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Rated 4 out of 5 by from Good for the mathematically non-gifted I am a retired person whose last math class was 50 years ago and who is not especially gifted when it comes to numbers. I've watched all of the episodes of this course and Professor Sellers' Algebra I as well. On the whole, he explains mathematical principles and ideas clearly and illustrates them with helpful examples. If you are not mathematically gifted and want to learn or relearn algebra, this course might well be for you. If you've watched Professor Sellers' Algebra I, however, you should be warned that there is a good deal of repetition of the material treated there. In my judgment, there is too much repetition, even granting that some review of the earlier material is called for. Additionally, in Algebra II, Professor Sellers rushes through certain more advanced topics, making it difficult to follow his explanations. Some of the examples he discusses in his lectures on logarithms and probability, in particular, suffer from this problem. That said, Professor Sellers clearly has devoted considerable effort to explaining algebraic concepts and principles in a way that those of us who are not mathematically talented can understand, and he has largely succeeded in that effort. I certainly (re)learned much from his courses.
Date published: 2022-05-05
Rated 5 out of 5 by from A Practical, Useful Approach Took this 2011 course as a refresher since I am working with high school students at an after-school program. One of my concerns was being prepared for the so-called “new math”. I did observe with Mr. Sellers course a few such oddities. But they enabled me "to speak the same language" with the kids as a result. For example, years ago we learned that when you have two equations f(x) and g(x), if you wanted to solve f(g(x)), you simply SUBSTITUTED g(x) for the x in f(x). Made sense and simple. Now it’s called a "COMPOSITION" and such nomenclature, though unnecessary and distracting, is not really that big of a hill to climb. Another example is that the "rules” for differences in the graphs of equations are presented before the student “does the homework”. An example: y= absolute value of [x-3] "shifts the graph of y = absolute value of [x] to the right" (not the "intuitive" left). The problem is that if you do not verify this yourself by doing the homework examples you have a rule but no experience to prove the rule true. “In the old days", you did the work first and then the pattern was pointed out. This “rules" rather than “discovery" may well lead to less homework and thus less mastery. When I tutor Algebra, I use Sellers to “bridge the gap”, watch the student solve his own homework, then do the additional step of relating his math to real world problems. For example, manual pulmonary spirometry calculations (lung air flow based on medical conditions) dramatically illustrate the math. They answer the “Why do I have to do this” common question. SUMMARY: Seller’s course is an excellent interface between generations. As he is a home-school teacher himself (see L1), it is very useful for home schooling. Additionally, his explanations are very well organized. Any student with “math trouble” could benefit. Some may be concerned that there is no “Guide" with this course, only a "Workbook”. However, each chapter of the workbook begins with a review of the lecture, so no worries. Because of the need to improve a grandchild's math I also own the Great Course’ (discontinued?) Algebra II course by Siegel (2005). It did contain a Guidebook as well as a Workbook. Siegel (of Sam Houston State) taught math teachers. Though Siegel’s formal approach was more "old school' (and therefore “up my alley"), I suspect that today’s students would be better off with Sellers' course.
Date published: 2022-04-04
Rated 4 out of 5 by from A great class! I was really impressed with the coursework of this class and would recommend it to others as well.
Date published: 2022-02-09
Rated 5 out of 5 by from great review This course has enabled me to understand and help my teenage grandson with advanced algebra
Date published: 2021-09-05
Rated 3 out of 5 by from too rudimentary I am not sure who are the intended audience of this course. The content is too basic. Not many explanations on why. The teaching style reminds me of elementary school math classroom.
Date published: 2021-03-24
Rated 5 out of 5 by from Thoroughly enjoyable and illuminating! I just retired and want to learn calculus for the first time. Therefore, I watched Professor Sellers' two Algebra courses, and have just finished Algebra II. As with his Algebra I course, his teaching is entirely clear and helpful. He anticipates a degree of math anxiety that viewers may have, and addresses it very well. His course builds in a nice step-wise fashion. I feel much more confident about proceeding to pre-calculus and then calculus for having taken these wonderful two courses from Professor Sellers.
Date published: 2021-03-01
Rated 5 out of 5 by from Very clear Dr Sellers is very clear and concise in what he teaches. I was always afraid of anything to do with numbers, especially Mathematics but his style of teaching made this comprehensible and easy to follow, even what I feel are complex topics.
Date published: 2021-02-10
Rated 5 out of 5 by from A great review It's been a while since I first studied algebra and this was a great review to prepare me for Pre-Calculus and beyond. Thank you for this course.
Date published: 2021-02-06

