequalities example 3. Writing and using inequalities. Dogs cats and bears in a pet store visual argument. Dogs cats and bears in a pet store analytic argument. Reasoning through inequality expressions. Using expressions to understand relationships. Structure in expressions 1. Inequalities Using Multiplication and Division. One-step inequality with multiplication and division example. Constructing and solving one-step inequality. One step inequalities. One-Step inequality involving addition. Inequalities Using Addition and Subtraction. Two-step inequality example. Multi-Step Inequalities. Multi-Step Inequalities 2. Multi-Step Inequalities 3. Multi-step linear inequalities. Interpreting Inequalities. Writing and using inequalities 2. Writing and using inequalities 3. Interpreting and solving linear inequalities. Inequality examples. Compound Inequalities. Compound Inequalities. Compound Inequalities 2. Compound Inequalities 3. Compound Inequalities 4. Compound inequalities. Absolute Value Inequalities. Absolute value inequalities Example 1. Absolute Value Inequalities Example 2. Absolute value inequalities example 3. Writing and using inequalities. Dogs cats and bears in a pet store visual argument. Dogs cats and bears in a pet store analytic argument. Reasoning through inequality expressions. Using expressions to understand relationships. Structure in expressions 1.

This topic will add a ton of tools to your algebraic toolbox. You'll be able to multiply any expression and learn to factor a bunch a well. This will allow you to solve a broad array of problems in algebra. Factoring Special Products. Example 1: Factoring difference of squares. Factoring difference of squares 1. Example 2: Factoring difference of squares. Factoring difference of squares 2. Factoring to produce difference of squares. Factoring difference of squares 3. Example: Factoring perfect square trinomials. Example: Factoring a fourth degree expression. Example: Factoring special products. Multiplying Monomials. Dividing Monomials. Multiplying and Dividing Monomials 1. Multiplying and Dividing Monomials 2. Multiplying and Dividing Monomials 3. Monomial Greatest Common Factor. Multiplying binomials word problem. FOIL for multiplying binomials. Multiplying Binomials with Radicals. Multiplying binomials example 1. FOIL method for multiplying binomials example 2. Square a Binomial. Special Products of Binomials. Multiplying binomials to get difference of squares. Squaring a binomial. Multiplying expressions 0.5. Squaring a binomial example 2. Classic multiplying binomials video. Multiplying expressions 1. Factoring and the Distributive Property 3. Factoring linear binomials. Factoring linear binomials. Factoring and the Distributive Property. Factoring and the Distributive Property 2. Factor expressions using the GCF. Factoring quadratic expressions. Examples: Factoring simple quadratics. Example 1: Factoring quadratic expressions. Factoring polynomials 1. Example 1: Factoring trinomials with a common factor. Factoring polynomials 2. Factor by Grouping and Factoring Completely. Example: Basic grouping. Example 1: Factoring by grouping. Example 2: Factoring by grouping. Example 3: Factoring by grouping. Example 4: Factoring by grouping. Example 5: Factoring by grouping. Example 6: Factoring by grouping. Factoring polynomials by grouping. Factoring quadratics with two variables. Factoring quadratics with two variables example. Factoring polynomials with two variables. 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 by Polynomials. Multiplying Polynomials. Multiplying Polynomials 3. More multiplying polynomials. Multiplying polynomials. 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. Factoring Special Products. Example 1: Factoring difference of squares. Factoring difference of squares 1. Example 2: Factoring difference of squares. Factoring difference of squares 2. Factoring to produce difference of squares. Factoring difference of squares 3. Example: Factoring perfect square trinomials. Example: Factoring a fourth degree expression. Example: Factoring special products. Multiplying Monomials. Dividing Monomials. Multiplying and Dividing Monomials 1. Multiplying and Dividing Monomials 2. Multiplying and Dividing Monomials 3. Monomial Greatest Common Factor. Multiplying binomials word problem. FOIL for multiplying binomials. Multiplying Binomials with Radicals. Multiplying binomials example 1. FOIL method for multiplying binomials example 2. Square a Binomial. Special Products of Binomials. Multiplying binomials to get difference of squares. Squaring a binomial. Multiplying expressions 0.5. Squaring a binomial example 2. Classic multiplying binomials video. Multiplying expressions 1. Factoring and the Distributive Property 3. Factoring linear binomials. Factoring linear binomials. Factoring and the Distributive Property. Factoring and the Distributive Property 2. Factor expressions using the GCF. Factoring quadratic expressions. Examples: Factoring simple quadratics. Example 1: Factoring quadratic expressions. Factoring polynomials 1. Example 1: Factoring trinomials with a common factor. Factoring polynomials 2. Factor by Grouping and Factoring Completely. Example: Basic grouping. Example 1: Factoring by grouping. Example 2: Factoring by grouping. Example 3: Factoring by grouping. Example 4: Factoring by grouping. Example 5: Factoring by grouping. Example 6: Factoring by grouping. Factoring polynomials by grouping. Factoring quadratics with two variables. Factoring quadratics with two variables example. Factoring polynomials with two variables. 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 by Polynomials. Multiplying Polynomials. Multiplying Polynomials 3. More multiplying polynomials. Multiplying polynomials. 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.

