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  • What is a data structure for quickly finding non-empty intersections of a list of sets?

    - by Andrey Fedorov
    I have a set of N items, which are sets of integers, let's assume it's ordered and call it I[1..N]. Given a candidate set, I need to find the subset of I which have non-empty intersections with the candidate. So, for example, if: I = [{1,2}, {2,3}, {4,5}] I'm looking to define valid_items(items, candidate), such that: valid_items(I, {1}) == {1} valid_items(I, {2}) == {1, 2} valid_items(I, {3,4}) == {2, 3} I'm trying to optimize for one given set I and a variable candidate sets. Currently I am doing this by caching items_containing[n] = {the sets which contain n}. In the above example, that would be: items_containing = [{}, {1}, {1,2}, {2}, {3}, {3}] That is, 0 is contained in no items, 1 is contained in item 1, 2 is contained in itmes 1 and 2, 2 is contained in item 2, 3 is contained in item 2, and 4 and 5 are contained in item 3. That way, I can define valid_items(I, candidate) = union(items_containing[n] for n in candidate). Is there any more efficient data structure (of a reasonable size) for caching the result of this union? The obvious example of space 2^N is not acceptable, but N or N*log(N) would be.

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  • Mathematics - Why is Differential Calculus (MVP) in PHP a tabu?

    - by Email
    Hi I want to do a Mean-Variance-Optimization (Markowitz) but i never found anything written in php that does this. MVP needs differential calculus. Can it be done in php and why arent there any classes/works from universities? For a webapplication (regarding performance) would another language be the better choice to handle heavy calculations? Thanks so much for any help/answer on this

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  • How to use constraint programming for optimizing shopping baskets?

    - by tangens
    I have a list of items I want to buy. The items are offered by different shops and different prices. The shops have individual delivery costs. I'm looking for an optimal shopping strategy (and a java library supporting it) to purchase all of the items with a minimal total price. Example: Item1 is offered at Shop1 for $100, at Shop2 for $111. Item2 is offered at Shop1 for $90, at Shop2 for $85. Delivery cost of Shop1: $10 if total order < $150; $0 otherwise Delivery cost of Shop2: $5 if total order < $50; $0 otherwise If I buy Item1 and Item2 at Shop1 the total cost is $100 + $90 +$0 = $190. If I buy Item1 and Item2 at Shop2 the total cost is $111 + $85 +$0 = $196. If I buy Item1 at Shop1 and Item2 at Shop2 the total cost is $100 + $10 + $85 + $0 = 195. I get the minimal price if I order Item1 and Item2 at Shop1: $190 What I tried so far I asked another question before that led me to the field of constraint programming. I had a look at cream and choco, but I did not figure out how to create a model to solve my problem. | shop1 | shop2 | shop3 | ... ----------------------------------------- item1 | p11 | p12 | p13 | item2 | p21 | p22 | p23 | . | | | | . | | | | ----------------------------------------- shipping | s1 | s2 | s3 | limit | l1 | l2 | l3 | ----------------------------------------- total | t1 | t2 | t3 | ----------------------------------------- My idea was to define these constraints: each price "p xy" is defined in the domain (0, c) where c is the price of the item in this shop only one price in a line should be non zero if one or more items are bought from one shop and the sum of the prices is lower than limit, then add shipping cost to the total cost shop total cost is the sum of the prices of all items in a shop total cost is the sum of all shop totals The objective is "total cost". I want to minimize this. In cream I wasn't able to express the "if then" constraint for conditional shipping costs. In choco these constraints exist, but even for 5 items and 10 shops the program was running for 10 minutes without finding a solution. Question How should I express my constraints to make this problem solvable for a constraint programming solver?

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  • why do we need advanced knowledge of mathematics & physics for programming?

    - by Sumeet
    Guys, I have been very good in mathematics and physics in my schools and colleges. Right now I am a programmer. Even in the colleges I have to engrossed my self into computers and programming things all the time. As I used to like it very much. But I have always felt the lack of advanced mathematics and physics in all the work I have done (Programs). Programming never asked me any advanced mathematics and physics knowledge in what I was very good. It always ask u some optimized loops, and different programming technologies which has never been covered in advanced mathematics and physics. Even at the time of selection in big College , such a kind of advanced knowledge is required. Time by time I got out of touch of all that facts and concepts (advanced mathematics and physics). And now after, 5 years in job I found it hard to resolve Differentiations and integrations from Trigonometry. Which sometimes make me feel like I have wasted time in those concepts because they are never used. (At that time I knew that I am going to be a programmer) If one need to be a programmer why do all this advanced knowledge is required. One can go with elementry knowledge a bit more. You never got to think like scientists and R&D person in your Schols and colleges for being a programmer? Just think and let me know your thoughts. I must be wrong somewhere in what I think , but not able to figure that out..? Regards Sumeet

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  • What's the fastest way to approximate the period of data using Octave?