Overview

Make sense of Algebra II in the company of master educator and award-winning Professor James A. Sellers. Algebra II gives you all the tools you need to thrive in a core skill of mathematics. In 36 engaging half-hour lectures, Professor Sellers walks you through hundreds of problems, showing every step in their solution and highlighting the most common missteps made by students. Designed for learners of all ages, this course will prove that algebra can be an exciting intellectual adventure and not nearly as difficult as many students fear. If you are shaky on basic math facts, algebra will be harder for you than it needs to be. Spend every day reviewing flashcards of math facts, and you will be surprised at how much better at math you are!

INSTITUTION

The Pennsylvania State University
Dr. James A. Sellers is Professor of Mathematics and Director of Undergraduate Mathematics at The Pennsylvania State University. He earned his B.S. in Mathematics from The University of Texas at San Antonio and his Ph.D. in Mathematics from Penn State. In the past few years, Professor Sellers has received the Teresa Cohen Mathematics Service Award from the Penn State Department of Mathematics and the Mathematical Association of America Allegheny Mountain Section Mentoring Award. More than 60 of Professor Sellers's research articles on partitions and related topics have been published in a wide variety of peer-reviewed journals. In 2008, he was a visiting scholar at the Isaac Newton Institute at the University of Cambridge. Professor Sellers has enjoyed many interactions at the high school and middle school levels. He has served as an instructor of middle-school students in the TexPREP program in San Antonio, Texas. He has also worked with Saxon Publishers on revisions to a number of its high-school textbooks. As a home educator and father of five, he has spoken to various home education organizations about mathematics curricula and teaching issues.

#### By This Professor #### Trailer #### 01: An Introduction to Algebra II

Professor Sellers explains the topics covered in the course, the importance of algebra, and how you can get the most out of these lessons. You then launch into the fundamentals of algebra by reviewing the order of operations and trying your hand at several problems.

32 min #### 02: Solving Linear Equations

Explore linear equations, starting with one-step equations and then advancing to those requiring two or more steps to solve. Next, apply the distributive property to simplify certain problems, and then learn about the three categories of linear equations.

31 min #### 03: Solving Equations Involving Absolute Values

Taking your knowledge of linear equations a step further, look at examples involving absolute values, which can be thought of as a distance on a number line, always expressed as a positive value. Use your critical-thinking skills to recognize absolute value problems that have limited or no solutions.

31 min #### 04: Linear Equations and Functions

Moving into the visual realm, learn how linear equations are represented as straight lines on graphs using either the slope-intercept or point-slope forms of the function. Next, investigate parallel and perpendicular lines and how to identify them by the value of their slopes.

29 min #### 05: Graphing Essentials

Reversing the procedure from the previous lesson, start with an equation and draw the line that corresponds to it. Then test your knowledge by matching four linear equations to their graphs. Finally, learn how to rewrite an equation to move its graph up, down, left, or right-or flip it entirely.

29 min #### 06: Functions-Introduction, Examples, Terminology

Functions are crucially important not only for algebra, but for precalculus, calculus, and higher mathematics. Learn the definition of a function, the notation, and associated concepts such as domain and range. Then try out the vertical line test for determining whether a given curve is a graph of a function.

31 min #### 07: Systems of 2 Linear Equations, Part 1

Practice solving systems of two linear equations by graphing the corresponding lines and looking for the intersection point. Discover that there are three possible outcomes: no solution, infinitely many solutions, and exactly one solution.

