Catalog Search Results
Series
Great Courses volume 9
Publisher
The Great Courses
Pub. Date
2016.
Language
English
Description
Logic is intellectual self-defense against such assaults on reason and also a method of quality control for checking the validity of your own views. But beyond these very practical benefits, informal logic—the kind we apply in daily life—is the gateway to an elegant and fascinating branch of philosophy known as formal logic, which is philosophy’s equivalent to calculus. Formal logic is a breathtakingly versatile tool. Much like a Swiss army...
Publisher
The Great Courses
Language
English
Description
We commonly define the Pythagorean theorem using the formula a2 + b2 = c2. But Pythagoras himself would have been confused by that. Explore how this famous theorem can be explained using common geometric shapes (no fancy algebra required), and how it’s a critical foundation for the rest of geometry.
Publisher
The Great Courses
Pub. Date
2009.
Language
English
Description
Conclude the course by examining more types of number sequences, discovering how rich and enjoyable the mathematics of pattern recognition can be. As in previous lessons, employ your reasoning skills and growing command of algebra to find order - and beauty - where once all was a confusion of numbers.
Publisher
The Great Courses
Pub. Date
2017.
Language
English
Description
Multiple linear regression lets you deal with data that has multiple predictors. Begin with an R data set on diabetes in Pima Indian women that has an array of potential predictors. Evaluate these predictors for significance. Then turn to data where you fit a multiple regression model by adding explanatory variables one by one.
Publisher
The Great Courses
Pub. Date
2009.
Language
English
Description
Discover 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.
Publisher
The Great Courses
Pub. Date
2017.
Language
English
Description
Professor 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 complexproofs by existenceandinduction, and ends with a checkerboard challenge.
Publisher
The Great Courses
Pub. Date
2015.
Language
English
Description
Investigate a puzzle that defied some of the most brilliant minds in mathematics: the Monty Hall problem, named after the host of Let's Make a Deal! Hall would let contestants change their guess about the location of a hidden prize after revealing new information about where it was not.
Publisher
The Great Courses
Pub. Date
2009.
Language
English
Description
Drawing 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."
Publisher
The Great Courses
Pub. Date
2014.
Language
English
Description
Continue the work of classification with triangles. Find out what mathematicians mean when they use words like scalene, isosceles, equilateral, acute, right, and obtuse. Then, learn how to use the Pythagorean theorem to determine the type of triangle (even if you don’t know the measurements of the angles).
Publisher
The Great Courses
Pub. Date
2015.
Language
English
Description
Leap into puzzles and mind-benders that teach you the rudiments of game theory. Divide loot with bloodthirsty pirates, ponder the two-envelope problem, learn about Newcomb's paradox, visit the island where everyone has blue eyes, and try your luck at prisoner's dilemma.
Publisher
The Great Courses
Pub. Date
2017.
Language
English
Description
Another indispensable number to learn ise= 2.71828 ... Defined as the base of the natural logarithm,eplays a central role in calculus, and it arises naturally in many spheres of mathematics, including calculations of compound interest.
Publisher
The Great Courses
Pub. Date
2014.
Language
English
Description
Classify all different types of four-sided polygons (called quadrilaterals) and learn the surprising characteristics about the diagonals and interior angles of rectangles, rhombuses, trapezoids, and more. Also see how real-life objects—like ironing boards—exhibit these geometric characteristics.
Publisher
The Great Courses
Pub. Date
2009.
Language
English
Description
Apply 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.
Publisher
The Great Courses
Pub. Date
2014.
Language
English
Description
So far, you’ve seen how to calculate the sine, cosine, and tangents of basic angles (0°, 30°, 45°, 60°, and 90°). What about calculating them for other angles—without a calculator? You’ll use the Pythagorean theorem to come up with formulas for sums and differences of the trig identities, which then allow you to calculate them for other angles.
Publisher
The Great Courses
Pub. Date
2014.
Language
English
Description
Explore the origins of one of the oldest branches of mathematics. See how geometry not only deals with practical concerns such as mapping, navigation, architecture, and engineering, but also offers an intellectual journey in its own right—inviting big, deep questions.
Publisher
The Great Courses
Pub. Date
2015.
Language
English
Description
Learn how Georg Cantor tamed infinity and astonished the mathematical world by showing that some infinite sets are larger than others. Then use a matching game inspired by dodge ball to prove that the set of real numbers is infinitely larger than the set of natural numbers, which is also infinite.
Publisher
The Great Courses
Pub. Date
2016.
Language
English
Description
One sheet of paper lying directly atop another has all its points aligned with the bottom sheet. But what if the top sheet is crumpled? Do any of its points still lie directly over the corresponding point on the bottom sheet? See a marvelous visual proof of this fixed-point theorem.
Publisher
The Great Courses
Pub. Date
2017.
Language
English
Description
Dip into R, which is a popular open-source programming language for use in statistics and data science. Consider the advantages of R over spreadsheets. Walk through the installation of R, installation of a companion IDE (integrated development environment) RStudio, and how to download specialized data packages from within RStudio.
Publisher
The Great Courses
Pub. Date
2015.
Language
English
Description
Randomly pick a real number between 0 and 1. What is the probability that the number is a fraction, such as ¼? Would you believe that the probability is zero? Probe this and other mind-bending facts about infinite sets, including the discovery that made Cantor exclaim, "I see it, but I don't believe it!"
Publisher
The Great Courses
Pub. Date
2017.
Language
English
Description
A 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.
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