    - by John
    I have a set of data that is periodic (but not sinusoidal). I have a set of time values in one vector and a set of amplitudes in a second vector. I'd like to quickly approximate the period of the function. Any suggestions? Specifically, here's my current code. I'd like to approximate the period of the vector x(:,2) against the vector t. Ultimately, I'd like to do this for lots of initial conditions and calculate the period of each and plot the result. function xdot = f (x,t) xdot(1) =x(2); xdot(2) =-sin(x(1)); endfunction x0=[1;1.75]; #eventually, I'd like to try lots of values for x0(2) t = linspace (0, 50, 200); x = lsode ("f", x0, t) plot(x(:,1),x(:,2)); Thank you! John

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  • Efficient implementation of natural logarithm (ln) and exponentiation

    - by Donotalo
    Basically, I'm looking for implementation of log() and exp() functions provided in C library <math.h>. I'm working with 8 bit microcontrollers (OKI 411 and 431). I need to calculate Mean Kinetic Temperature. The requirement is that we should be able to calculate MKT as fast as possible and with as little code memory as possible. The compiler comes with log() and exp() functions in <math.h>. But calling either function and linking with the library causes the code size to increase by 5 Kilobytes, which will not fit in one of the micro we work with (OKI 411), because our code already consumed ~12K of available ~15K code memory. The implementation I'm looking for should not use any other C library functions (like pow(), sqrt() etc). This is because all library functions are packed in one library and even if one function is called, the linker will bring whole 5K library to code memory.

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  • optimized grid for rectangular items

    - by peterchen
    I have N rectangular items with an aspect ratio Aitem (X:Y). I have a rectangular display area with an aspect ratio Aview The items should be arranged in a table-like layout (i.e. r rows, c columns). what is the ideal grid rows x columns, so that individual items are largest? (rows * colums = N, of course - i.e. there may be "unused" grid places). A simple algorithm could iterate over rows = 1..N, calculate the required number of columns, and keep the row/column pair with the largest items. I wonder if there's a non-iterative algorithm, though (e.g. for Aitem = Aview = 1, rows / cols can be approximated by sqrt(N)).

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  • How computer multiplies 2 numbers?

    - by ckv
    How does a computer perform a multiplication on 2 numbers say 100 * 55. My guess was that the computer did repeated addition to achieve multiplication. Of course this could be the case for integer numbers. However for floating point numbers there must be some other logic. Note: This was asked in an interview.

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  • Merging and splitting overlapping rectangles to produce non-overlapping ones

    - by uj
    I am looking for an algorithm as follows: Given a set of possibly overlapping rectangles (All of which are "not rotated", can be uniformly represented as (left,top,right,bottom) tuplets, etc...), it returns a minimal set of (non-rotated) non-overlapping rectangles, that occupy the same area. It seems simple enough at first glance, but prooves to be tricky (at least to be done efficiently). Are there some known methods for this/ideas/pointers? Methods for not necessarily minimal, but heuristicly small, sets, are interesting as well, so are methods that produce any valid output set at all.

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  • Getting confused why i dont get expected amount ?

    - by Stackfan
    I have 1 result and which i will receive in Bank account, Based on that account i have to Put a balance to user account. How can you find the Handling cost from total tried 491.50 / 0.95 = 517.36 which is wrong ? It should be 500.00 (to my expectation) User balance requires 500.00 When 500.00 selected he gets 5% discount There is a handling cost for this ex: 1) Discount: 500.00 - 5% = 475.00 2) Handling cost: (475.00 x 0.034) + 0.35 = 16.50 3) Total: 475.00 + 16.50 = 491.50 So problem is from 491.50, i have to find atleast handling cost to get promised Balance. Any solution ? Cant figure it out myself...

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  • Speeding up Math calculations in Java

    - by Simon
    I have a neural network written in Java which uses a sigmoid transfer function defined as follows: private static double sigmoid(double x) { return 1 / (1 + Math.exp(-x)); } and this is called many times during training and computation using the network. Is there any way of speeding this up? It's not that it's slow, it's just that it is used a lot, so a small optimisation here would be a big overall gain.