29 min #### 08: Systems of 2 Linear Equations, Part 2

Explore two other techniques for solving systems of two linear equations. First, the method of substitution solves one of the equations and substitutes the result into the other. Second, the method of elimination adds or subtracts the equations to see if a variable can be eliminated.

30 min #### 09: Systems of 3 Linear Equations

As the number of variables increases, it becomes unwieldy to solve systems of linear equations by graphing. Learn that these problems are not as hard as they look and that systems of three linear equations often yield to the strategy of successively eliminating variables.

31 min #### 10: Solving Systems of Linear Inequalities

Make the leap into systems of linear inequalities, where the solution is a set of values on one side or another of a graphed line. An inequality is an assertion such as "less than" or "greater than," which encompasses a range of values.

29 min #### 11: An Introduction to Quadratic Functions

Begin your investigation of quadratic functions by visualizing what these functions look like when graphed. They always form a U-shaped curve called a parabola, whose location on the coordinate plane can be predicted based on the individual terms of the equation.

32 min #### 12: Quadratic Equations-Factoring

One of the most important skills related to quadratics is factoring. Review the basics of factoring, and learn to recognize a very useful special case known as the difference of two squares. Close by working on a word problem that translates into a quadratic equation.

32 min #### 13: Quadratic Equations-Square Roots

The square root approach to solving quadratic equations works not just for perfect squares, such as 3 × 3 = 9, but also for values that don't seem to involve squares at all. Probe the idea behind this technique, and also venture into the strange world of complex numbers.

31 min #### 14: Completing the Square

Turn a quadratic equation into an easily solvable form that includes a perfect square-a technique called completing the square. An important benefit of this approach is that the rewritten form gives the coordinates for the vertex of the parabola represented by the equation.

30 min #### 15: Using the Quadratic Formula

When other approaches fail, one tool can solve every quadratic equation: the quadratic formula. Practice this formula on a wide range of problems, learning how a special expression called the discriminant immediately tells how many real-number solutions the equation has....

30 min #### 16: Solving Quadratic Inequalities

Extending the exercises on inequalities from lecture 10, step into the realm of quadratic inequalities, where the boundary graph is not a straight line but a parabola. Use your skills analyzing quadratic expressions to sketch graphs quickly and solve systems of quadratic inequalities.

30 min #### 17: Conic Sections-Parabolas and Hyperbolas

Delve into the algebra of conic sections, which are the cross-sectional shapes produced by slicing a cone at different angles. In this lesson, study parabolas and hyperbolas, which differ in how many variable terms are squared in each. Also learn how to sketch a hyperbola from its equation.

32 min #### 18: Conic Sections-Circles and Ellipses

Investigate the algebraic properties of the other two conic sections: ellipses and circles. Ellipses resemble stretched circles and are defined by their major and minor axes, whose ratio determines the ellipse's eccentricity. Circles are ellipses whose eccentricity = 1, with the major and minor axes equal.

32 min #### 19: An Introduction to Polynomials

Pause to examine the nature of polynomials-a class of algebraic expressions that you've been working with since the beginning of the course. Professor Sellers introduces several useful concepts, such as the standard form of polynomials and their degree, domain, range, and leading coefficients.

32 min #### 20: Graphing Polynomial Functions

Deepen your insight into polynomial functions by graphing them to see how they differ from non-polynomials. Then learn how the general shape of the graph can be predicted from the highest exponent of the polynomial, known as its degree. Finally, explore how other terms in the function also affect the graph.

31 min #### 21: Combining Polynomials

Switch from graphs to the algebraic side of polynomial functions, learning how to combine them in many different ways, including addition, subtraction, multiplication, and even long division, which is easier than it seems. Discover which of these operations produce new polynomials and which do not.

34 min #### 22: Solving Special Polynomial Equations

Learn how to solve polynomial equations where the degree is greater than two by turning them into expressions you already know how to handle. Your "toolbox" includes techniques called the difference of two squares, the difference of two cubes, and the sum of two cubes.

