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## Episodes

- S1 E1 - An Introduction to the CourseNovember 8, 200933minProfessor Sellers introduces the general topics and themes for the course, describing his approach and recommending a strategy for making the best use of the lessons and supplementary workbook. Warm up with some simple problems that demonstrate signed numbers and operations.#Science & MathematicsFree trial of The Great Courses Signature Collection or buy
- S1 E2 - Order of OperationsNovember 8, 200930minThe order in which you do simple operations of arithmetic can make a big difference. Learn how to solve problems that combine adding, subtracting, multiplying, and dividing, as well as raising numbers to various powers. These same concepts also apply when you need to simplify algebraic expressions, making it critical to master them now.Free trial of The Great Courses Signature Collection or buy
- S1 E3 - Percents, Decimals, and FractionsNovember 8, 200930minContinue your study of math fundamentals by exploring various procedures for converting between percents, decimals, and fractions. Professor Sellers notes that it helps to see these procedures as ways of presenting the same information in different forms.Free trial of The Great Courses Signature Collection or buy
- S1 E4 - Variables and Algebraic ExpressionsNovember 8, 200930minAdvance to the next level of problem solving by using variables as the building blocks to create algebraic expressions, which are combinations of mathematical symbols that might include numbers, variables, and operation symbols. Also learn some tricks for translating the language of problems (phrases in English) into the language of math (algebraic expressions).Free trial of The Great Courses Signature Collection or buy
- S1 E5 - Operations and ExpressionsNovember 8, 200931minDiscover that by following basic rules on how to treat coefficients and exponents, you can reduce very complicated algebraic expressions to much simpler ones. You start by using the commutative property of multiplication to rearrange the terms of an expression, making combining them relatively easy.Free trial of The Great Courses Signature Collection or buy
- S1 E6 - Principles of Graphing in 2 DimensionsNovember 8, 200928minUsing graph paper and pencil, begin your exploration of the coordinate plane, also known as the Cartesian plane. Learn how to plot points in the four quadrants of the plane, how to choose a scale for labeling the x and y axes, and how to graph a linear equation.Free trial of The Great Courses Signature Collection or buy
- S1 E7 - Solving Linear Equations, Part 1November 8, 200930minIn this lesson, work through simple one- and two-step linear equations, learning how to isolate the variable by different operations. Professor Sellers also presents a word problem involving a two-step equation and gives tips for how to solve it.Free trial of The Great Courses Signature Collection or buy
- S1 E8 - Solving Linear Equations, Part 2November 8, 200929minInvestigating more complicated examples of linear equations, learn that linear equations fall into three categories. First, the equation might have exactly one solution. Second, it might have no solutions at all. Third, it might be an identity, which means every number is a solution.Free trial of The Great Courses Signature Collection or buy
- S1 E9 - Slope of a LineNovember 8, 200928minExplore the concept of slope, which for a given straight line is its rate of change, defined as the rise over run. Learn the formula for calculating slope with coordinates only, and what it means to have a positive, negative, and undefined slope.Free trial of The Great Courses Signature Collection or buy
- S1 E10 - Graphing Linear Equations, Part 1November 8, 200931minUse what you've learned about slope to graph linear equations in the slope-intercept form, y = mx + b, where m is the slope, and b is the y intercept. Experiment with examples in which you calculate the equation from a graph and from a table of pairs of points.Free trial of The Great Courses Signature Collection or buy
- S1 E11 - Graphing Linear Equations, Part 2November 8, 200930minA more versatile approach to writing the equation of a line is the point-slope form, in which only two points are required, and neither needs to intercept the y axis. Work through several examples and become comfortable determining the equation using the line and the line using the equation.Free trial of The Great Courses Signature Collection or buy
- S1 E12 - Parallel and Perpendicular LinesNovember 8, 200931minApply what you've discovered about equations of lines to two very special types of lines: parallel and perpendicular. Learn how to tell if lines are parallel or perpendicular from their equations alone, without having to see the lines themselves. Also try your hand at word problems that feature both types of lines.Free trial of The Great Courses Signature Collection or buy
- S1 E13 - Solving Word Problems with Linear EquationsNovember 8, 200931minLinear equations reflect the behavior of real-life phenomena. Practice evaluating tables of numbers to determine if they can be represented as linear equations. Conclude with an example about the yearly growth of a tree. Does it increase in size at a linear rate?Free trial of The Great Courses Signature Collection or buy