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  • Wpf. Chart optimization. More than million points

    - by Evgeny
    I have custom control - chart with size, for example, 300x300 pixels and more than one million points (maybe less) in it. And its clear that now he works very slowly. I am searching for algoritm which will show only few points with minimal visual difference. I have link to component which have functionallity exactly what i need (2 million points demo): http://www.mindscape.co.nz/demo/SilverlightElements/demopage.html#/ChartOverviewPage I will be grateful for any matherials, links or thoughts how to realize such functionallity.

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  • O&rsquo;Reilly E-Book of the Day 15/Aug/2014 - Advanced Quantitative Finance with C++

    - by TATWORTH
    Originally posted on: http://geekswithblogs.net/TATWORTH/archive/2014/08/15/orsquoreilly-e-book-of-the-day-15aug2014---advanced-quantitative-finance.aspxToday’s half-price book of the Day offer from O’Reilly at http://shop.oreilly.com/product/9781782167228.do?code=MSDEAL is Advanced Quantitative Finance with C++. “This book will introduce you to the key mathematical models used to price financial derivatives, as well as the implementation of main numerical models used to solve them. In particular, equity, currency, interest rates, and credit derivatives are discussed. In the first part of the book, the main mathematical models used in the world of financial derivatives are discussed. Next, the numerical methods used to solve the mathematical models are presented. Finally, both the mathematical models and the numerical methods are used to solve some concrete problems in equity, forex, interest rate, and credit derivatives.”

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  • Apache FOP - Table top and bottom borders missing pagebreak inside table