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.

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.

From simulating complex phenomenon on supercomputers to storing the coordinates needed in modern 3D printing, data is a huge and growing part of our world. A major tool to manipulate and study this data is linear algebra. This course is part 1 of a 2-part course. In this part, we’ll learn basics of matrix algebra with an emphasis on application. This class has a focus on computer graphics while also containing examples in data mining. We’ll learn to make an image transparent, fade from one image to another, and rotate a 3D wireframe model. We’ll also mine data; for example, we will find similar movies that one might enjoy seeing. In the topic of sports ranking, we’ll be ready to participate in March Madness and submit our own mathematically generated brackets to compete against millions of others. The lectures are developed to encourage you to explore and create your own ideas either through your own programming but also with online tools developed for the course. Come to this course ready to investigate your own ideas.

*Courses offered via edX.org are not eligible for academic credit from Davidson College. A passing score in a DavidsonX course(s) will only be eligible for a verified certificate generated by edX.org.*

Our world is in a data deluge with ever increasing sizes of datasets. Linear algebra is a tool to manage and analyze such data.

This course is part 2 of a 2-part course, with this part extending smoothly from the first. Note, however, that part 1, is not a prerequisite for part 2. In this part of the course, we'll develop the linear algebra more fully than part 1. This class has a focus on data mining with some applications of computer graphics. We'll discuss, in further depth than part 1, sports ranking and ways to rate teams from thousands of games. We’ll apply the methods to March Madness. We'll also learn methods behind web search, utilized by such companies as Google. We'll also learn to cluster data to find similar groups and also how to compress images to lower the amount of storage used to store them. The tools that we learn can be applied to applications of your interest. For instance, clustering data to find similar movies can be applied to find similar songs or friends. So, come to this course ready to investigate your own ideas.

*Courses offered via edX.org are not eligible for academic credit from Davidson College. A passing score in a DavidsonX course(s) will only be eligible for a verified certificate generated by edX.org.*

We will explain how to start with raw data, and perform the standard processing and normalization steps to get to the point where one can investigate relevant biological questions. Throughout the case studies, we will make use of exploratory plots to get a general overview of the shape of the data and the result of the experiment. We start with RNA-seq data analysis covering basic concepts of RNA-seq and a first look at FASTQ files. We will also go over quality control of FASTQ files; aligning RNA-seq reads; visualizing alignments and move on to analyzing **RNA-seq at the gene-level**: counting reads in genes; Exploratory Data Analysis and variance stabilization for counts; count-based differential expression; normalization and batch effects. Finally, we cover **RNA-seq at the transcript-level**: inferring expression of transcripts (i.e. alternative isoforms); differential exon usage. We will learn the basic steps in analyzing DNA methylation data, including reading the raw data, normalization, and finding regions of differential methylation across multiple samples. The course will end with a brief description of the basic steps for analyzing ChIP-seq datasets, from read alignment, to peak calling, and assessing differential binding patterns across multiple samples.

Given the diversity in educational background of our students we have divided the series into seven parts. You can take the entire series or individual courses that interest you. If you are a statistician you should consider skipping the first two or three courses, similarly, if you are biologists you should consider skipping some of the introductory biology lectures. Note that the statistics and programming aspects of the class ramp up in difficulty relatively quickly across the first three courses. By the third course will be teaching advanced statistical concepts such as hierarchical models and by the fourth advanced software engineering skills, such as parallel computing and reproducible research concepts.

These courses make up 2 XSeries and are self-paced:

PH525.1x: Statistics and R for the Life Sciences

PH525.3x: Statistical Inference and Modeling for High-throughput Experiments

PH525.4x: High-Dimensional Data Analysis

PH525.5x: Introduction to Bioconductor: annotation and analysis of genomes and genomic assays

PH525.6x: High-performance computing for reproducible genomics

PH525.7x: Case studies in functional genomics

This class was supported in part by NIH grant R25GM114818.

