The Measurement of Science Albert Einstein’s greatest scientific “blunder” (his word) came as a sequel to his greatest scientific achievement. That achievement was his theory of gravity, the general theory of relativity, which he introduced in 1915. Two years later, in 1917, Einstein ran into a problem while trying to apply general relativity to the Universe as a whole. At the time, Einstein believed that on large scales the Universe is static and unchanging. But he realized that general relativity predicts that such a Universe can’t exist: it would spontaneously collapse in on itself. To solve this problem, Einstein modified the equations of general relativity, adding an extra term involving what is called the “cosmological constant” , which, roughly speaking, is a type of pressure which keeps a static Universe from collapsing. Twelve years later, in 1929, Edwin Hubble discovered that the Universe isn’t static and unchanging, but is actually expanding. The story doesn’t end there. One metric to rule them all
Gaussianos Big Data 101: Data Visualization For All | Centric Digital As companies try to make sense of the vast amounts of data they’ve collected, data visualization becomes crucial. The contextualization and execution of this information is really where the money is—but how do you get started? Change is a challenge for any company, but the businesses who adapt are the ones who tend to thrive. One of the major changes companies are faced with today is the vast amounts of data available at their fingertips and the insights all this information can provide. While businesses know this data is a gold mine, many are having trouble finding strategic ways to sift through so much information and present it in an impactful way. Enter data visualization. Yet, creating big data visualization capabilities for your company takes a lot of work. Four elements to displaying data There are four simple elements to keep in mind when starting a data visualization strategy. When creating a visual dataset, it’s important to: What to avoid Approaches to consider
Derivatives of Trig Functions Trigonometric functions are useful in our practical lives in diverse areas such as astronomy, physics, surveying, carpentry etc. How can we find the derivatives of the trigonometric functions? Our starting point is the following limit: Using the derivative language, this limit means that . To see why, it is enough to rewrite the expression involving the cosine as But , so we have This limit equals and thus In fact, we may use these limits to find the derivative of and at any point x=a. So which implies So we have proved that exists and Similarly, we obtain that exists and that Since , and are all quotients of the functions , we can compute their derivatives with the help of the quotient rule: It is quite interesting to see the close relationship between (and also between From the above results we get These two results are very useful in solving some differential equations. Example 1. . So using the product rule, we get which implies, using trigonometric identities, Exercise 1. at the point Answer. Exercise 2.
Are You Living in a Computer Simulation? Math Alive Course Instructors Ingrid DaubechiesShannon Hughes 218 (ID)/217 (SH) Fine Hall, Washington Road Princeton, NJ 08540-1000 You can find other contact information on a Contact us page. How is life different from 25 or even 10 years ago? Cryptography Error correction & compression Probability & Statistics Birth, Growth, Death & Chaos Graph Theory Voting & Social Choice You can navigate through the units using the navigation bar on the left. Each unit is divided into two parts. Don't forget to check the latest announcements on the Announcements page. Problem Sets: You need to look at the On-Line Labs and at the Problem Sets (clickable on the left). The videotaped lectures of Spring 2003 course are available on blackboard. References: For All Practical Purposes : Introduction to Contemporary Mathematics. 4th edition (December 1997). If you have any questions, Send Mail To: Math Alive Help
Connecting with the Dots - on data visualization, empathy, and representing people with dots Dots or people—what do you want your readers to think? (Ryan Norton via Flickr.) Jake Harris on data visualization, empathy, and representing people with dots One of my favorite movies is the classic 1949 thriller “The Third Man.” You know, I never feel comfortable on these sort of things. From a distance, it’s easy to forget the dots are people. Ultimately, I think the graphic produced by the Times did an excellent job of reminding readers about the human costs of the violence. Before it was a final graphic though, it was a demo piece I hastily hacked into Google Earth using its KML format. All of this has made me wonder what other approaches people have used to anchor their graphics in empathy. Near and Far These graphics illustrate a common and successful technique for bringing the reader back down to earth by focusing on a smaller range of data. Unfortunately, many data journalism examples focus exclusively on the far distance and leave out the near view. Putting People First
Table of Trigonometric Identities [Geometry][Algebra][Differential Equations] [Calculus][Complex Variables][Matrix Algebra] S.O.S MATHematics home page Do you need more help? Please post your question on our S.O.S. Copyright © 1999-2024 MathMedics, LLC. World of Ends - what the internet is Online texts Professor Jim Herod and I have written Multivariable Calculus ,a book which we and a few others have used here at Georgia Tech for two years. We have also proposed that this be the first calculus course in the curriculum here, but that is another story.... Although it is still in print, Calculus,by Gilbert Strang is made available through MIT's OpenCourseWare electronic publishing initiative. Here is one that has also been used here at Georgia Tech. Linear Methods of Applied Mathematics, by Evans Harrell and James Herod.