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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
2014.
Language
English
Description
So far, you’ve figured out all kinds of fun properties with two-dimensional shapes. But what if you go up to three dimensions? In this lecture, you classify common 3-D shapes such as cones and cylinders, and learn some surprising definitions. Finally, you study the properties (like volume) of these shapes.
Publisher
The Great Courses
Pub. Date
2017.
Language
English
Description
Pi 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.
Publisher
The Great Courses
Pub. Date
2015.
Language
English
Description
Study the discovery that destroyed the dream of an axiomatic system that could prove all mathematical truths - Kurt Gödel's demonstration that mathematical consistency is a mirage and that the price for avoiding paradoxes is incompleteness. Outline Gödel's proof, seeing how it relates to the liar's paradox from Lecture 1.
Publisher
The Great Courses
Pub. Date
2009.
Language
English
Description
Quadratic functions often arise in real-world settings. Explore a number of problems, including calculating the maximum height of a rocket and determining how long an object dropped from a tree takes to reach the ground. Learn that in finding a solution, graphing can often help.
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
2016.
Language
English
Description
Consider the oddity of the long-multiplication algorithm most of us learned in school. Discover a completely new way to multiply that is graphical--and just as strange! Then analyze how these two systems work. Finally, solve the mystery of why negative times negative is always positive.
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.
10) 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
2016.
Language
English
Description
Keep playing with the approach from the previous lecture, applying it to algebra problems, counting paths in a grid, and Pascal’s triangle. Then explore some of the beautiful patterns in Pascal’s triangle, including its connection to the powers of eleven and the binomial theorem.
Publisher
The Great Courses
Pub. Date
2017.
Language
English
Description
Delve into ANOVA, short for analysis of variance, which is used for comparing three or more group means for statistical significance. ANOVA answers three questions: Do categories have an effect? How is the effect different across categories? Is this significant? Learn to apply the F-test and Tukey's honest significant difference (HSD) test.
Publisher
The Great Courses
Pub. Date
2009.
Language
English
Description
In previous lessons, you moved from linear, quadratic, and rational functions to the graphs that display them. Now do the same with radical functions. For these, it's important to pay attention to the domain of the functions to ensure that negative values are not introduced beneath the root symbol.
Publisher
The Great Courses
Pub. Date
2009.
Language
English
Description
Anytime you see a root symbol - for example, the symbol for a square root - then you're dealing with what mathematicians call a radical. Learn how to simplify radical expressions and perform operations on them, such as multiplication, division, addition, and subtraction, as well as combinations of these operations.
Publisher
The Great Courses
Pub. Date
2014.
Language
English
Description
You’ve seen geometric tiling patterns on your bathroom floor and in the works of great artists. But what would happen if you made repeating patterns in 3-D space? In this lecture, discover the five platonic solids! Also, become an artist and create your own beautiful patterns—even using more than one type of shape.
Publisher
The Great Courses
Pub. Date
2017.
Language
English
Description
Spatial analysis is a set of statistical tools used to find additional order and patterns in spatial phenomena. Drawing on libraries for spatial analysis in R, use a type of graph called a semivariogram to plot the spatial autocorrelation of the measured sample points. Try your hand at data sets involving the geographic incidence of various medical conditions.
Publisher
The Great Courses
Pub. Date
2015.
Language
English
Description
Many puzzles are optimization problems in disguise. Discover that nature often reveals shortcuts to the solutions. See how light, bubbles, balloons, and other phenomena provide powerful hints to these conundrums. Close with the surprising answer to the Kakeya needle problem to determine the space required to turn a needle completely around.
Publisher
The Great Courses
Pub. Date
2014.
Language
English
Description
In lecture 6, you saw how 17th-century mathematician Rene Descartes united geometry and algebra with the invention of the coordinate plane. Now go a step further and explore the power and surprises that come from using the complex number plane. Examine how using complex numbers can help solve several tricky geometry problems.
Publisher
The Great Courses
Pub. Date
2017.
Language
English
Description
Turn to an entirely different approach for doing statistical inference: Bayesian statistics, which assumes a known prior probability and updates the probability based on the accumulation of additional data. Unlike the frequentist approach, the Bayesian method does not depend on an infinite number of hypothetical repetitions. Explore the flexibility of Bayesian analysis.
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