- S1 E14 - Linear Equations for Real-World DataNovember 8, 200930minInvestigating more real-world applications of linear equations, derive the formula for converting degrees Celsius to Fahrenheit; determine the boiling point of water in Denver, Colorado; and calculate the speed of a rising balloon and the time for an elevator to descend to the ground floor.Free trial of The Great Courses Signature Collection or buy
- S1 E15 - Systems of Linear Equations, Part 1November 8, 200930minWhen two lines intersect, they form a system of linear equations. Discover two methods for finding a solution to such a system: by graphing and by substitution. Then try out a real-world example, involving a farmer who wants to plant different crops in different proportions.Free trial of The Great Courses Signature Collection or buy
- S1 E16 - Systems of Linear Equations, Part 2November 8, 200932minExpand your tools for solving systems of linear equations by exploring the method of solving by elimination. This technique allows you to eliminate one variable by performing addition, subtraction, or multiplication on both sides of an equation, allowing a straightforward solution for the remaining variable.Free trial of The Great Courses Signature Collection or buy
- S1 E17 - Linear InequalitiesNovember 8, 200931minShift gears to consider linear inequalities, which are mathematical expressions featuring a less than sign or a greater than sign instead of an equal sign. Discover that these kinds of problems have some very interesting twists, and they come up frequently in business applications.Free trial of The Great Courses Signature Collection or buy
- S1 E18 - An Introduction to Quadratic PolynomialsNovember 8, 200931minTransition to a more complex type of algebraic expression, which incorporates squared terms and is therefore known as quadratic. Learn how to use the FOIL method (first, outer, inner, last) to multiply linear terms to get a quadratic expression.Free trial of The Great Courses Signature Collection or buy
- S1 E19 - Factoring TrinomialsNovember 8, 200931minBegin to find solutions for quadratic equations, starting with the FOIL technique in reverse to find the binomial factors of a quadratic trinomial (a binomial expression consists of two terms, a trinomial of three). Professor Sellers explains the tricks of factoring such expressions, which is a process almost like solving a mystery.Free trial of The Great Courses Signature Collection or buy
- S1 E20 - Quadratic Equations - FactoringNovember 8, 200932minIn some circumstances, quadratic expressions are given in a special form that allows them to be factored quickly. Focus on two such forms: perfect square trinomials and differences of two squares. Learning to recognize these cases makes factoring easy.Free trial of The Great Courses Signature Collection or buy
- S1 E21 - Quadratic Equations - The Quadratic FormulaNovember 8, 200930minFor those cases that defy simple factoring, the quadratic formula provides a powerful technique for solving quadratic equations. Discover that this formidable-looking expression is not as difficult as it appears and is well worth committing to memory. Also learn how to determine if a quadratic equation has no solutions.Free trial of The Great Courses Signature Collection or buy
- S1 E22 - Quadratic Equations - Completing the SquareNovember 8, 200931minAfter learning the definition of a function, investigate an additional approach to solving quadratic equations: completing the square. This technique is very useful when rewriting the equation of a quadratic function in such a way that the graph of the function is easily sketched.Free trial of The Great Courses Signature Collection or buy
- S1 E23 - Representations of Quadratic FunctionsNovember 8, 200929minDrawing on your experience solving quadratic functions, analyze the parabolic shapes produced by such functions when represented on a graph. Use your algebraic skills to determine the parabola's vertex, its x and y intercepts, and whether it opens in an upward "cup" or downward in a "cap."Free trial of The Great Courses Signature Collection or buy
- S1 E24 - Quadratic Equations in the Real WorldNovember 8, 200932minQuadratic functions often arise in real-world settings. Explore a number of problems, including calculating the maximum height of a rocket and determining how long an object dropped from a tree takes to reach the ground. Learn that in finding a solution, graphing can often help.Free trial of The Great Courses Signature Collection or buy
- S1 E25 - The Pythagorean TheoremNovember 8, 200931minBecause it involves terms raised to the second power, the famous Pythagorean theorem, a2 + b2 = c2, is actually a quadratic equation. Discover how techniques you have previously learned for analyzing quadratic functions can be used for solving problems involving right triangles.Free trial of The Great Courses Signature Collection or buy

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