Catalog Search Results
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.
Author
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
Pub. Date
2009.
Language
English
Description
When one polynomial is divided by another, the result is called a rational function because it is the ratio of two polynomials. These functions play an important role in algebra. Learn how to add and subtract rational functions by first finding their common divisor.
4) Geometry
Publisher
The Great Courses
Pub. Date
2014.
Language
English
Description
Inscribed over the entrance of Plato’s Academy were the words, "Let no one ignorant of geometry enter my doors."To ancient scholars, geometry was the gateway to knowledge. Its core skills of logic and reasoning are essential to success in school, work, and many other aspects of life. Yet sometimes students, even if they have done well in other math courses, can find geometry a challenge. Now, in the 36 innovative lectures of Geometry: An Interactive...
Publisher
The Great Courses
Pub. Date
2015.
Language
English
Description
Prove that some sets can't be measured - a result that is crucial to understanding the Banach-Tarski paradox, the strangest theorem in all of mathematics, which is presented in Lecture 23. Start by asking why mathematicians want to measure sets. Then learn how to construct a non-measurable set.
Publisher
The Great Courses
Pub. Date
2009.
Language
English
Description
Linear equations reflect the behavior of real-life phenomena. Practice evaluating tables of numbers to determine if they can be represented as linear equations. Conclude with an example about the yearly growth of a tree. Does it increase in size at a linear rate?
Publisher
The Great Courses
Pub. Date
2017.
Language
English
Description
While a creative statistical analysis can sometime salvage a poorly designed experiment, gain an understanding of how experiments can be designed in from the outset to collect far more reliable statistical data. Consider the role of randomization, replication, blocking, and other criteria, along with the use of ANOVA to analyze the results. Work several examples in R.
Publisher
The Great Courses
Pub. Date
2017.
Language
English
Description
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.
Publisher
The Great Courses
Pub. Date
2017.
Language
English
Description
Combinatoricsis 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.
Publisher
The Great Courses
Pub. Date
2009.
Language
English
Description
A more versatile approach to writing the equation of a line is the point-slope form, in which only two points are required, and neither needs to intercept the y axis. Work through several examples and become comfortable determining the equation using the line and the line using the equation.
Publisher
The Great Courses
Pub. Date
2017.
Language
English
Description
Polynomial regression is a form of regression analysis in which the relationship between the independent and dependent variables is modelled as the power of a polynomial. Step functions fit smaller, local models instead of one global model. Or, if we have binary data, there is logistic regression, in which the response variable has categorical values such as true/false or 0/1.
Publisher
The Great Courses
Pub. Date
2009.
Language
English
Description
Continuing your exploration of rational expressions, try your hand at multiplying and dividing them. The key to solving these complicated-looking equations is to proceed one step at a time. Close the lesson with a problem that brings together all you've learned about rational functions.
Publisher
The Great Courses
Pub. Date
2014.
Language
English
Description
In your study of lines, you used the combination of geometry and algebra to determine all kinds of interesting properties and characteristics. Now, you’ll do the same for circles, including deriving the algebraic equation for a circle.
Publisher
The Great Courses
Pub. Date
2016.
Language
English
Description
Ponder a question posed by mathematician Georg Cantor: what makes two sets the same size? Start by matching the infinite counting numbers with other infinite sets, proving they're the same size. Then discover an infinite set that's infinitely larger than the counting numbers. In fact, find an infinite number of them!
Publisher
The Great Courses
Pub. Date
2016.
Language
English
Description
Probability problems can be confusing as you try to decide what to multiply and what to divide. But visual models come to the rescue, letting you solve a series of riddles involving coins, dice, medical tests, and the granddaddy of probability problems that was posed to French mathematician Blaise Pascal in the 17th century.
Publisher
The Great Courses
Pub. Date
2017.
Language
English
Description
A geometric arrangement of binomial coefficients calledPascal's triangleis 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?
Publisher
The Great Courses
Pub. Date
2009.
Language
English
Description
Shift gears to consider linear inequalities, which are mathematical expressions featuring a less than sign or a greater than sign instead of an equal sign. Discover that these kinds of problems have some very interesting twists, and they come up frequently in business applications.
Publisher
The Great Courses
Pub. Date
2017.
Language
English
Description
Extend the method of hypothesis testing to see whether data from two different samples could have come from the same population - for example, chickens on different feed types or an ice skater's speed in two contrasting maneuvers. Using R, learn how to choose the right tool to differentiate between independent and dependent samples. One such tool is the matched pairs t-test.
Publisher
The Great Courses
Pub. Date
2017.
Language
English
Description
What 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.
Publisher
The Great Courses
Pub. Date
2017.
Language
English
Description
You can combine features of regression and ANOVA to perform what is called analysis of covariance, or ANCOVA. And that's not all: Just as you can extend simple linear regression to multiple linear regression, you can also extend ANOVA to multiple ANOVA, known as MANOVA, or multivariate analysis of variance. Learn when to apply each of these techniques.
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