    - by Thomas
    I am using Apache FOP to generate a PDF from a XLS FO document. I have created a test XLS FO document that contains a table with collapsed borders that with several tall rows. One of the rows starts on one page and ends on the next and this works as expected. The problem is that the bottom border of the table on the first page is missing and the top border of the table on the second pages is also missing. Below is the sample XLS FO document. <?xml version="1.0" encoding="utf-8"?> <fo:root xmlns:fo="http://www.w3.org/1999/XSL/Format" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance"> <!-- defines the layout master --> <fo:layout-master-set> <fo:simple-page-master master-name="first" page-height="29.7cm" page-width="21cm" margin-top="1cm" margin-bottom="2cm" margin-left="2.5cm" margin-right="2.5cm"> <fo:region-body margin-top="3cm"/> <fo:region-before extent="3cm"/> <fo:region-after extent="1.5cm"/> </fo:simple-page-master> </fo:layout-master-set> <!-- starts actual layout --> <fo:page-sequence master-reference="first"> <fo:title>Sample Doc</fo:title> <fo:flow flow-name="xsl-region-body" font-size="x-small" font="Times New Roman"> <!-- table start --> <fo:table table-layout="fixed" width="100%" border-collapse="collapse"> <fo:table-column column-width="35mm"/> <fo:table-column column-width="100mm"/> <fo:table-column column-width="20mm"/> <fo:table-body> <fo:table-row> <fo:table-cell border-width="0.5mm" border-style="solid"> <fo:block>Column 1</fo:block> </fo:table-cell> <fo:table-cell border-width="0.5mm" border-style="solid"> <fo:block>Columns 2</fo:block> </fo:table-cell> <fo:table-cell border-width="0.5mm" border-style="solid"> <fo:block>Column 3</fo:block> </fo:table-cell> </fo:table-row> <fo:table-row> <fo:table-cell border-width="0.5mm" border-style="solid"> <fo:block>Row 1</fo:block> </fo:table-cell> <fo:table-cell border-width="0.5mm" border-style="solid"> <fo:block>Lorem Ipsum is simply dummy text of the printing and typesetting industry. Lorem Ipsum has been the industry's standard dummy text ever since the 1500s, when an unknown printer took a galley of type and scrambled it to make a type specimen book. It has survived not only five centuries, but also the leap into electronic typesetting, remaining essentially unchanged. It was popularised in the 1960s with the release of Letraset sheets containing Lorem Ipsum passages, and more recently with desktop publishing software like Aldus PageMaker including versions of Lorem Ipsum.</fo:block> <fo:block>Lorem Ipsum Lorem Ipsum Lorem Ipsum Lorem Ipsum Lorem Ipsum</fo:block> <fo:block>Lorem Ipsum Lorem Ipsum Lorem Ipsum Lorem Ipsum Lorem Ipsum</fo:block> <fo:block>Lorem Ipsum Lorem Ipsum Lorem Ipsum Lorem Ipsum Lorem Ipsum</fo:block> <fo:block>It is a long established fact that a reader will be distracted by the readable content of a page when looking at its layout.</fo:block> <fo:block>Lorem Ipsum Lorem Ipsum Lorem Ipsum Lorem Ipsum Lorem Ipsum</fo:block> <fo:block>Lorem Ipsum Lorem Ipsum Lorem Ipsum Lorem Ipsum Lorem Ipsum</fo:block> <fo:block>Lorem Ipsum Lorem Ipsum Lorem Ipsum Lorem Ipsum Lorem Ipsum</fo:block> <fo:block>Lorem Ipsum Lorem Ipsum Lorem Ipsum Lorem Ipsum Lorem Ipsum</fo:block> <fo:block>Lorem Ipsum Lorem Ipsum Lorem Ipsum Lorem Ipsum Lorem Ipsum</fo:block> </fo:table-cell> <fo:table-cell border-width="0.5mm" border-style="solid"> <fo:block>Some text</fo:block> </fo:table-cell> </fo:table-row> <fo:table-row> <fo:table-cell border-width="0.5mm" border-style="solid"> <fo:block>Row 2</fo:block> </fo:table-cell> <fo:table-cell border-width="0.5mm" border-style="solid"> <fo:block>Lorem Ipsum is simply dummy text of the printing and typesetting industry. Lorem Ipsum has been the industry's standard dummy text ever since the 1500s, when an unknown printer took a galley of type and scrambled it to make a type specimen book. It has survived not only five centuries, but also the leap into electronic typesetting, remaining essentially unchanged. It was popularised in the 1960s with the release of Letraset sheets containing Lorem Ipsum passages, and more recently with desktop publishing software like Aldus PageMaker including versions of Lorem Ipsum.</fo:block> <fo:block>Lorem Ipsum Lorem Ipsum Lorem Ipsum Lorem Ipsum Lorem Ipsum</fo:block> <fo:block>Lorem Ipsum Lorem Ipsum Lorem Ipsum Lorem Ipsum Lorem Ipsum</fo:block> <fo:block>Lorem Ipsum Lorem Ipsum Lorem Ipsum Lorem Ipsum Lorem Ipsum</fo:block> <fo:block>It is a long established fact that a reader will be distracted by the readable content of a page when looking at its layout.</fo:block> <fo:block>Lorem Ipsum Lorem Ipsum Lorem Ipsum Lorem Ipsum Lorem Ipsum</fo:block> <fo:block>Lorem Ipsum Lorem Ipsum Lorem Ipsum Lorem Ipsum Lorem Ipsum</fo:block> <fo:block>Lorem Ipsum Lorem Ipsum Lorem Ipsum Lorem Ipsum Lorem Ipsum</fo:block> <fo:block>Lorem Ipsum Lorem Ipsum Lorem Ipsum Lorem Ipsum Lorem Ipsum</fo:block> <fo:block>Lorem Ipsum Lorem Ipsum Lorem Ipsum Lorem Ipsum Lorem Ipsum</fo:block> </fo:table-cell> <fo:table-cell border-width="0.5mm" border-style="solid"> <fo:block>Some text</fo:block> </fo:table-cell> </fo:table-row> <fo:table-row> <fo:table-cell border-width="0.5mm" border-style="solid"> <fo:block>Row 3</fo:block> </fo:table-cell> <fo:table-cell border-width="0.5mm" border-style="solid"> <fo:block>Lorem Ipsum is simply dummy text of the printing and typesetting industry. Lorem Ipsum has been the industry's standard dummy text ever since the 1500s, when an unknown printer took a galley of type and scrambled it to make a type specimen book. It has survived not only five centuries, but also the leap into electronic typesetting, remaining essentially unchanged. It was popularised in the 1960s with the release of Letraset sheets containing Lorem Ipsum passages, and more recently with desktop publishing software like Aldus PageMaker including versions of Lorem Ipsum.