HarvardX requires individuals who enroll in its courses on edX to abide by the terms of the edX honor code. HarvardX will take appropriate corrective action in response to violations of the edX honor code, which may include dismissal from the HarvardX course; revocation of any certificates received for the HarvardX course; or other remedies as circumstances warrant. No refunds will be issued in the case of corrective action for such violations. Enrollees who are taking HarvardX courses as part of another program will also be governed by the academic policies of those programs.

HarvardX pursues the science of learning. By registering as an online learner in an HX course, you will also participate in research about learning. Read our research statement to learn more.

Harvard University and HarvardX are committed to maintaining a safe and healthy educational and work environment in which no member of the community is excluded from participation in, denied the benefits of, or subjected to discrimination or harassment in our program. All members of the HarvardX community are expected to abide by Harvard policies on nondiscrimination, including sexual harassment, and the edX Terms of Service. If you have any questions or concerns, please contact harvardx@harvard.edu and/or report your experience through the edX contact form.

In the PH525 case studies, we will explore the data analysis of an experimental protocol in depth, using various open source software, including R and Bioconductor. We will explain how to start with raw data, and perform the standard processing and normalization steps to get to the point where one can investigate relevant biological questions. Throughout the case studies, we will make use of exploratory plots to get a general overview of the shape of the data and the result of the experiment.

We will learn the basic steps in analyzing DNA methylation data, including reading the raw data, normalization, and finding regions of differential methylation across multiple samples.

This class was supported in part by NIH grant R25GM114818.

This course is part of a larger set of 8 total courses running Self-Paced through **September 15th, 2015**:

PH525.1x: Statistics and R for the Life Sciences

PH525.3x: Advanced Statistics for the Life Sciences

PH525.4x: Introduction to Bioconductor

PH525.5x: Case study: RNA-seq data analysis

PH525.6x: Case study: Variant Discovery and Genotyping

PH525.7x: Case study: ChIP-seq data analysis

PH525.8x: Case study: DNA methylation data analysis

HarvardX requires individuals who enroll in its courses on edX to abide by the terms of the edX honor code. HarvardX will take appropriate corrective action in response to violations of the edX honor code, which may include dismissal from the HarvardX course; revocation of any certificates received for the HarvardX course; or other remedies as circumstances warrant. No refunds will be issued in the case of corrective action for such violations. Enrollees who are taking HarvardX courses as part of another program will also be governed by the academic policies of those programs.

HarvardX pursues the science of learning. By registering as an online learner in an HX course, you will also participate in research about learning. Read our research statement to learn more.

Harvard University and HarvardX are committed to maintaining a safe and healthy educational and work environment in which no member of the community is excluded from participation in, denied the benefits of, or subjected to discrimination or harassment in our program. All members of the HarvardX community are expected to abide by Harvard policies on nondiscrimination, including sexual harassment, and the edX Terms of Service. If you have any questions or concerns, please contact harvardx@harvard.edu and/or report your experience through the edX contact form.

In this college level Algebra course, you will learn to apply algebraic reasoning to solve problems effectively. You’ll develop skills in linear and quadratic functions, general polynomial functions, rational functions, and exponential and logarithmic functions. You will also study systems of linear equations. This course will emphasize problem-solving techniques, specifically by means of discussing concepts in each of these topics.

Content in this course will be adaptive, allowing you to achieve mastery in a certain concept before moving on to the next. Utilizing the ALEKS learning system, students in this personalized, self-paced course will be instructed on the topics they are most ready to learn while also providing individualized coaching as you move through each topic.

This 3 credit hour course satisfies the Mathematical Studies (MA) general studies requirement at Arizona State University. This course may satisfy a general education requirement at other institutions; however, it is strongly encouraged that you consult with your institution of choice to determine how these credits will be applied to their degree requirements prior to transferring the credit.

This course serves as an introduction to computational techniques arising in aerospace engineering. Applications are drawn from aerospace structures, aerodynamics, dynamics and control, and aerospace systems. Techniques include: numerical integration of systems of ordinary differential equations; finite-difference, finite-volume, and finite-element discretization of partial differential equations; numerical linear algebra; eigenvalue problems; and optimization with constraints.

This course provides a review of linear algebra, including applications to networks, structures, and estimation, Lagrange multipliers. Also covered are: differential equations of equilibrium; Laplace's equation and potential flow; boundary-value problems; minimum principles and calculus of variations; Fourier series; discrete Fourier transform; convolution; and applications.

Note: This course was previously called "Mathematical Methods for Engineers I."