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## Episodes

- S1 E1 - The Joy of Math - The Big PictureApril 10, 200731minProfessor Benjamin introduces the ABCs of math appreciation: The field can be loved for its applications, its beauty and structure, and its certainty. Most of all, mathematics is a source of endless delight through creative play with numbers.#Science & MathematicsFree trial of The Great Courses Signature Collection or buy
- S1 E2 - The Joy of NumbersApril 10, 200729minHow do you add all the numbers from 1 to 100 - instantly? What makes a square number square and a triangular number triangular? Why do the rules of arithmetic really work, and how do you calculate in bases other than 10?Free trial of The Great Courses Signature Collection or buy
- S1 E3 - The Joy of PrimesApril 10, 200730minA number is prime if it is evenly divisible by only itself and one: for example, 2, 3, 5, 7, 11. Professor Benjamin proves that there are an infinite number of primes and shows how they are the building blocks of our number system.Free trial of The Great Courses Signature Collection or buy
- S1 E4 - The Joy of CountingApril 10, 200728minCombinatorics 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.Free trial of The Great Courses Signature Collection or buy
- S1 E5 - The Joy of Fibonacci NumbersApril 10, 200730minThe 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.Free trial of The Great Courses Signature Collection or buy
- S1 E6 - The Joy of AlgebraApril 10, 200731minArguably 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.Free trial of The Great Courses Signature Collection or buy
- S1 E7 - The Joy of Higher AlgebraApril 10, 200731minThis lecture shows how to solve quadratic (second-degree) equations from the technique of completing the square and the quadratic formula. The quadratic formula reveals the connection between Fibonacci numbers and the golden ratio.Free trial of The Great Courses Signature Collection or buy
- S1 E8 - The Joy of Algebra Made VisualApril 10, 200732minAlgebra 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.Free trial of The Great Courses Signature Collection or buy
- S1 E9 - The Joy of 9April 10, 200732minAdding the digits of a multiple of 9 always gives a multiple of 9. For example: 9 x 4 = 36, and 3 + 6 = 9. In modular arithmetic, this property allows checking answers by "casting out nines." A related trick: mentally computing the day of the week for any date in history.Free trial of The Great Courses Signature Collection or buy
- S1 E10 - The Joy of ProofsApril 10, 200731minProfessor Benjamin begins his discussion of mathematical proofs with intuitive cases like "even plus even is even" and "odd times odd is odd." He builds to more complex proofs by existence and induction, and ends with a checkerboard challenge.Free trial of The Great Courses Signature Collection or buy
- S1 E11 - The Joy of GeometryApril 10, 200731minGeometry 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.Free trial of The Great Courses Signature Collection or buy
- S1 E12 - The Joy of PiApril 10, 200731minPi is the ratio of the circumference of a circle to its diameter. It starts 3.14 and continues in an infinite nonrepeating sequence. Professor Benjamin shows how to learn the first hundred digits of this celebrated number, making it look as easy as pie.Free trial of The Great Courses Signature Collection or buy
- S1 E13 - The Joy of TrigonometryApril 10, 200732minTrigonometry 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.Free trial of The Great Courses Signature Collection or buy
- S1 E14 - The Joy of the Imaginary Number iApril 10, 200731minCould 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.Free trial of The Great Courses Signature Collection or buy
- S1 E15 - The Joy of the Number eApril 10, 200730minAnother indispensable number to learn is e = 2.71828 ... Defined as the base of the natural logarithm, e plays a central role in calculus, and it arises naturally in many spheres of mathematics, including calculations of compound interest.Free trial of The Great Courses Signature Collection or buy
- S1 E16 - The Joy of InfinityApril 10, 200730minWhat is the meaning of infinity? Are some infinite sets "more" infinite than others? Could there possibly be an infinite number of levels of infinity? This lecture explores some of the strange ideas associated with mathematical infinity.Free trial of The Great Courses Signature Collection or buy
- S1 E17 - The Joy of Infinite SeriesApril 10, 200731minStarting with the analysis of the proposition 0.999999999 ... = 1, this lecture explores what it means to add up an infinite series of numbers. Some infinite series converge on a definite value, while others grow arbitrarily large.Free trial of The Great Courses Signature Collection or buy
- S1 E18 - The Joy of Differential CalculusApril 10, 200732minCalculus is the mathematics of change, and answers questions such as: How fast is a function growing? This lecture introduces the concepts of limits and derivatives, which allow the slope of a curve to be measured at any point.Free trial of The Great Courses Signature Collection or buy
- S1 E19 - The Joy of Approximating with CalculusApril 10, 200731minExploiting 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.Free trial of The Great Courses Signature Collection or buy
- S1 E20 - The Joy of Integral CalculusApril 10, 200732minGeometry 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.Free trial of The Great Courses Signature Collection or buy
- S1 E21 - The Joy of Pascal's TriangleApril 10, 200732minA geometric arrangement of binomial coefficients called Pascal's triangle is a treasure trove of beautiful number patterns. It even provides an answer to the song "The Twelve Days of Christmas": Exactly how many gifts did my true love give to me?Free trial of The Great Courses Signature Collection or buy
- S1 E22 - The Joy of ProbabilityApril 10, 200730minMathematics can draw detailed inferences about random events. This lecture covers major concepts in probability, such as the law of large numbers, the central limit theorem, and how to measure variance.Free trial of The Great Courses Signature Collection or buy
- S1 E23 - The Joy of Mathematical GamesApril 10, 200731minThis lecture applies the law of total probability and other concepts from the course to predict the long-term losses to be expected from playing games such as roulette and craps and understand what is known as the "Gambler's Ruin Problem."Free trial of The Great Courses Signature Collection or buy
- S1 E24 - The Joy of Mathematical MagicApril 10, 200731minClosing 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.Free trial of The Great Courses Signature Collection or buy

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