</fo:block> <fo:block>Lorem Ipsum Lorem Ipsum Lorem Ipsum Lorem Ipsum Lorem Ipsum</fo:block> <fo:block>Lorem Ipsum Lorem Ipsum Lorem Ipsum Lorem Ipsum Lorem Ipsum</fo:block> <fo:block>Lorem Ipsum Lorem Ipsum Lorem Ipsum Lorem Ipsum Lorem Ipsum</fo:block> <fo:block>It is a long established fact that a reader will be distracted by the readable content of a page when looking at its layout.</fo:block> <fo:block>Lorem Ipsum Lorem Ipsum Lorem Ipsum Lorem Ipsum Lorem Ipsum</fo:block> <fo:block>Lorem Ipsum Lorem Ipsum Lorem Ipsum Lorem Ipsum Lorem Ipsum</fo:block> <fo:block>Lorem Ipsum Lorem Ipsum Lorem Ipsum Lorem Ipsum Lorem Ipsum</fo:block> <fo:block>Lorem Ipsum Lorem Ipsum Lorem Ipsum Lorem Ipsum Lorem Ipsum</fo:block> <fo:block>Lorem Ipsum Lorem Ipsum Lorem Ipsum Lorem Ipsum Lorem Ipsum</fo:block> </fo:table-cell> <fo:table-cell border-width="0.5mm" border-style="solid"> <fo:block>Some text</fo:block> </fo:table-cell> </fo:table-row> <fo:table-row> <fo:table-cell border-width="0.5mm" border-style="solid"> <fo:block>Row 4</fo:block> </fo:table-cell> <fo:table-cell border-width="0.5mm" border-style="solid"> <fo:block>Lorem Ipsum is simply dummy text of the printing and typesetting industry. Lorem Ipsum has been the industry's standard dummy text ever since the 1500s, when an unknown printer took a galley of type and scrambled it to make a type specimen book. It has survived not only five centuries, but also the leap into electronic typesetting, remaining essentially unchanged. It was popularised in the 1960s with the release of Letraset sheets containing Lorem Ipsum passages, and more recently with desktop publishing software like Aldus PageMaker including versions of Lorem Ipsum.</fo:block> <fo:block>Lorem Ipsum Lorem Ipsum Lorem Ipsum Lorem Ipsum Lorem Ipsum</fo:block> <fo:block>Lorem Ipsum Lorem Ipsum Lorem Ipsum Lorem Ipsum Lorem Ipsum</fo:block> <fo:block>Lorem Ipsum Lorem Ipsum Lorem Ipsum Lorem Ipsum Lorem Ipsum</fo:block> <fo:block>It is a long established fact that a reader will be distracted by the readable content of a page when looking at its layout.</fo:block> <fo:block>Lorem Ipsum Lorem Ipsum Lorem Ipsum Lorem Ipsum Lorem Ipsum</fo:block> <fo:block>Lorem Ipsum Lorem Ipsum Lorem Ipsum Lorem Ipsum Lorem Ipsum</fo:block> <fo:block>Lorem Ipsum Lorem Ipsum Lorem Ipsum Lorem Ipsum Lorem Ipsum</fo:block> <fo:block>Lorem Ipsum Lorem Ipsum Lorem Ipsum Lorem Ipsum Lorem Ipsum</fo:block> <fo:block>Lorem Ipsum Lorem Ipsum Lorem Ipsum Lorem Ipsum Lorem Ipsum</fo:block> </fo:table-cell> <fo:table-cell border-width="0.5mm" border-style="solid"> <fo:block>Some text</fo:block> </fo:table-cell> </fo:table-row> <fo:table-row> <fo:table-cell border-width="0.5mm" border-style="solid"> <fo:block>Row 5</fo:block> </fo:table-cell> <fo:table-cell border-width="0.5mm" border-style="solid"> <fo:block>Lorem Ipsum is simply dummy text of the printing and typesetting industry. Lorem Ipsum has been the industry's standard dummy text ever since the 1500s, when an unknown printer took a galley of type and scrambled it to make a type specimen book. It has survived not only five centuries, but also the leap into electronic typesetting, remaining essentially unchanged. It was popularised in the 1960s with the release of Letraset sheets containing Lorem Ipsum passages, and more recently with desktop publishing software like Aldus PageMaker including versions of Lorem Ipsum.</fo:block> <fo:block>Lorem Ipsum Lorem Ipsum Lorem Ipsum Lorem Ipsum Lorem Ipsum</fo:block> <fo:block>Lorem Ipsum Lorem Ipsum Lorem Ipsum Lorem Ipsum Lorem Ipsum</fo:block> <fo:block>Lorem Ipsum Lorem Ipsum Lorem Ipsum Lorem Ipsum Lorem Ipsum</fo:block> <fo:block>It is a long established fact that a reader will be distracted by the readable content of a page when looking at its layout.</fo:block> <fo:block>Lorem Ipsum Lorem Ipsum Lorem Ipsum Lorem Ipsum Lorem Ipsum</fo:block> <fo:block>Lorem Ipsum Lorem Ipsum Lorem Ipsum Lorem Ipsum Lorem Ipsum</fo:block> <fo:block>Lorem Ipsum Lorem Ipsum Lorem Ipsum Lorem Ipsum Lorem Ipsum</fo:block> <fo:block>Lorem Ipsum Lorem Ipsum Lorem Ipsum Lorem Ipsum Lorem Ipsum</fo:block> <fo:block>Lorem Ipsum Lorem Ipsum Lorem Ipsum Lorem Ipsum Lorem Ipsum</fo:block> </fo:table-cell> <fo:table-cell border-width="0.5mm" border-style="solid"> <fo:block>Some text</fo:block> </fo:table-cell> </fo:table-row> </fo:table-body> </fo:table> <!-- table end --> </fo:flow> </fo:page-sequence> </fo:root> This Image shows the bottom border on page 1 missing and the top border on page 2 missing, but all text seams to be there: Please note that I have allready experimented with using an empty header and footer with borders, for example. This works, but I need to use these functions for other things than fixing this issue so what I need to know is if there is an other sollution to the problem?

