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Students are asked: "How can you predict future power requirements? The interactive file can be used to demonstrate some of the important aspects of growth and decline. The activity offers good opportunities to consolidate work on geometric progression. Many machines compress or expand gas or fluid as part of their working design. Examples include a simple bicycle pump, a refrigerator, and an internal combustion engine. To compress gas energy needs to be expended to reduce its volume.

When gas is allowed to expand energy is released. In this engineering resource students are asked the question: "How can you calculate the energy used, or made available, when the volume of a gas is changed? Isothermal change and adiabatic change are considered. An interactive file graphs the motion of a piston in a cylinder. The mathematics students will be required to use in this activity is to:. This video explores the research and technology behind Opta Sports data and provides first-hand information directly from interviews with the engineers and sports professionals involved.

Opta Sports data uses leading edge technology to compile team and player performance data for a range of sports and has quickly become a staple for a variety of organisations. These range from broadcasters using the data to develop innovative television graphics solutions, to coaches using the information to monitor and compare team and player performances from week to week.

In the information age, Opta Sports data has become business critical to both media and sports professionals alike who rely on the innovation and information to evolve and stay ahead of the competition.

In this activity, students are asked the question "How can the most efficient design be determined, taking both building and running costs into account? There follows an explanation of the concept of kilowatt hours. A video accompanies the resource explaining thermal conductivity. Using statistics to solve engineering problems These resources support the use of statistics to solve engineering problems with particular reference to measures of location, measures of spread volume of 3D shapes and common measures. The resources support students to achieve the assessment outcomes of: calculate the mean, median and modal averages determine cumulative frequency, variance and standard deviation describe and explain how statistical data in engineering and quality systems In some cases the mathematical concepts are those found in the GCSE mathematics syllabus, but the application of these concepts in an engineering context requires skills beyond GCSE level.

Monitoring Vibration Levels in Steam Turbines Category: Engineering In this resource students explore the application of mathematics within the mechanical and electrical engineering power industry. The Study of Engineers' Data 1 Category: Engineering In this resource students explore the application of mathematics when investigating the volume of registration of engineers. Category: Design and technology In this resource students create a presentation that provides a justified answer to the question "Does engineering design make a difference to a wheelchair athlete's performance?

Power Demand Category: Mathematics One important area of civil engineering is electrical power production. Analysing the Game Category: Engineering This video explores the research and technology behind Opta Sports data and provides first-hand information directly from interviews with the engineers and sports professionals involved. Heat Loss from Buildings Category: Mathematics In this activity, students are asked the question "How can the most efficient design be determined, taking both building and running costs into account?

Subject s n. Anonymous not verified 06th February If four bits have been corrupted, the received bits may be equally close to two different possible corrections. In one sense, Golay codes are very simple: just multiply by a binary matrix. Where did the magic matrix above come from? Also, how would you implement it in practice? There are more efficient approaches than to directly carry out a matrix multiplication.

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To give just a hint of the hidden structure in the generator matrix, split the matrix half, giving an identity matrix on the left and a matrix M on the right. The first row corresponds to quadratic residues mod That is, if you number the columns starting from 0, the zeros are in columns 1, 3, 4, 5, and 9. These are the non-zero squares mod Also, the subsequent rows are rotations of the first row. Golay codes are practical for error correction—they were used to transmit the photo at the top of the post back to Earth—but they also have deep connections to other parts of math, including sphere packing and sporadic groups.

Yesterday I wrote a post looking at the frequency of Koine Greek letters and the corresponding entropy. David Littleboy asked what an analogous calculation would look like for a language like Japanese.

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This post answers that question. I put alphabet and letter in quotes because information theory uses these terms for any collection of symbols. The collection could be a literal alphabet, like the Greek alphabet, or it could be something very different, such as a set of musical notes.

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For this post it will be a set of Chinese characters. The original question mentioned Japanese, but I chose to look at Chinese because I found an excellent set of data from Jun Da. See that site for details. By comparison, the entropy of the English alphabet is 3.

MAT 110 Basic Statistics Lesson 1 (video 1).mp4

Symbols are not independent, and so the information content of a sequence of symbols will be less than just multiplying the information content per symbol by the number of symbols. If this is the case, just looking at the entropy of single characters underestimates the relative information density of Chinese writing.

Although writing vary substantially in how much information they convey per symbol, spoken languages may all convey about the same amount of information per unit of time.


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A few weeks ago I wrote about new research suggesting that all human languages convey information at about the same rate. Some languages carry more information per syllable than others, as measured by Shannon entropy, but these languages are typically spoken more slowly. The net result is that people convey about 40 bits of information per second, independent of their language. Of course there are variations by region, by individual, etc. And there are limits to any study, though the study in question did consider a wide variety of languages. Kenneth G.

Libbrecht has posted a page book on snow to arXiv. Would the letters in an ancient Greek text carry more or less information than in modern English? To address this question, I downloaded a copy of the Greek New Testament from Project Gutenberg and ran the word frequency script from my previous post. From this I calculated the Shannon entropy of a Greek letter to be 4. Using English letter frequencies I found on Wikipedia, I calculated the corresponding entropy for English to be 3.

So in this regard, the two languages are pretty similar. The most common letters in Greek line up roughly with their English counterparts.

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I first wrote this post just looking at the New Testament, written in Koine Greek. The frequencies are very similar, and they lead to very similar entropy calculations: 4. Once in a while I need to know what characters are in a file and how often each appears. One reason I might do this is to look for statistical anomalies. A few days ago Fatih Karakurt left an elegant solution to this problem in a comment :.

The fold function breaks the content of a file in to lines 80 characters long by default, but you can specify the line width with the -w option. Setting that to 1 makes each character its own line. Then sort prepares the input for uniq , and the -c option causes uniq to display counts. For a Unicode file, you might do something like the following Python code.

A few days ago I wrote about computational survivalists , people who prepare to be able to work on computers with only software that is available everywhere. If you need to edit a text file on a Windows computer, you can count on Notepad being there. And if you know how to use Windows, you know how to use Notepad.

You may not know advanced features does Notepad even have advanced features? On a Unix-like computer, you can count on vi being there. It was written about four decades ago and ships with every Unix-like system. This post will explain the bare minimum to use vi in a pinch. Arrow keys should work as expected. Use trial and error until you figure out which way each one moves. Typing an h, for example, does not insert an h into your text but instead moves the cursor to the left. To edit a file, you can enter insert mode by typing i. Now the characters you type will be inserted into your file.

What if you want to delete a character? The arrow keys still navigate, but typing an h, for example, will insert an h into your file. To go back to command mode to navigate more, type the Escape key. If you have made changes, you can use :wq to save the file and exit, and :q! How much difference your participation makes is made precise in terms of probability statements.


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The system will allow someone to ask one question that uses the whole privacy budget, or a series of questions whose total impact is no more than that one question. Some metaphors are dangerous, but the idea of comparing cumulative privacy impact to a financial budget is a good one. You have a total amount you can spend, and you can chose how you spend it. There are several ways to mitigate this. A simple way to stretch privacy budgets is to cache query results. Recall that differential privacy adds a little random noise to query results to protect privacy.

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