Catalog Search Results
Publisher
The Great Courses
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.
Series
Great Courses volume 9
Publisher
The Great Courses
Pub. Date
2016.
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
2015.
Description
Delve into Bertrand Russell's profoundly simple paradox that undermined Cantor's theory of sets. Then follow the scramble to fix set theory and all of mathematics with a new set of axioms, designed to avoid all paradoxes and keep mathematics consistent - a goal that was partly met by the Zermelo-Fraenkel set theory.
Publisher
The Great Courses
Pub. Date
2016.
Description
Put your dots-and-boxes machine to work solving long-division problems, making them easy while shedding light on the rationale behind the confusing long-division algorithm taught in school. Then watch how the machine quickly handles scary-looking division problems in polynomial algebra.
Publisher
The Great Courses
Pub. Date
2016.
Description
Drawing on the bizarre conclusions from the previous lecture, reach even more peculiar results by mapping all of the fractions (i.e., rational numbers) onto the number line, discovering that they take up no space at all! And this is just the start of the weirdness.
Publisher
The Great Courses
Pub. Date
2015.
Description
While some statistics are deliberately misleading, others are the product of confused thinking due to Simpson's paradox and similar errors of statistical reasoning. See how this problem arises in sports, social science, and especially medicine, where it can lead to inappropriate treatments.
Publisher
The Great Courses
Pub. Date
2015.
Description
Discover the timeless riddles and paradoxes that have confounded the greatest philosophical, mathematical, and scientific minds in history. Stretching your mind to try to solve a puzzle, even when the answer eludes you, can help sharpen your mind and focus - and it’s an intellectual thrill!
Publisher
The Great Courses
Pub. Date
2017.
Description
The ability of statistics to extract insights from a random collection of facts is one of the most astonishing and useful feats of applied mathematics. This course surveys college-level statistics through dozens of exercises conducted through the statistical programming language R, a free, open-source computer language with millions of users worldwide.
Publisher
The Great Courses
Pub. Date
2015.
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
2017.
Description
What do you do if your data doesn't follow linear model assumptions? Learn how to transform the data to eliminate increasing or decreasing variance (called heteroscedasticity), thereby satisfying the assumptions of normality, independence, and linearity. One of your test cases uses the R data set for miles per gallon versus weight in 1973-74 model automobiles.
Publisher
The Great Courses
Pub. Date
2014.
Description
If you double the side-lengths of a shape, what happens to its area? If the shape is three-dimensional, what happens to its volume? In this lecture, you explore the concept of scale. You use this idea to re-derive one of our fundamental assumptions of geometry, the Pythagorean theorem, using the areas of any shape drawn on the edges of the right triangle—not just squares.
Publisher
The Great Courses
Pub. Date
2009.
Description
Investigating more complicated examples of linear equations, learn that linear equations fall into three categories. First, the equation might have exactly one solution. Second, it might have no solutions at all. Third, it might be an identity, which means every number is a solution.
Publisher
The Great Courses
Pub. Date
2017.
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.
Publisher
The Great Courses
Pub. Date
2017.
Description
Time series analysis provides a way to model response data that is correlated with itself, from one point in time to the next, such as daily stock prices or weather history. After disentangling seasonal changes from longer-term patterns, consider methods that can model a dependency on time, collectively known as ARIMA (autoregressive integrated moving average) models.
Publisher
The Great Courses
Pub. Date
2014.
Description
Let’s say you don’t have a marked ruler to measure lengths or a protractor to measure angles. Can you still draw the basic geometric shapes? Explore how the ancient Greeks were able to construct angles and basic geometric shapes using no more than a straight edge for marking lines and a compass for drawing circles.
Publisher
The Great Courses
Pub. Date
2017.
Description
When are two variables correlated? Learn how to measure covariance, which is the association between two random variables. Then use covariance to obtain a dimensionless number called the correlation coefficient. Using an R data set, plot correlation values for several variables, including the physical measurements of a sample population.
Publisher
The Great Courses
Pub. Date
2009.
Description
Sketch the graphs of several rational functions by first calculating the vertical and horizontal asymptotes, the x and y intercepts, and then plotting several points in the function. In the final exercise, you must simplify the expression in order to extract the needed information.
Publisher
The Great Courses
Pub. Date
2014.
Description
Build on the side-angle-side postulate and derive other ways of testing whether triangles are similar or congruent. Also dive into several practical applications, including a trick botanists use for estimating the heights of trees and a way to measure the width of a river using only a baseball cap.
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