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  • Discrete Math and Computing Course

    - by ShrimpCrackers
    I was recently admitted into a Computing and Software Systems program (basically software engineering) and one of the first courses I'll be taking is called Mathematical Principles of Computing. The course description: "Integrating mathematical principles with detailed instruction in computer programming. Explores mathematical reasoning and discrete structures through object-oriented programming. Includes algorithm analysis, basic abstract data types, and data structures." I'm not a fan of math, but I've been doing well in all my math classes mostly A's and B's ever since I started two years ago, and I've been doing math every quarter - never took a quarter without math - so I've been doing it all in sequence without gaps. However, I'm worried about this class. I've read briefly on what discrete math is and from what my advisor told me, its connection with computer science is that it has alot to do with proving algorithms. One thing that my instructors briefly touched on and never went into detail was proving algorithms, and when I tried, I just wasn't very good at mathematical induction. It's one of the things that I ignored every time it showed up in a homework problem (usually in Calculus III which I'm finishing up right now). Questions: 1. What can I expect from this class? 2. How can I prepare myself for this class? 3. Other tips? Thank you.

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  • Generic applet style system for publishing mathematics demonstrations?

    - by Alex
    Anyone who's tried to study mathematics using online resources will have come across these Java applets that demonstrate a particular mathematical idea. Examples: http://www.math.ucla.edu/~tao/java/Mobius.html http://www.mathcs.org/java/programs/FFT/index.html I love the idea of this interactive approach because I believe it is very helpful in conveying mathematical principles. I'd like to create a system for visually designing and publishing these 'mathlets' such that they can be created by teachers with little programming experience. So in order to create this app, i'll need a GUI and a 'math engine'. I'll probably be working with .NET because thats what I know best and i'd like to start experimenting with F#. Silverlight appeals to me as a presentation framework for this project (im not worried about interoperability right now). So my questions are: does anything like this exist already in full form? are there any GUI frameworks for displaying mathematical objects such as graphs & equations? are there decent open source libraries that exposes a mathematical framework (Math.NET looks good, just wondering if there is anything else out there) is there any existing work on taking mathematical models/demos built with maple/matlab/octave/mathematica etc and publishing them to the web?

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  • VirtualBox - split partitioned VDI into separate VDIs

    - by mathematical.coffee
    I'm very new to VirtualBox. I set up an Arch Linux VM and a Ubuntu VM (Ubuntu host), both sharing the same .vdi like so (I had in my mind a dual-boot situation): VDI file (25GB) |- /dev/sda1: 5GB (Arch Linux) |- /dev/sda2: [Ubuntu] |- /dev/sda5 (swap, 1GB) |- /dev/sda6 Ubuntu /, 9GB |- /dev/sda7 Ubuntu /home, 10GB I've now realised that I don't want a dual-boot-type setup, I'd rather boot each machine independently (my initial thought was to share /home between Ubunto and Arch). So, my question: Can I split /dev/sda1 and /dev/sda2 each to their own .vdi files so I can use them as completely separate machines? I'd rather not have to re-install either Arch (because it took me ages to work it out!) or Ubuntu (because I've already done a few GB of updates and don't want to redo them). I haven't been able to find anything about this - most questions I see are about converting a .vdi to a partition on the host, or splitting a .vdi into multiple smaller files (that are not independent), or converting a partition on the host to a .vdi file. cheers.

