4: The Joy of Counting
Combinatorics is the study of counting questions such as: How many outfits are possible if you own 8 shirts, 5 pairs of pants, and 10 ties? A trickier question: How many ways are there to arrange 10 books on a shelf? Combinatorics can also be used to analyze numbering systems, such as ZIP Codes or license plates, as well as games of chance....
8: The Joy of Algebra Made Visual
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.
11: The Joy of Geometry
Geometry is based on a handful of definitions and axioms involving points, lines, and angles. These lead to important conclusions about the properties of polygons. This lecture uses geometric reasoning to derive the Pythagorean theorem and other interesting results....
13: The Joy of Trigonometry
Trigonometry deals with the sides and angles of triangles. This lecture defines sine, cosine, and tangent, along with their reciprocals, the cosecant, secant, and cotangent. Extending these definitions to the unit circle allows a handy measure of angle: the radian....
19: The Joy of Approximating with Calculus
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....
20: The Joy of Integral Calculus
Geometry and trigonometry are used to determine the areas of simple figures such as triangles and circles. But how are more complex shapes measured? Calculus comes to the rescue with a technique called integration, which adds the simple areas of many tiny quantities....
24: The Joy of Mathematical Magic
Closing the course with a magician's flair, Professor Benjamin shows a trick for producing anyone's phone number, how to create a magic square based on your birthday, how to play "mathematical survivor," a technique for computing cube roots in your head, and a card trick to ponder.
As a professor, I have always wanted to bring math to the masses. The Great Courses has helped make that dream come true.
About Arthur T. Benjamin
Dr. Arthur T. Benjamin is Professor of Mathematics at Harvey Mudd College. He earned a Ph.D. in Mathematical Sciences from Johns Hopkins University in 1989. Professor Benjamin's teaching has been honored repeatedly by the Mathematical Association of America (MAA). In 2000, he received the MAA Deborah and Franklin Tepper Haimo National Award for Distinguished College or University Teaching of Mathematics. The MAA also named Professor Benjamin the 2006-2008 George Pólya Lecturer. In 2012, Princeton Review profiled him in The Best 300 Professors. He is a professional magician, whose techniques are explained in his book Secrets of Mental Math: The Mathemagician's Guide to Lightning Calculation and Amazing Math Tricks. Professor Benjamin also served for five years as coeditor of Math Horizons magazine. An avid games player, Dr. Benjamin is a past winner of the American Backgammon Tour and has written more than 15 papers on the mathematics of games and puzzles. Professor Benjamin has appeared on dozens of television and radio programs and has been featured in publications, including Scientific American, People, and The New York Times. In 2005, Reader's Digest called him America's Best Math Whiz.