32 min #### 23: Rational Roots of Polynomial Equations

Going beyond the approaches you've learned so far, discover how to solve polynomial equations by applying two powerful tools for finding rational roots: the rational roots theorem and the factor theorem. Both will prove very useful in succeeding lessons.

32 min #### 24: The Fundamental Theorem of Algebra

Explore two additional tools for identifying the roots of polynomial equations: Descartes' rule of signs, which narrows down the number of possible positive and negative real roots; and the fundamental theorem of algebra, which gives the total of all roots for a given polynomial.

32 min #### 25: Roots and Radical Expressions

Shift gears away from polynomials to focus on expressions involving roots, including square roots, cube roots, and roots of higher degrees-all known as radical expressions. Practice multiplying, dividing, adding, and subtracting a wide variety of radical expressions.

32 min #### 26: Solving Equations Involving Radicals

Drawing on your experience with roots and radicals from the previous lesson, try your hand at solving equations with these expressions. Begin by learning how to manipulate rational, or fractional, exponents. Then practice with simple equations, while being on the lookout for extraneous, or "imposter," solutions.

31 min #### 27: Graphing Power, Radical, and Root Functions

Using graph paper, experiment with curves formed by simple radical functions. First, determine the domain of the function, which tells you the general location of the graph on the coordinate plane. Then, investigate how different terms in the function alter the graph in predictable ways.

32 min #### 28: An Introduction to Rational Functions

Shift your focus to graphs of rational functions-functions that are the ratio of two polynomials. These graphs are more complicated than those from the previous lesson, but their general characteristics can be quickly determined by calculating the domain, the x- and y-intercepts, and the vertical and horizontal asymptotes....

31 min #### 29: The Algebra of Rational Functions

Combine rational functions using addition, subtraction, multiplication, division, and composition. The trick is to start each problem by putting the expressions in factored form, which makes the calculations go more smoothly. Leaving the answer in factored form also allows other operations, such as graphing, to be easily performed.

31 min #### 30: Partial Fractions

Now that you know how to add rational expressions, try the opposite procedure of splitting a more complicated rational expression into its component parts. Called partial fraction decomposition, this approach is a topic in introductory calculus and is used for solving a wide range of more advanced math problems.

30 min #### 31: An Introduction to Exponential Functions

Exponential functions are important in real-world applications involving growth and decay rates, such as compound interest and depreciation. Experiment with simple exponential functions, exploring such concepts as the base, growth factor, and decay factor, and how different values for these terms affect the graph of the function.

30 min #### 32: An Introduction to Logarithmic Functions

Plot a logarithmic function on the coordinate plane to see how it is the mirror image of a corresponding exponential function. Just like a mirror image, logarithms can be disorienting at first; but by studying their properties you will discover how they make certain calculations much simpler.

32 min #### 33: Uses of Exponential and Logarithmic Functions

Delve deeper into exponential and logarithmic functions with the goal of solving a typical financial investment problem using the "Pert" formula. To prepare, study the change of base formula for logarithms and the special function of the base called e....

30 min #### 34: The Binomial Theorem

Pascal's triangle is a famous triangular array of numbers that corresponds to the coefficients of binomials of different powers. In a lesson connecting a branch of mathematics called combinatorics with algebra, investigate the formula for each value in Pascal's triangle, the factorial function, and the binomial theorem.

31 min #### 35: Permutations and Combinations

Continue your study of the link between combinatorics and algebra by using the factorial function to solve problems in permutations and combinations. For example, what are all the permutations of the letters a, b, c? And how many combinations of four books are possible when you have six to choose from?...

32 min #### 36: Elementary Probability

After a short introduction to probability, celebrate your completion of the course with a deck of cards. Can you use the principles of probability, permutations, and combinations to calculate the probability of being dealt different hands? As with the rest of algebra, once you know the rules, it's simplicity itself!

34 min