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  • Ada and 'The Book'

    - by Phil Factor
    The long friendship between Charles Babbage and Ada Lovelace created one of the most exciting and mysterious of collaborations ever to have resulted in a technological breakthrough. The fireworks that created by the collision of two prodigious mathematical and creative talents resulted in an invention, the Analytical Engine, which went on to change society fundamentally. However, beyond that, we just don't know what the bulk of their collaborative work was about:;  it was done in strictest secrecy. Even the known outcome of their friendship, the first programmable computer, was shrouded in mystery. At the time, nobody, except close friends and family, had any idea of Ada Byron's contribution to the invention of the ‘Engine’, and how to program it. Her great insight was published in August 1843, under the initials AAL, standing for Ada Augusta Lovelace, her title then being the Countess of Lovelace. It was contained in a lengthy ‘note’ to her translation of a publication that remains the best description of Babbage's amazing Analytical Engine. The secret identity of the person behind those enigmatic initials was finally revealed by Prince de Polignac who, seventy years later, wrote to Ada's daughter to seek confirmation that her mother had, indeed, been the author of the brilliant sentences that described so accurately how Babbage's mechanical computer could be programmed with punch-cards. L.F. Menabrea's paper on the Analytical Engine first appeared in the 'Bibliotheque Universelle de Geneve' in October 1842, and Ada translated it anonymously for Taylor's 'Scientific Memoirs'. Charles Babbage was surprised that she had not written an original paper as she already knew a surprising amount about the way the machine worked. He persuaded her to at least write some explanatory notes. These notes ended up extending to four times the length of the original article and represented the first published account of how a machine could be programmed to perform any calculation. Her example of programming the Bernoulli sequence would have worked on the Analytical engine had the device’s construction been completed, and gave Ada an unassailable claim to have invented the art of programming. What was the reason for Ada's secrecy? She was the only legitimate child of Lord Byron, who was probably the best known celebrity of the age, so she was already famous. She was a senior aristocrat, with titles, a fortune in money and vast estates in the Midlands. She had political influence, and was the cousin of Lord Melbourne, who was the Prime Minister at that time. She was friendly with the young Queen Victoria. Her mathematical activities were a pastime, and not one that would be considered by others to be in keeping with her roles and responsibilities. You wouldn't dare to dream up a fictional heroine like Ada. She was dazzlingly beautiful and talented. She could speak several languages fluently, and play some musical instruments with professional skill. Contemporary accounts refer to her being 'accomplished in science, art and literature'. On top of that, she was a brilliant mathematician, a talent inherited from her mother, Annabella Milbanke. In her mother's circle of literary and scientific friends was Charles Babbage, and Ada's friendship with him dates from her teenage zest for Mathematics. She was one of the first people he'd ever met who understood what he had attempted to achieve with the 'Difference Engine', and with whom he could converse as intellectual equals. He arranged for her to have an education from the most talented academics in the country. Ada melted the heart of the cantankerous genius to the point that he became a faithful and loyal father-figure to her. She was one of the very few who could grasp the principles of the later, and very different, ‘Analytical Engine’ which was designed from the start to tackle a variety of tasks. Sadly, Ada Byron's life ended less than a decade after completing the work that assured her long-term fame, in November 1852. She was dying of cancer, her gambling habits had caused her to run up huge debts, she'd had more than one affairs, and she was being blackmailed. Her brilliant but unempathic mother was nursing her in her final illness, destroying her personal letters and records, and repaying her debts. Her husband was distraught but helpless. Charles Babbage, however, maintained his steadfast paternalistic friendship to the end. She appointed her loyal friend to be her executor. For years, she and Babbage had been working together on a secret project, known only as 'The Book'. We have a clue to what it was in a letter written by her nine years earlier, on 11th August 1843. It was a joint project by herself and Lord Lovelace, her husband, and was intended to involve Babbage's 'undivided energies'. It involved 'consulting your Engine' (it required Babbage’s computer). The letter gives no hint about the project except for the high-minded nature of its purpose, and its highly mathematical nature.  From then on, the surviving correspondence between the two gives only veiled references to 'The Book'. There isn't much, since Babbage later destroyed any letters that could have damaged her reputation within the Establishment. 