The Joy of Higher Algebra

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Algebra
The 18 videos in this collection focus on all aspects of Algebra, from logarithms to quadratic equations and partial fractions.
Making Use of Linear Equations
Episode 11 of Geometry
Delve deeper into the connections between algebra and geometry by looking at lines and their equations. Use the three basic assumptions from previous lectures to prove that parallel lines have the same slope and to calculate the shortest distance between a point and a line.
The Joy of Algebra
Episode 6 of The Joy of Mathematics
Arguably the most important area of mathematics, algebra introduces the powerful idea of using an abstract variable to represent an unknown quantity. This lecture demonstrates algebra's golden rule: Do unto one side of an equation as you do unto the other.
The Joy of Algebra Made Visual
Episode 8 of The Joy of Mathematics
Algebra can be used to solve geometrical problems, such as finding where two lines cross. The technique is useful in real-life problems, for example, in choosing a telephone plan. Graphs help us better understand everything from lines to equations with negative or fractional exponents.
Complex Numbers in Geometry
Episode 35 of Geometry
In lecture 6, you saw how 17th-century mathematician Rene Descartes united geometry and algebra with the invention of the coordinate plane. Now go a step further and explore the power and surprises that come from using the complex number plane. Examine how using complex numbers can help solve several tricky…
The Joy of Approximating with Calculus
Episode 19 of The Joy of Mathematics
Exploiting the idea of the derivative, we can approximate just about any function using simple polynomials. This lecture also shows why a formula sometimes known as "God's equation" (involving e, i, p, 1, and 0) is true, and how to calculate square roots in your head.
Math in Your Head!
Episode 1 of Secrets of Mental Math
Dive right into the joys of mental math. First, learn the fundamental strategies of mental arithmetic (including the value of adding from left to right, unlike what you do on paper). Then, discover how a variety of shortcuts hold the keys to rapidly solving basic multiplication problems and finding squares.
Advanced Multiplication
Episode 11 of Secrets of Mental Math
Professor Benjamin shows you how to do enormous multiplication problems in your head, such as squaring three-digit and four-digit numbers; cubing two-digit numbers, and multiplying two-digit and three-digit numbers. While you may not frequently encounter these large problems, knowing how to mentally solve them cements your knowledge of basic mental…
The Joy of the Imaginary NumberĀ i
Episode 14 of The Joy of Mathematics
Could the apparently nonsensical number the square root of -1 be of any use? Very much so, as this lecture shows. Such imaginary and complex numbers play an indispensable role in physics and other fields, and are easier to understand than they appear.
The Joy of Mathematics
Ready to exercise those brain cells? Humans have been having fun with mathematics for thousands of years. Along the way, they've discovered the amazing utility of this field--in science, engineering, finance, games of chance, and many other aspects of life. This course of 24 half-hour lectures celebrates the sheer joy…
Distance, Midpoints, and Folding Ties
Episode 6 of Geometry
Learn how watching a fly on his ceiling inspired the mathematician Rene Descartes to link geometry and algebra. Find out how this powerful connection allows us to use algebra to calculate distances, midpoints, and more.
The Joy of Fibonacci Numbers
Episode 5 of The Joy of Mathematics
The Fibonacci numbers follow the simple pattern 1, 1, 2, 3, 5, 8, etc., in which each number is the sum of the two preceding numbers. Fibonacci numbers have many beautiful and unexpected properties, and show up in nature, art, and poetry.