Computer Science, Maths, Raspberry Pi
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1 Computer Science, Maths, Raspberry Pi Alan Mycroft Computer Laboratory, University of Cambridge and Raspberry Pi Foundation Sheffield Cutlers Ambassadors 3 Oct 2013 Computer Science, Maths, Raspberry Pi 1 Sheffield Cutlers Ambassadors 3 Oct 2013
2 Structure of this talk Computer Science and ICT Raspberry Pi: what and how Computing meets Maths Computer Science, Maths, Raspberry Pi 2 Sheffield Cutlers Ambassadors 3 Oct 2013
3 A question I asked school students Question: tell us about the most interesting program you ve written. Answer c. 1990: used a BBC micro to write a program which... [Building, Creating] Answer c. 2010: written a web page and used a package to... [Using, Consuming] During UK applications for Computer Science degrees halved. Mismatch between student perception and industry demand. School computing (ICT) seemed boring. [Good news: Cambridge 2013 applications are best ever.] Computer Science, Maths, Raspberry Pi 3 Sheffield Cutlers Ambassadors 3 Oct 2013
![.. [Using, Consuming] During 2000 2010 UK applications for Computer Science degrees halved.](/docs-images/48/18332897/images/page_3.jpg "Mismatch between student perception and industry demand. School computing (ICT) seemed boring.")
4 Royal Society Analysis about School Computing Three separate concepts: Digital Literacy Using menu systems, using a web browser, Facebook IT (often ICT Information and Communication Technology) Designing big systems, out of components Computer Science Understanding the basic ideas associated with Computing The last two are commercially important, and both involve programming. Computer Science focuses more on fundamentals. Inventing stuff, or consuming the products of Microsoft and Google? (But: re-inventing is good for learning, but not commercially unless you do it better!). Sorting versus using Microsoft Excel? Computer Science, Maths, Raspberry Pi 4 Sheffield Cutlers Ambassadors 3 Oct 2013
5 Did computers get easier or harder to use? In the last 30 years? Easier: they are more powerful, with many great things like Facebook, and amazing graphics. Harder: how do I draw a few dots on the screen? Make my computer turns on a light? Questions: how many computers do you have in your house and car, and how many can you use? How many in the world? Can you program your phone? Computer Science, Maths, Raspberry Pi 5 Sheffield Cutlers Ambassadors 3 Oct 2013
6 Structure of this talk Computer Science and ICT Raspberry Pi: what and how Computing meets Maths Computer Science, Maths, Raspberry Pi 6 Sheffield Cutlers Ambassadors 3 Oct 2013
7 Raspberry Pi design (1) (credit-card size) Computer Science, Maths, Raspberry Pi 7 Sheffield Cutlers Ambassadors 3 Oct 2013
8 Raspberry Pi design (2) Computer Science, Maths, Raspberry Pi 8 Sheffield Cutlers Ambassadors 3 Oct 2013
9 Package on Package (PoP) Two chips mounted on top of each other. Memory top (left) and SoC bottom (right) as seen from below. Computer Science, Maths, Raspberry Pi 9 Sheffield Cutlers Ambassadors 3 Oct 2013
10 Package on Package (2) [source: Wikipedia] Computer Science, Maths, Raspberry Pi 10 Sheffield Cutlers Ambassadors 3 Oct 2013
11 Etymology Pi: from the original plan to make Python the operating system, shortened to Pi instead of Py (as everyone knows about π). Raspberry: computers were traditionally named after fruit: Apple, Acorn [grew into ARM], Apricot, (recent) VIA Banana. Raspberry has additional subversive/disrespectful/ challenging-of-authority meaning in English ( blow a raspberry )! Computer Science, Maths, Raspberry Pi 11 Sheffield Cutlers Ambassadors 3 Oct 2013
![Raspberry: computers were traditionally named after fruit: Apple, Acorn [grew into ARM], Apricot, (recent) VIA](/docs-images/48/18332897/images/page_11.jpg "Banana.")