'I cannot spare the book today, which I am very sorry for. At the moment I want it for constant reference, but I think you can have it tomorrow' (Oct 1844)  And 'I will send you the book directly, and you can say, when you receive it, how long you will want to keep it'. (Nov 1844)  The two of them were obviously intent on the work: She writes, four years later, 'I have an engagement for Wednesday which will prevent me from attending to your wishes about the book' (Dec 1848). This was something that they both needed to work on, but could not do in parallel: 'I will send the book on Tuesday, and it can be left with you till Friday' (11 Feb 1849). After six years work, it had been so well-handled that it was beginning to fall apart: 'Don't forget the new cover you promised for the book. The poor book is very shabby and wants one' (20 Sept 1849). So what was going on? The word 'book' was not a code-word: it was a real book, probably a 'printer's blank', plain paper, but properly bound so printers and publishers could show off how the published work might look. The hints from the correspondence are of advanced mathematics. It is obvious that the book was travelling between them, back and forth, each one working on it for less than a week before passing it back. Ada and her husband were certainly involved in gambling large sums of money on the horses, and so most biographers have concluded that the three of them were trying to calculate the mathematical odds on the horses. This theory has three large problems. Firstly, Ada's original letter proposing the project refers to its high-minded nature. Babbage was temperamentally opposed to gambling and would scarcely have given so much time to the project, even though he was devoted to Ada. Secondly, Babbage would have very soon have realized the hopelessness of trying to beat the bookies. This sort of betting never attracts his type of intellectual background. The third problem is that any work on calculating the odds on horses would not need a well-thumbed book to pass back and forth between them; they would have not had to work in series. The original project was instigated by Ada, along with her husband, William King-Noel, 1st Earl of Lovelace. Charles Babbage was invited to join the project after the couple had come up with the idea. What could William have contributed? One might assume that William was a Bertie Wooster character, addicted only to the joys of the turf, but this was far from the truth. He was a scientist, a Cambridge graduate who was later elected to be a Fellow of the Royal Society. After Eton, he went to Trinity College, Cambridge. On graduation, he entered the diplomatic service and acted as secretary under Lord Nugent, who was Lord Commissioner of the Ionian Islands. William was very friendly with Babbage too, able to discuss scientific matters on equal terms. He was a capable engineer who invented a process for bending large timbers by the application of steam heat. He delivered a paper to the Institution of Civil Engineers in 1849, and received praise from the great engineer, Isambard Kingdom Brunel. As well as being Lord Lieutenant of the County of Surrey for most of Victoria's reign, he had time for a string of scientific and engineering achievements. Whatever the project was, it is unlikely that William was a junior partner. After Ada's death, the project disappeared. Then, two years later, Babbage, through one of his occasional outbursts of temper, demonstrated that he was able to decrypt one of the most powerful of secret codes, Vigenère's autokey cipher.  All contemporary diplomatic and military messages used a variant of this cipher. Babbage had made three important discoveries, namely, the mathematical law of this cipher, the principle of the key periodicity, and the technique of the symmetry of position. The technique is now known as the Kasiski examination, also called the Kasiski test, but Babbage got there first. At one time, he listed amongst his future projects, the writing of a book 'The Philosophy of Decyphering', but it never came to anything. This discovery was going to change the course of history, since it was used to decipher the Russians’ military dispatches in the Crimean war. Babbage himself played a role during the Crimean War as a cryptographical adviser to his friend, Rear-Admiral Sir Francis Beaufort of the Admiralty. This is as much as we can be certain about in trying to make sense of the bulk of the time that Charles Babbage and Ada Lovelace worked together. Nine years of intensive work, involving the 'Engine' and a great deal of mathematics and research seems to have been lost: or has it? I've argued in the past http://www.simple-talk.com/community/blogs/philfactor/archive/2008/06/13/59614.aspx that the cracking of the Vigenère autokey cipher, was a fundamental motive behind the British Government's support and funding of the 'Difference Engine'. The Duke of Wellington, whose understanding of the military significance of being able to read enemy dispatches, was the most steadfast advocate of the project. If the three friends were actually doing the work of cracking codes by mathematical techniques that used the techniques of key periodicity, and symmetry of position (the use of a book being passed quickly to and fro is very suggestive), intending to then use the 'Engine' to do the routine cracking of each dispatch, then this is a rather different story. The project was Ada and William's idea. (William had served in the diplomatic service and would be familiar with the use of codes). This makes Ada Lovelace the initiator of a project which, by giving both Britain, and probably the USA, a diplomatic and military advantage in the second part of the Nineteenth century, changed world history. Ada would never have wanted any credit for cracking the cipher, and developing the method that rendered all contemporary military and diplomatic ciphering techniques nugatory; quite the reverse. And it is clear from the gaps in the record of the letters between the collaborators that the evidence was destroyed, probably on her request by her irascible but intensely honorable executor, Charles Babbage. Charles Babbage toyed with the idea of going public, but the Crimean war put an end to that. The British Government had a valuable secret, and intended to keep it that way. Ada and Charles had quite often discussed possible moneymaking projects that would fund the development of the Analytic Engine, the first programmable computer, but their secret work was never in the running as a potential cash cow. I suspect that the British Government was, even then, working on the concealment of a discovery whose value to the nation depended on it remaining so. The success of code-breaking in the Crimean war, and the American Civil war, led to the British and Americans  subsequently giving much more weight and funding to the science of decryption. Paradoxically, this makes Ada's contribution even closer to the creation of Colossus, the first digital computer, at Bletchley Park, specifically to crack the Nazi’s secret codes.

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