12 Why the Raspberry Pi? It s just an slightly under-powered computer without a screen, and anything you can do on it you could do on a laptop. Yes, but it s cheap, it s light (45g), you can t wreck it with software access to physical pins it changes mindsets The Raspberry Pi Foundation charitable aim is to promote the study of computer science and related topics, especially at school level, and to put the fun back into learning computing. So: if someone starts selling competing kit (e.g. 10, of half the size and twice the memory and processor speed as Raspberry Pi) then this benefits our aims too! Computer Science, Maths, Raspberry Pi 12 Sheffield Cutlers Ambassadors 3 Oct 2013
13 Moore s Law [source: Wikipedia] Computer Science, Maths, Raspberry Pi 13 Sheffield Cutlers Ambassadors 3 Oct 2013
14 Who would make Raspberry Pi chips? Remember: fabricating ( fabbing ) a new chip costs tens of $M. But: people already had built similar chips for HDTV set-top boxes. Computer Science, Maths, Raspberry Pi 14 Sheffield Cutlers Ambassadors 3 Oct 2013
15 Structure of this talk Computer Science and ICT Raspberry Pi: what and how Computing meets Maths Computer Science, Maths, Raspberry Pi 15 Sheffield Cutlers Ambassadors 3 Oct 2013
16 Let do some programming How? Do we need a computer? What language? [For learning programming, we like Python, but I m going to do unplugged programming to make you think!] Computer Science, Maths, Raspberry Pi 16 Sheffield Cutlers Ambassadors 3 Oct 2013
17 Use an Algorithm! The essence of a program (a precise description of a process for solving a problem like a recipe). Why precise? Because computers are stupid (very fast, but very stupid). How precise? like all mathematics precise enough for the task in hand. We might assume the reader knows (say) long division when explaining some algorithm which uses it. Computer Science, Maths, Raspberry Pi 17 Sheffield Cutlers Ambassadors 3 Oct 2013
18 Practical problem Take a pack of cards, and sort out the diamond suit into order A, 2, 3,...,9, 10, J, Q, K. Think carefully: how did you do it? This is your algorithm! Computer Science, Maths, Raspberry Pi 18 Sheffield Cutlers Ambassadors 3 Oct 2013
19 Our first algorithm Problem: given a list of integers as input, produce a list containing the same integers, but in increasing order ( sorting ). Algorithm: ( selection sort ) find the smallest, output it and remove it from the input list. Repeat this process until the list is empty. An issues I don t know how to find the smallest. Need to explain down to a level the reader can understand. When programming the reader is a dumb computer. Computer Science, Maths, Raspberry Pi 19 Sheffield Cutlers Ambassadors 3 Oct 2013
20 Finding the minimum of a list Provided the list is non-empty then: Take the first element as provisional minimum. For each remaining element (maybe zero of them!) if this element is less than the provisional minimum then use this value as new provisional minimum. The provisional minimum now is the result. This is programming unplugged without all the typing! Computer Science, Maths, Raspberry Pi 20 Sheffield Cutlers Ambassadors 3 Oct 2013
21 How fast is selection sort? How many comparison steps? Suppose we have just 5 cards. Computer Science, Maths, Raspberry Pi 21 Sheffield Cutlers Ambassadors 3 Oct 2013
22 How fast is selection sort? How many comparison steps? Suppose we have just 5 cards. 1. Find smallest in 4 steps 2. Find 2nd smallest in 3 steps 3. Find 3nd smallest in 2 steps 4. Find 4nd smallest in 1 steps 5. Only the biggest left: find it in 0 steps! Total = =? Computer Science, Maths, Raspberry Pi 22 Sheffield Cutlers Ambassadors 3 Oct 2013
23 A bit of maths If we had 101 cards, we would require Total = =? steps. Who can add this up? Story about Gauss s teacher... Computer Science, Maths, Raspberry Pi 23 Sheffield Cutlers Ambassadors 3 Oct 2013
24 A bit of maths (2) Total = = 5050 Why: pair off the numbers from each end: , , ,..., How many numbers? All are 101. So total is 5050 (easy?). Computer Science, Maths, Raspberry Pi 24 Sheffield Cutlers Ambassadors 3 Oct 2013
25 Experts only Total = n = 1 2 n (n + 1) or Total = n = n 2 /2 + n/2 or Total = n n 2 /2 So if the input gets 10 times bigger the program runs 100 time slower! Computer Science, Maths, Raspberry Pi 25 Sheffield Cutlers Ambassadors 3 Oct 2013
26 Summary Playing with computers is fun (building your own games is even more fun than playing others). Programming is how you do it Algorithms are the core idea behind programming. We designed Raspberry Pi to re-attract people to Computer Science. Computer Science, Maths, Raspberry Pi 26 Sheffield Cutlers Ambassadors 3 Oct 2013
27 Taster: The Inside-or-Outside Problem Given a closed polygon, expressed as a list of points [(x 1, y 1 ), (x 2, y 2 ),...,(x n, y n )] then is another point (x 0, y 0 ) inside it or outside it? Two-year old humans can do it, but it s really quite non-obvious how to program a computer to do it! It is simple to start by reading 2n + 2 numbers but then...??? Wikipedia tells you how, but it needs more maths. Computer Science, Maths, Raspberry Pi 27 Sheffield Cutlers Ambassadors 3 Oct 2013
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